Magnetic Effects of Electric Current

The compass needle deflects.

It indicates a magnetic field.

Electricity and magnetism

<p>Radio, television, or fiber optics</p> Signup and view all the answers

<p>Oersted</p> Signup and view all the answers

<p>Copper wire</p> Signup and view all the answers

<p>Perpendicular</p> Signup and view all the answers

<p>Pass current through the circuit</p> Signup and view all the answers

<p>The position change of the compass needle.</p> Signup and view all the answers

<p>He discovered the relationship between electricity and magnetism.</p> Signup and view all the answers

<p>The deflection of the compass needle.</p> Signup and view all the answers

<p>He demonstrated that electricity and magnetism are related phenomena.</p> Signup and view all the answers

<p>It suggests a magnetic field is generated around the wire.</p> Signup and view all the answers

<p>The deflection would be in the opposite direction.</p> Signup and view all the answers

<p>Electric current produces a magnetic field, linking electricity and magnetism as related phenomena.</p> Signup and view all the answers

<p>It would likely increase the deflection of the needle.</p> Signup and view all the answers

<p>Radio, television, and fiber optics.</p> Signup and view all the answers

<p>The oersted, named after Hans Christian Oersted.</p> Signup and view all the answers

<p>The compass needle would not deflect.</p> Signup and view all the answers

<p>It established a fundamental relationship between electricity and magnetism, paving the way for electromagnetic technologies.</p> Signup and view all the answers

<p>It demonstrated they were related phenomena, not separate.</p> Signup and view all the answers

<p>The deflection of the compass needle.</p> Signup and view all the answers

<p>To maximize the magnetic field's effect on the compass.</p> Signup and view all the answers

<p>The deflection would occur in the opposite direction.</p> Signup and view all the answers

<p>The movement of electric charge.</p> Signup and view all the answers

<p>By enabling the development of electromagnetic technologies.</p> Signup and view all the answers

<p>It measures magnetic field strength, and it's named to honor his discovery of electromagnetism.</p> Signup and view all the answers

<p>The compass needle would deflect more strongly, due to a stronger magnetic field.</p> Signup and view all the answers

<p>In designing and building electromagnets.</p> Signup and view all the answers

<p>The wires would exert a force on each other.</p> Signup and view all the answers

<p>He might have observed quantum entanglement or spin polarization effects, leading to faster quantum technology development.</p> Signup and view all the answers

<p>Expect quantized conductance leading to discrete magnetic field changes; quantum electrodynamics framework is needed.</p> Signup and view all the answers

<p>The needle will precess around the external field, described by a damped harmonic oscillator model or a Lagrangian including the external field's potential energy.</p> Signup and view all the answers

<p>Detection of extremely weak magnetic fields caused by electron spins and discovery of any topological defects near the surface.</p> Signup and view all the answers

<p>The magnetic field should exhibit a radial component, and the integral of the magnetic field over a closed surface enclosing the wire would be non-zero, showing presence magnetic charge.</p> Signup and view all the answers

<p>The magnetic field can induce vortices in the condensate, or excite Bogoliubov quasiparticles, impacting the condensate's density distribution.</p> Signup and view all the answers

<p>The nanorods will align along the flow-induced magnetic field gradients forming dynamic structures observable via microscopy methods.</p> Signup and view all the answers

<p>The metamaterial inverts the magnetic field near the wire, altering needle deflection; FDTD simulations capture this complex field.</p> Signup and view all the answers

<p>Surface currents create unique magnetic signatures dependent on surface quality, which is modeled using Berry phase calculations.</p> Signup and view all the answers

<p>Spacetime curvature distorts the magnetic field and can induce Unruh radiation; use quantum field theory in curved spacetime to analyze.</p> Signup and view all the answers

<p>Hans Christian Oersted</p> Signup and view all the answers

<p>Radio/Television/Fiber optics</p> Signup and view all the answers

<p>Oersted</p> Signup and view all the answers

<p>Place a compass near a wire in an electric circuit; when current flows, the compass needle deflects.</p> Signup and view all the answers

<p>An electric current produces a magnetic effect.</p> Signup and view all the answers

<p>Oersted's experiment revealed the relationship between electricity and magnetism, leading to the development of technologies like radio and fiber optics.</p> Signup and view all the answers

<p>By moving a magnet near a conductor, you would induce an electric current in the conductor.</p> Signup and view all the answers

<p>He could use a Hall effect sensor to precisely measure the magnetic field strength at various distances from a current-carrying wire, allowing him to empirically derive the mathematical relationship between current and magnetic field intensity.</p> Signup and view all the answers

<p>Using a solenoid would have concentrated and amplified the magnetic field due to the additive effect of each coil's field, demonstrating a method to create stronger electromagnets and enabling the exploration of magnetic material properties within the intensified field.</p> Signup and view all the answers

<p>The compass needle gets deflected.</p> Signup and view all the answers

<p>North pole</p> Signup and view all the answers

<p>They repel each other.</p> Signup and view all the answers

<p>They align themselves along field lines.</p> Signup and view all the answers

<p>Magnetic field lines.</p> Signup and view all the answers

<p>Magnetic field</p> Signup and view all the answers

<p>Magnetic field lines.</p> Signup and view all the answers

<p>A small compass</p> Signup and view all the answers

<p>Near the north pole of the magnet</p> Signup and view all the answers

<p>The iron filings align themselves along the magnetic field lines, visually representing the area where the magnet's force is detectable.</p> Signup and view all the answers

<p>A magnetic field is the region around a magnet where its magnetic force can be detected.</p> Signup and view all the answers

<p>Like poles repel each other, while unlike poles attract each other.</p> Signup and view all the answers

<p>The compass needle would align itself tangent to the magnetic field line at that point, with the north pole of the compass pointing in the direction of the field.</p> Signup and view all the answers

<p>Measure how far away each magnet can deflect a compass needle or attract iron filings; the magnet that exerts its influence from a greater distance is stronger.</p> Signup and view all the answers

<p>To prevent interference with the magnetic field being observed, ensuring accurate results.</p> Signup and view all the answers

<p>Increasing the number of turns in a coil increases the strength of the magnetic field.</p> Signup and view all the answers

<p>Increasing the current increases the strength of the electromagnet.</p> Signup and view all the answers

<p>The strength of the magnetic field decreases as the distance from the magnet increases.</p> Signup and view all the answers

<p>Place a ferromagnetic material, like iron, in close proximity to a strong permanent magnet. The ferromagnetic material becomes temporarily magnetized.</p> Signup and view all the answers

<p>The iron filings align themselves along the magnetic field lines due to the force exerted by the magnet, which influences the region surrounding it.</p> Signup and view all the answers

<p>A magnetic field is the region around a magnet where its magnetic force can be detected.</p> Signup and view all the answers

<p>Increasing the strength of the magnet would cause the pattern to extend farther out from the magnet.</p> Signup and view all the answers

<p>The magnetic field lines would repel each other, creating a region with few or no field lines directly between the magnets.</p> Signup and view all the answers

<p>The compass needle, being a small magnet itself, aligns with the Earth's magnetic field because its magnetic poles are attracted to the opposite magnetic poles of earth.</p> Signup and view all the answers

<p>The bar magnet would align itself with the Earth's magnetic field, with its north pole pointing towards the Earth's magnetic north pole (which is geographically close to the South Pole).</p> Signup and view all the answers

<p>A smaller compass provides a more localized and accurate indication of the magnetic field direction at a given point, minimizing the averaging effect that a larger compass would have.</p> Signup and view all the answers

<p>The closer the magnetic field lines are to each other, the stronger the magnetic field is in that region.</p> Signup and view all the answers

<p>Yes, each piece will become a new magnet with its own north and south poles. Magnetic poles always exist in pairs; you cannot isolate a single north or south pole.</p> Signup and view all the answers

<p>The closed-loop nature of magnetic field lines implies that magnetic fields are created by circulating electric currents or intrinsic magnetic moments, rather than isolated magnetic charges (monopoles).</p> Signup and view all the answers

<p>The torque $\tau$ on the sphere is given by $\tau = M \times B$, where <em>M</em> is the magnetic dipole moment of the sphere and <em>B</em> is the external magnetic field. This torque tends to align <em>M</em> with <em>B</em>, minimizing the potential energy.</p> Signup and view all the answers

<p>From Maxwell's equation, $\nabla \cdot B = 0$, the divergence of the magnetic field is always zero. This implies there are no magnetic monopoles (sources or sinks) for magnetic field lines, hence they must form closed loops.</p> Signup and view all the answers

<p>Balance one magnet horizontally on a pivot. Bring the second magnet close, end-to-end, causing the balanced magnet to deflect. The magnet producing a greater deflection possesses the stronger magnetic moment. The torque experienced is proportional to the product of magnetic moments; a larger deflection indicates a greater torque and thus a larger magnetic moment.</p> Signup and view all the answers

<p>The magnetic field transforms according to $B' = \gamma (B - v \times E/c^2)$ where $\gamma$ is the Lorentz factor. For a pure magnetic dipole, a stationary observer will observe both electric and magnetic fields due to the relativistic transformation.</p> Signup and view all the answers

<p>Cooper pairs form and create a supercurrent at the surface, generating a magnetic field that cancels the external field within the superconductor. London's equations describe this, leading to field penetration over a characteristic length. Flux quantization dictates that the enclosed magnetic flux is an integer multiple of the flux quantum.</p> Signup and view all the answers

<p>The magnetic force per unit length is given by $F/L = \frac{\mu_0 I_1 I_2}{2 \pi r}$. Since the currents are in opposite directions, the force is repulsive because the magnetic fields produced by each wire exert a force pushing the other wire away.</p> Signup and view all the answers

<p>Near the edges, the field lines fringe out, becoming nearly parallel to the surface. This behavior arises from effective magnetic surface charge densities at the edges, analogous to electric charges, which create a field directed away from the 'north' edge and towards the 'south' edge.</p> Signup and view all the answers

<p>The electron experiences zero net force when the magnetic force equals and opposes the electric force, i.e., when $qE = qvB$, or $E = vB$.</p> Signup and view all the answers

<p>Inside the shell, the magnetic field remains unchanged. Outside, the field is modified due to induced surface currents on the conductor, which create a field equal and opposite to that of the dipole for $r &gt; R$, shielding the outside world from the dipole's field.</p> Signup and view all the answers

<p>MRI uses a strong static magnetic field to align nuclear spins. Radio waves excite these spins, and magnetic field gradients spatially encode the emitted radiofrequency signals. The frequency and phase of these signals, when processed, create detailed images.</p> Signup and view all the answers

<p>A magnetic field is the region surrounding a magnet where its magnetic force can be detected.</p> Signup and view all the answers

<p>Magnetic field lines represent the direction and strength of the magnetic field.</p> Signup and view all the answers

<p>Tapping the board allows the iron filings to overcome friction and align themselves according to the magnetic field lines.</p> Signup and view all the answers

<p>To prevent movement of the magnet or paper during the tracing of the magnetic field lines, ensuring an accurate representation.</p> Signup and view all the answers

<p>A higher density of magnetic field lines indicates a stronger magnetic field, while a lower density indicates a weaker field.</p> Signup and view all the answers

<p>Place the magnets at varying distances from a compass. The magnet that deflects the compass from a greater distance is the stronger magnet.</p> Signup and view all the answers

<p>No, you would not obtain isolated poles. Each half would become its own bar magnet with both a north and a south pole.</p> Signup and view all the answers

<ol> <li>Insufficient tapping to overcome friction. 2) External magnetic interference distorting the field. 3) Non-uniform distribution of iron filings, resulting in clumping and uneven alignment.</li> </ol> Signup and view all the answers

<p>Lines representing the magnetic field around a magnet.</p> Signup and view all the answers

<p>The degree of closeness of the field lines.</p> Signup and view all the answers

<p>North pole.</p> Signup and view all the answers

<p>From the south pole to the north pole.</p> Signup and view all the answers

<p>The direction of the magnetic field.</p> Signup and view all the answers

<p>Because a compass needle would point in two directions at the intersection.</p> Signup and view all the answers

<p>Direction and magnitude.</p> Signup and view all the answers

<p>The deflection increases.</p> Signup and view all the answers

<p>Electric current through a metallic conductor.</p> Signup and view all the answers

<p>Magnetic field lines emerge from the north pole of a magnet and merge into the south pole, continuing inside the magnet from south to north, thus forming a closed loop.</p> Signup and view all the answers

<p>If magnetic field lines intersected, the compass needle at that point would have to point in two directions simultaneously, which is impossible.</p> Signup and view all the answers

<p>By convention, magnetic field lines emerge from the north pole and merge into the south pole outside the magnet.</p> Signup and view all the answers

<p>By placing the compass needle at different points and marking the direction it points, then connecting these points with a smooth curve.</p> Signup and view all the answers

<p>Inside the magnet, the direction of the field lines is from its south pole to its north pole.</p> Signup and view all the answers

<p>The deflection of the compass needle increases as it is moved towards the poles.</p> Signup and view all the answers

<p>An electric current flowing through a metallic conductor produces a magnetic field around it.</p> Signup and view all the answers

<p>The magnetic field not only has strength (magnitude) but also a specific orientation in space (direction).</p> Signup and view all the answers

<p>Place the compass near the magnet, mark the needle's ends, move the compass so the south pole is at the previous north pole position, and repeat. Connect the marks to form a field line.</p> Signup and view all the answers

<p>If magnetic field lines intersected, a compass needle at the intersection point would have to point in two directions simultaneously, which is not possible.</p> Signup and view all the answers

<p>The closer the magnetic field lines are to each other, the stronger the magnetic field in that region. Conversely, the farther apart, the weaker the field.</p> Signup and view all the answers

<p>Outside the magnet, magnetic field lines are conventionally depicted as emerging from the north pole and merging into the south pole. Inside the magnet, the direction is from the south pole to the north pole.</p> Signup and view all the answers

<p>The deflection of the compass needle increases as it is moved closer to the poles of the magnet. This is because the magnetic field is stronger near the poles.</p> Signup and view all the answers

<p>Magnetic field lines form closed loops because they continue inside the magnet from the south pole to the north pole, completing the path that starts outside the magnet from north to south.</p> Signup and view all the answers

<p>The compass needle aligns with the magnetic field's direction, indicating its direction. The degree of deflection indicates relative strength, with greater deflections signifying stronger fields.</p> Signup and view all the answers

<p>The magnetic field exists as a region in space where a magnetic force is exerted on magnets or magnetic materials. The direction indicates the direction a north pole would move, and the strength is proportional to the force's magnitude.</p> Signup and view all the answers

<p>Moving the needle step by step ensures accurate mapping because each step relies on the previous position to guide the alignment, minimizing cumulative errors in illustrating the field lines.</p> Signup and view all the answers

<p>Magnitude indicates the strength of the force exerted and the direction specifies the orientation of this force's effect on magnetic materials or moving charges in the area.</p> Signup and view all the answers

<p>Inside a magnet, the field lines run from the south pole to the north pole, contrasting the exterior where they run from north to south, ensuring the closed-loop nature of magnetic fields.</p> Signup and view all the answers

<p>A magnetic monopole would experience a net force along the field line, either towards or away from the bar magnet, depending on its polarity. Consequently, field lines would originate or terminate at the monopole, violating the closed-loop nature observed with dipoles.</p> Signup and view all the answers

<p>The needle's alignment would deviate due to the torque exerted by the field gradient. The precise alignment represents a compromise between aligning with the local field direction and minimizing energy given the field's spatial variation across the needle's volume.</p> Signup and view all the answers

<p>Measure the magnetic field at a high density of points near a magnet. The compass needle traces field lines as a macroscopic approximation. However at microscopic level near the atomic structure, the magnetic field would show discontinuities due to individual atomic dipoles, revealing a granular structure not captured by continuous field lines.</p> Signup and view all the answers

<p>The statement is misleading when field lines are not orthogonal to the area being considered or when considering fields in three dimensions. A more accurate approach involves calculating the magnetic flux density (B) through a given area.</p> Signup and view all the answers

<p>The superconducting ring's field lines, unlike the bar magnet's, originate and terminate solely on the ring itself owing to it being a pure current loop. At large distances, both fields approximate a dipole field, but the multipole moments differ significantly closer to the source.</p> Signup and view all the answers

<p>The compass needle's inertia would prevent it from tracking rapid field changes. Use magnetohydrodynamic simulations calibrated with telescope data to infer magnetic field properties or use Faraday rotation measurements from polarized radio waves.</p> Signup and view all the answers

<p>Magnetic field lines represent the spatial derivative of the magnetic vector potential. The vector potential inherently provides a more complete description, allowing the calculation of Aharonov-Bohm effect which demonstrates that particles can be affected by electromagnetic fields even in regions where the magnetic field is zero, implying a physical significance to the potential itself.</p> Signup and view all the answers

<p>The field lines would bend towards and concentrate within the permeable material, minimizing the reluctance of the magnetic circuit. This increases field strength inside the material and reduces it in regions outside, particularly in the 'shadowed' areas behind the material relative to the magnet.</p> Signup and view all the answers

<p>Magnetic reconnection breaks and reconfigures field lines, converting magnetic energy into kinetic and thermal energy, violating the static picture. Solar flares and magnetospheric substorms (auroras) are driven by magnetic reconnection.</p> Signup and view all the answers

<p>Spacetime curvature could cause the magnetic field lines to converge or diverge, depending on the nature of the curvature. Strong gravitational lensing could distort the apparent distribution of field lines, creating multiple images or arcs of the magnetic field.</p> Signup and view all the answers

<p>Direction and magnitude</p> Signup and view all the answers

<p>Emerge from the north pole and merge at the south pole.</p> Signup and view all the answers

<p>By the closeness of the field lines; the closer the lines, the stronger the field.</p> Signup and view all the answers

<ol> <li>Place the compass near the magnet and mark the needle's ends.</li> <li>Move the compass so the south pole is at the previous north pole mark.</li> <li>Repeat, marking positions until reaching the magnet's south pole.</li> <li>Join the marks with a smooth curve.</li> </ol> Signup and view all the answers

<p>The deflection increases.</p> Signup and view all the answers

<p>By observing the deflection of a compass needle placed near the current-carrying conductor. The deflection indicates the presence of a magnetic field. The direction of deflection changes with the direction of the current.</p> Signup and view all the answers

<p>If monopoles existed, field lines would originate from a north monopole and terminate at a south monopole (or extend to infinity), thus the lines would not be closed curves. Magnetic field lines would start or end on these magnetic charges, similar to how electric field lines behave with electric charges.</p> Signup and view all the answers

<p>A compass</p> Signup and view all the answers

<p>It deflects</p> Signup and view all the answers

<p>Copper</p> Signup and view all the answers

<p>It deflects in the opposite direction</p> Signup and view all the answers

<p>1.5 V</p> Signup and view all the answers

<p>To control the flow of current</p> Signup and view all the answers

<p>To control the amount of current flowing in the circuit.</p> Signup and view all the answers

<p>To hold the wire in place.</p> Signup and view all the answers

<p>Ammeter</p> Signup and view all the answers

<p>12 V</p> Signup and view all the answers

<p>The compass needle deflects in the opposite direction.</p> Signup and view all the answers

<p>East</p> Signup and view all the answers

<p>A copper wire, battery, plug key and compass needle.</p> Signup and view all the answers

<p>To handle the higher current without overheating.</p> Signup and view all the answers

<p>To provide a flat plane that the copper wire runs through.</p> Signup and view all the answers

<p>The direction of the magnetic field is dependent on the direction of the electric current.</p> Signup and view all the answers

<p>The shape of the conductor determines the pattern of the magnetic field.</p> Signup and view all the answers

<p>The rheostat controls the amount of current flowing through the wire, thus affecting the strength of the magnetic field.</p> Signup and view all the answers

<p>The deflection of the compass needle would increase.</p> Signup and view all the answers

<p>To maintain a consistent spatial relationship between the wire and the plane of observation.</p> Signup and view all the answers

<p>The deflection of the compass needle would increase because a stronger current generates a stronger magnetic field.</p> Signup and view all the answers

<p>The iron sheet would distort the magnetic field lines as it is a ferromagnetic material and concentrates the magnetic field.</p> Signup and view all the answers

<p>The outcome would be similar, with the compass needle deflecting. Aluminum is also a conductor, but it has slightly higher resistance than copper. Therefore there may be a decrease in the magnetic field due to decreased current.</p> Signup and view all the answers

<p>The magnetic field pattern would resemble that of a bar magnet, with concentrated field lines entering and exiting at the ends of the solenoid.</p> Signup and view all the answers

<p>The deflection would still occur, but potentially with a different orientation, depending on the specific geometry. The compass needle aligns with the direction of the magnetic field, which circles the wire due to current.</p> Signup and view all the answers

<p>There would be no difference. The magnetic field's existence and properties are not dependent on the presence of air or any other medium.</p> Signup and view all the answers

<p>Point your right thumb in the direction of the current. Your fingers will curl in the direction of the magnetic field. The compass needle's north pole will align with the direction of the magnetic field.</p> Signup and view all the answers

<p>The magnetic field would fluctuate in direction and magnitude corresponding to the frequency of the AC current. The compass needle would oscillate back and forth rapidly or show no net deflection at all.</p> Signup and view all the answers

<p>The magnetic field pattern would be more complex and asymmetrical. The field lines would concentrate more on the inner side of the curve and be sparser on the outer side.</p> Signup and view all the answers

<p>The deflection of the compass needle would be significantly reduced or eliminated because mu-metal shields the compass from external magnetic fields by providing a low reluctance path for the magnetic field lines, effectively diverting them away from the compass.</p> Signup and view all the answers

<p>The magnetic field strength produced by the wire is approximately $1.15 \times 10^{-5}$ T, calculated using $\tan(\theta) = B_{wire} / B_{earth}$, assuming the wire's field is perpendicular to Earth's.</p> Signup and view all the answers

<p>A thinner wire would concentrate the current closer to its surface due to the skin effect (negligible at DC) and increase the resistance. With constant current, the magnetic field pattern would remain qualitatively similar, but Joule heating may be more pronounced. Assuming the resistance change has no effect on the properties, the magnetic field would be unchanged.</p> Signup and view all the answers

<p>The magnetic field lines would concentrate inside the solenoid, becoming more uniform. Outside, the field would resemble that of a bar magnet. Ampère's law, $\oint B \cdot dl = \mu_0 I_{enc}$, helps quantify the field's integral around a closed loop related to the enclosed current.</p> Signup and view all the answers

<p>With a superconducting wire, the Meissner effect would expel any external magnetic field, including that of the compass needle. If the superconductor reaches a critical temperature or field, the magnetic field would penetrate it again, although this would not affect the needle's deflection.</p> Signup and view all the answers

<p>In a vacuum, heat dissipation is limited to radiative transfer and conduction through the wire's supports. Reduced convection leads to higher wire temperature, calculated via the Stefan-Boltzmann law: $P = \epsilon \sigma A T^4$, where $P$ equals power input, $\epsilon$ equals emissivity, $\sigma$ equals the Stefan-Boltzmann constant, $A$ equals surface area, and $T$ equals absolute temperature.</p> Signup and view all the answers

<p>The observer would see no magnetic field in their frame. In the wire's frame, the magnetic field arises due to the relativistic length contraction of the positive ions. The observer co-moving with electrons sees no current or magnetic field.</p> Signup and view all the answers

<p>Magnetostriction in the cardboard would cause mechanical strain proportional to the magnetic field, altering the material's magnetic permeability. The magnetic field pattern would be locally altered but without significant change in the compass deflection due to the small effect.</p> Signup and view all the answers

<p>The Faraday cage will not affect the deflection of the compass needle, as it shields against external electromagnetic fields but not the static magnetic field produced by the wire's current, which induces a steady, unshielded magnetic field.</p> Signup and view all the answers

<p>A pulsed current would induce a time-varying magnetic field that induces eddy currents in the cardboard. Skin effect would concentrate current to the surface of the wire, with eddy current losses proportional to the frequency squared.</p> Signup and view all the answers

<p>With a metamaterial wire, the magnetic field lines may exhibit unusual patterns due to the negative refractive index. The field could be focused or reversed in certain regions near the wire but without overall change to the field distribution or compass deflection.</p> Signup and view all the answers

<p>Remove the plug to stop current flow; orient the wire perpendicular to the needle.</p> Signup and view all the answers

<p>To control and vary the amount of current flowing through the circuit.</p> Signup and view all the answers

<p>Towards the west.</p> Signup and view all the answers

<p>Thick wire lowers resistance, allowing higher current without overheating.</p> Signup and view all the answers

<p>The deflection would increase due to the concentrated magnetic field inside the solenoid.</p> Signup and view all the answers

<p>It would have no impact, because the cardboard is only present as physical support and not part of the circuit.</p> Signup and view all the answers

<p>The magnetic field strength is directly proportional to the current: $B \propto I$</p> Signup and view all the answers

<p>The external field would cause additional deflection, obscuring the effect of the wire. Shielding the compass or accounting for the external field's influence are mitigations.</p> Signup and view all the answers

<p>The needle would oscillate back and forth as the current direction changes periodically.</p> Signup and view all the answers

<p>Concentric circles</p> Signup and view all the answers

<p>Magnetic field lines</p> Signup and view all the answers

<p>Using a compass</p> Signup and view all the answers

<p>It gets reversed</p> Signup and view all the answers

<p>Deflection increases</p> Signup and view all the answers

<p>Rheostat</p> Signup and view all the answers

<p>Ammeter</p> Signup and view all the answers

<p>Copper</p> Signup and view all the answers

<p>It increases</p> Signup and view all the answers

<p>It remains vertically straight</p> Signup and view all the answers

<p>The iron filings align themselves in a pattern of concentric circles around the copper wire, indicating the shape of the magnetic field.</p> Signup and view all the answers

<p>Increasing the current through the wire increases the magnitude of the magnetic field produced at a given point.</p> Signup and view all the answers

<p>A compass is used. The direction of the north pole of the compass needle indicates the direction of the magnetic field lines.</p> Signup and view all the answers

<p>The deflection of the compass needle reverses, indicating a change in the direction of the magnetic field.</p> Signup and view all the answers

<p>The experiment shows that an electric current flowing through a wire produces a magnetic field around it, illustrating the fundamental connection between electricity and magnetism.</p> Signup and view all the answers

<p>The cardboard acts as a surface for the iron filings to align on, making the pattern of the magnetic field visible.</p> Signup and view all the answers

<p>A rheostat is used to vary the current in the wire. This allows observation of how changes in current affect the magnetic field's magnitude.</p> Signup and view all the answers

<p>No magnetic field would be produced because current would not flow through the non-conducting material.</p> Signup and view all the answers

<p>Maintaining the wire's straightness ensures a consistent and predictable magnetic field pattern, simplifying observation and analysis.</p> Signup and view all the answers

<p>The density of the iron filings would decrease as you move further away from the wire, showing that the magnetic field's strength decreases with distance.</p> Signup and view all the answers

<p>The compass needle aligns itself tangent to the magnetic field lines produced by the current in the wire, demonstrating that electric current generates a magnetic field.</p> Signup and view all the answers

<p>Increasing the current increases the strength of the magnetic field. The increased deflection of the compass needle demonstrates this effect.</p> Signup and view all the answers

<p>The iron filings would align to show a magnetic field pattern similar to that of a bar magnet, with concentrated field lines at the ends of the coil.</p> Signup and view all the answers

<p>With alternating current, the compass needle would oscillate back and forth, as the direction of the magnetic field continually reverses with the changing current direction.</p> Signup and view all the answers

<p>Increasing the resistance would decrease the current, weakening the magnetic field. The concentric circles, as visualized by iron filings, would become less defined or dense.</p> Signup and view all the answers

<p>The magnetic field forms concentric cylinders around the wire, extending infinitely along the wire's length. Each cylinder represents a surface of constant magnetic field strength.</p> Signup and view all the answers

<p>The circular magnetic field lines observed around the wire directly illustrate Ampere's Law. The strength of the magnetic field is proportional to the current, aligning with the law's principles.</p> Signup and view all the answers

<p>Using a magnetometer to directly measure the magnetic field strength at various distances, and plotting the data to observe the relationship between distance and field strength would add a quantitative aspect.</p> Signup and view all the answers

<p>Iron filings are made of ferromagnetic material and align because each filing becomes magnetized, with its magnetic domains aligning with the external magnetic field.</p> Signup and view all the answers

<p>This experiment is the basis of the electromagnet principle, where electric current generates a magnetic field. This is used in motors, relays, and magnetic levitation.</p> Signup and view all the answers

<ol> <li>The Earth's magnetic field, 2. Air ionization.</li> </ol> Signup and view all the answers

<p>Use high-speed field sensors and computational fluid dynamics.</p> Signup and view all the answers

<p>The field pattern would be sharper, but iron filings don't work.</p> Signup and view all the answers

<p>Control particle size and magnetic susceptibility of the material.</p> Signup and view all the answers

<p>It would be unchanged, but eddy currents could appear.</p> Signup and view all the answers

<p>Use a Hall effect sensor.</p> Signup and view all the answers

<p>The filings would oscillate and a skin effect would occur.</p> Signup and view all the answers

<p>It wouldn't, but use electron beam deflection to measure the field.</p> Signup and view all the answers

<p>Low res, low sensitivity, use magneto-optical Kerr effect.</p> Signup and view all the answers

<p>The field nearly cancels, making visualization with iron filings impossible.</p> Signup and view all the answers

<p>Concentric circles</p> Signup and view all the answers

<p>Magnetic field lines</p> Signup and view all the answers

<p>By using a compass</p> Signup and view all the answers

<p>The deflection increases</p> Signup and view all the answers

<p>The magnetic field's magnitude increases.</p> Signup and view all the answers

<p>The magnitude of the magnetic field is proportional to the current.</p> Signup and view all the answers

<p>To reduce friction allowing alignment with Magnetic field.</p> Signup and view all the answers

<p>External magnetic fields and imperfections in the wire.</p> Signup and view all the answers

<p>There would be no noticeable difference.</p> Signup and view all the answers

<p>Right-hand thumb rule</p> Signup and view all the answers

<p>Direction of current</p> Signup and view all the answers

<p>Direction of magnetic field</p> Signup and view all the answers

<p>Become larger and larger</p> Signup and view all the answers

<p>Distance from it</p> Signup and view all the answers

<p>Clockwise when viewed from the east end</p> Signup and view all the answers

<p>Concentric circles</p> Signup and view all the answers

<p>Magnetic field</p> Signup and view all the answers

<p>It weakens</p> Signup and view all the answers

<p>The magnetic field strength decreases as the distance from the wire increases.</p> Signup and view all the answers

<p>The magnetic field will point towards the west.</p> Signup and view all the answers

<p>The magnetic field lines form concentric circles around each point of the loop, becoming larger as you move away from the wire.</p> Signup and view all the answers

<p>It provides a standard way to relate the direction of current and magnetic fields, ensuring consistent results and understanding.</p> Signup and view all the answers

<ol> <li>They form closed loops.</li> <li>They never intersect.</li> <li>The relative density of field lines indicates the strength of the magnetic field.</li> </ol> Signup and view all the answers

<p>If they intersected, it would mean that at the point of intersection, there would be two directions of the magnetic field, which is impossible.</p> Signup and view all the answers

<p>The magnetic field direction is towards the North.</p> Signup and view all the answers

<p>Increasing the current increases the strength of the magnetic field at the center of the loop.</p> Signup and view all the answers

<p>The magnetic field lines emerge from the North pole and enter the South pole, forming closed loops.</p> Signup and view all the answers

<p>The force on the wire is at its maximum when the current is perpendicular to the magnetic field.</p> Signup and view all the answers

<p>The right-hand thumb rule states that if you hold a current-carrying conductor in your right hand with your thumb pointing in the direction of the current, your fingers will curl in the direction of the magnetic field. A counterintuitive scenario might involve complex coil configurations, where the superposition of magnetic fields requires careful vector addition, making the overall field direction non-obvious.</p> Signup and view all the answers

<p>Increasing the electric current through a conductor directly increases the strength, or magnitude, of the magnetic field surrounding it. The relationship is linear; doubling the current doubles the magnetic field strength at any given point around the conductor.</p> Signup and view all the answers

<p>As you move away from a current-carrying straight wire, the magnetic field lines become less dense, indicating a weaker magnetic field. The field lines also form larger concentric circles, reflecting the diminishing influence of the current with distance.</p> Signup and view all the answers

<p>At the center of a current-carrying circular loop, the magnetic field is strongest and approximately uniform, pointing perpendicularly through the plane of the loop. Far away from the loop, the field resembles that of a magnetic dipole, with a field strength that diminishes more rapidly with distance.</p> Signup and view all the answers

<p>Magnetic field lines form closed loops because magnetic fields are produced by moving charges or magnetic dipoles (like those in atoms), not by isolated magnetic monopoles. The absence of magnetic monopoles means magnetic field lines must always have a 'source' and 'sink' together, creating closed loops, unlike electric field lines which can start and end on isolated charges.</p> Signup and view all the answers

<p>The magnetic field around a solenoid (a coil of wire) resembles that of a bar magnet, with a strong, uniform field inside and weaker fields looping around the outside. The field can be strengthened by increasing the current, increasing the number of turns of wire, or inserting a ferromagnetic core into the solenoid.</p> Signup and view all the answers

<p>A straight wire produces circular magnetic field lines around it, with the field strength decreasing inversely with distance. A circular loop produces a field that is strongest and most uniform at its center, resembling a dipole field at larger distances, with field lines passing through the loop's center.</p> Signup and view all the answers

<p>When two parallel wires carry current in opposite directions, they experience a repulsive force. This is because the magnetic field produced by each wire interacts with the current in the other wire, resulting in a force that pushes them apart.</p> Signup and view all the answers

<p>As temperature increases, the magnetic domains in ferromagnetic materials become more randomly oriented due to increased thermal energy, weakening their ferromagnetic properties. Above the Curie temperature, the material loses its spontaneous magnetization and becomes paramagnetic.</p> Signup and view all the answers

<p>Magnetic flux is the measure of the total magnetic field passing through a given area. It's crucial in electromagnetic induction because a change in magnetic flux through a loop of wire induces an electromotive force (EMF), driving current, as described by Faraday's law of induction: $EMF = -N \frac{d\Phi}{dt}$, where N is the number of turns and $\frac{d\Phi}{dt}$ is the rate of change of magnetic flux.</p> Signup and view all the answers

<p>The magnetic field will be proportional to $(I_1 - I_2)$ and inversely proportional to $d$. The magnetic field is zero when $I_1 = I_2$.</p> Signup and view all the answers

<p>The self-inductance can be calculated by integrating the magnetic flux density over the cross-sectional area and then using the definition of inductance. The self-inductance is then given by $L = \frac{\mu_0 N^2 h}{2\pi} ln(\frac{b}{a})$. The derivation assumes a uniform distribution of current and negligible fringing effects.</p> Signup and view all the answers

<p>The force is $\vec{F} = (\vec{m} \cdot \nabla) \vec{B}$, and the torque is $\vec{\tau} = \vec{m} \times \vec{B}$. For the net force to be zero, $\vec{B}$ must be uniform.</p> Signup and view all the answers

<p>When the net force on the particle is 0, the condition for constant velocity is $\vec{E} = - \vec{v} \times \vec{B}$. The electric and magnetic forces cancel each other.</p> Signup and view all the answers

<p>Ampère's Law, $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$, relates the magnetic field to the current. However, it is insufficient for time-varying fields where displacement current becomes significant, or in situations lacking sufficient symmetry to simplify the integral.</p> Signup and view all the answers

<p>The magnetic field can be written as the curl of a vector potential. $\vec{B} = \nabla \times \vec{A}$. This allows for an easier solutions to problems as we are dealing with a vector first order equation instead of a second order equation. However, the main problem is that the vector potential is not unique.</p> Signup and view all the answers

<p>The force of repulsion $F \approx \frac{3 \mu_0 m^2}{2 \pi r^4}$, where m is the magnetic moment of each magnet. If one magnet is rotated, they will become aligned and the force will become attractive of the same magnitude.</p> Signup and view all the answers

<p>Ferromagnetism: Parallel alignment, high positive susceptibility, loses order above Curie temperature. Antiferromagnetism: Anti-parallel alignment, low susceptibility, Néel temperature. Ferrimagnetism: Unequal anti-parallel moments, high susceptibility, Curie temperature.</p> Signup and view all the answers

<p>We consider an infinitesimal ring of charge and integrate over the entire sphere. The magnetic dipole moment is proportional to both angular velocity and total charge. Optimization involves maximizing both charge and angular velocity within material constraints.</p> Signup and view all the answers

<p>The Meissner effect is the expulsion of magnetic fields from a superconductor. It shows superconductivity is not just perfect conductivity because a perfectly conducting material would only prevent changes in magnetic flux, not actively expel the field. It occurs due to the formation of Cooper pairs acting to perfectly shield the interior from magnetic fields.</p> Signup and view all the answers

<p>If a current-carrying straight conductor is held in the right hand such that the thumb points towards the direction of the current, then the fingers will wrap around the conductor in the direction of the magnetic field lines.</p> Signup and view all the answers

<p>The magnetic field at a point directly below the power line turns clockwise when viewed from the east end.</p> Signup and view all the answers

<p>Magnetic field lines emerge from the north pole and enter the south pole outside the magnet, and they are closed curves.</p> Signup and view all the answers

<p>The magnetic field produced by a current-carrying straight wire depends inversely on the distance from it.</p> Signup and view all the answers

<p>The magnetic field lines are concentric circles around each point of the circular loop.</p> Signup and view all the answers

<p>As we move towards the center of the loop made of a current-carrying wire the concentric circles representing the magnetic field around it would become larger and larger.</p> Signup and view all the answers

<p>$2 \times 10^{-5}$ Tesla</p> Signup and view all the answers

<p>The force is repulsive. The magnetic field created by each wire interacts with the current in the other wire, resulting in a force pushing them apart.</p> Signup and view all the answers

<p>The magnetic dipole moment is $m = I \pi r^2$. The maximum torque is $\tau = I \pi r^2 B$.</p> Signup and view all the answers

<p>The magnetic field increases.</p> Signup and view all the answers

<p>A coil of many circular turns of insulated wire wrapped closely in the shape of a cylinder.</p> Signup and view all the answers

<p>Parallel straight lines.</p> Signup and view all the answers

<p>They are similar.</p> Signup and view all the answers

<p>A magnet formed by placing a magnetic material inside a current-carrying solenoid.</p> Signup and view all the answers

<p>Soft iron.</p> Signup and view all the answers

<p>It increases.</p> Signup and view all the answers

<p>Cylinder.</p> Signup and view all the answers

<p>The same.</p> Signup and view all the answers

<p>The poles reverse.</p> Signup and view all the answers

<p>The magnetic field strength increases proportionally to the number of turns.</p> Signup and view all the answers

<p>Parallel field lines indicate a uniform magnetic field, meaning the field strength is the same at all points inside the solenoid.</p> Signup and view all the answers

<p>The polarity of the magnetic field reverses; the north and south poles switch positions.</p> Signup and view all the answers

<p>An electromagnet is created by placing a magnetizable material, such as soft iron, inside a current-carrying solenoid. Soft iron is a suitable core material.</p> Signup and view all the answers

<p>Increase the current flowing through the solenoid or increase the number of turns of wire in the solenoid.</p> Signup and view all the answers

<p>The magnetic field at the center of the coil is directly proportional to the current; increasing the current increases the field strength.</p> Signup and view all the answers

<p>Both produce a magnetic field with distinct north and south poles, and the field lines form closed loops extending from one pole to the other.</p> Signup and view all the answers

<p>Insulation prevents the current from short-circuiting between adjacent turns of the wire, ensuring that the current flows through the entire coil.</p> Signup and view all the answers

<p>The solenoid with a smaller diameter will have a more uniform field inside. The larger diameter may cause slight non-uniformities near the edges.</p> Signup and view all the answers

<p>The magnetic field would remain essentially unchanged because copper is not a ferromagnetic material and does not significantly affect the magnetic field.</p> Signup and view all the answers

<p>The magnetic field is directly proportional to the number of turns. Increasing the number of turns $n$ in the coil increases the magnetic field by a factor of $n$.</p> Signup and view all the answers

<p>The magnetic field inside an ideal solenoid is uniform and parallel to the axis of the solenoid. This is because the field lines created by each loop of wire in the solenoid combine to form a consistent field.</p> Signup and view all the answers

<p>A solenoid can be used to create an electromagnet by inserting a magnetic material, such as soft iron, inside the coil. Soft iron is suitable because it easily magnetizes when a current flows through the solenoid but quickly loses its magnetism when the current is turned off.</p> Signup and view all the answers

<p>The patterns formed by the iron filings indicate the direction and strength of the magnetic field produced by the coil. The filings align themselves along the magnetic field lines, with denser regions indicating stronger field strength.</p> Signup and view all the answers

<p>The magnetic field lines are parallel straight lines inside a solenoid because the fields from each loop of wire in the solenoid combine constructively and uniformly. The fields tend to cancel out any components perpendicular to the solenoid's axis, leaving a consistent axial field.</p> Signup and view all the answers

<p>The strength of the magnetic field inside a solenoid is directly proportional to the current passing through it. Increasing the current increases the magnetic field strength proportionally.</p> Signup and view all the answers

<p>Using a material with higher resistivity would reduce the current flowing through the solenoid for a given voltage. Since the magnetic field strength is directly proportional to the current, the magnetic field produced would be weaker.</p> Signup and view all the answers

<p>Both solenoids and bar magnets produce similar magnetic fields, with defined north and south poles and field lines that loop from one pole to the other. However, the magnetic field of a solenoid can be easily controlled by adjusting the current, while a bar magnet's field is fixed.</p> Signup and view all the answers

<p>The principle of superposition states that the net magnetic field at a point is the vector sum of the magnetic fields produced by each individual turn of wire. This means that the contributions from each turn add together, taking both magnitude and direction into account, to determine the overall field.</p> Signup and view all the answers

<p>Introducing a ferromagnetic core into a solenoid would significantly increase the magnetic field inside the solenoid. This is because ferromagnetic materials have high permeability, allowing them to concentrate and enhance the magnetic field lines within the solenoid.</p> Signup and view all the answers

<p>The magnetic field can be approximated as $B \approx \mu_0 n_0 I$ with a small perturbation due to the non-uniformity. A more detailed calculation might involve Fourier analysis to account for the angular dependence.</p> Signup and view all the answers

<p>The rapid loss of superconductivity will cause a sudden increase in resistance, leading to rapid dissipation of the magnetic energy as heat, potentially causing significant thermal damage and a voltage spike due to inductive effects.</p> Signup and view all the answers

<p>The negative refractive index could lead to reversed wave propagation, novel focusing effects, and potentially enhanced or inhibited interaction with the solenoid's magnetic field, depending on the metamaterial's specific properties.</p> Signup and view all the answers

<p>Deriving an exact expression for <strong>A</strong> involves complex integrals. Approximations often involve neglecting end effects or using multipole expansions to simplify the calculation, especially far from the solenoid.</p> Signup and view all the answers

<p>Imperfections can introduce field inhomogeneities. Mitigation strategies include precise winding techniques, shimming coils to correct for deviations, and active feedback systems to compensate for environmental effects.</p> Signup and view all the answers

<p>Inductive coupling allows energy transfer between the solenoids and the capacitor, potentially leading to oscillatory behavior. The oscillation frequency depends on the inductance, capacitance, and coupling coefficient.</p> Signup and view all the answers

<p>Simple solenoids suffer from end losses and plasma instabilities. Alternative configurations like tokamaks and stellarators use more complex magnetic fields to improve confinement.</p> Signup and view all the answers

<p>Eddy currents oppose the changing magnetic field, slowing down the rise and fall times. Strategies to minimize their impact include using laminated cores or choosing materials with high resistivity.</p> Signup and view all the answers

<p>The elliptical cross-section will lead to a non-uniform magnetic field, with the field being stronger in regions where the curvature is higher. This requires solving Ampere's law with modified geometry.</p> Signup and view all the answers

<p>Nonlinear materials distort the field due to saturation and hysteresis effects. Modeling requires iterative numerical methods or finite element analysis incorporating a nonlinear B-H curve.</p> Signup and view all the answers

<p>The magnetic field strength is directly proportional to the number of turns in the coil. More turns result in a stronger magnetic field.</p> Signup and view all the answers

<p>Parallel straight lines.</p> Signup and view all the answers

<p>The soft iron becomes magnetized, forming an electromagnet.</p> Signup and view all the answers

<p>The magnetic fields from each loop of wire in the solenoid add together constructively inside the solenoid, resulting in a stronger overall field.</p> Signup and view all the answers

<p>Increasing the current increases the strength of the magnetic field.</p> Signup and view all the answers

<p>Both produce similar magnetic field patterns with distinct north and south poles. However, a solenoid's magnetic field can be easily turned on and off, and its strength adjusted, unlike a permanent bar magnet.</p> Signup and view all the answers

<p>Electromagnets are used in electric bells, lifting heavy loads, and magnetic levitation trains.</p> Signup and view all the answers

<p>The superconducting solenoid would sustain a constant magnetic field indefinitely without any external power source necessary to maintain the current, unlike the copper solenoid that would require continuous power input due to resistance.</p> Signup and view all the answers

<p>The magnetic flux density ($B$) is directly proportional to the relative permeability ($\mu_r$) of the core material: $B = \mu_r \mu_0 (N/L) I$, where $\mu_0$ is the permeability of free space, $L$ is length of the solenoid, and $N$ is the number of turns. Higher $\mu_r$ results in a significantly stronger magnetic field within the solenoid, as the material concentrates the magnetic flux.</p> Signup and view all the answers

<p>magnetic field</p> Signup and view all the answers

<p>is the same at all points</p> Signup and view all the answers

<p>perpendicular</p> Signup and view all the answers

<p>It reverses</p> Signup and view all the answers

<p>rheostat</p> Signup and view all the answers

<p>Andre-Marie Ampere</p> Signup and view all the answers

<p>aluminum</p> Signup and view all the answers

<p>horse-shoe magnet</p> Signup and view all the answers

<p>battery and key</p> Signup and view all the answers

<p>it is displaced</p> Signup and view all the answers

<p>The force exerted on the current-carrying conductor is perpendicular to both the direction of the current and the direction of the magnetic field.</p> Signup and view all the answers

<p>The force will act horizontally towards the south.</p> Signup and view all the answers

<p>Increasing the current increases the strength of the magnetic field.</p> Signup and view all the answers

<p>The direction of the force on the wire would also reverse.</p> Signup and view all the answers

<p>The magnetic field inside a long straight solenoid is the same at all points.</p> Signup and view all the answers

<p>The magnitude of the force is zero.</p> Signup and view all the answers

<p>The rheostat controls the amount of current flowing through the rod, and changing the resistance changes the magnitude of force.</p> Signup and view all the answers

<p>0.5N</p> Signup and view all the answers

<p>The force remains the same.</p> Signup and view all the answers

<p>Rotating the motor by magnetic force that exists between the magnetic field supplied by permanent magnets and the magnetic field produced by the current.</p> Signup and view all the answers

<p>The magnetic field strength is inversely proportional to the distance from the conductor. As the distance increases, the field strength decreases and vice versa.</p> Signup and view all the answers

<p>The magnetic force is perpendicular due to the nature of the cross product in the Lorentz force law, $\vec{F} = I \vec{L} \times \vec{B}$, where $I$ is the current, $\vec{L}$ is the length vector, and $\vec{B}$ is the magnetic field. The cross product results in a vector orthogonal to both.</p> Signup and view all the answers

<p>Place the compass near the wire. The compass needle will align itself tangent to the circular magnetic field lines. Moving the compass around the wire will map out the field direction.</p> Signup and view all the answers

<p>The magnetic force is zero. The force is given by $F = BILsin(\theta)$, where $\theta$ is the angle between the current and the field. When the wire is parallel, $\theta = 0$ degrees, so $sin(0) = 0$, resulting in zero force.</p> Signup and view all the answers

<p>Increasing turns increases the magnetic field inside the solenoid. More turns result in a higher concentration of magnetic field lines within the solenoid, strengthening the overall field.</p> Signup and view all the answers

<p>Magnetic domains are regions where atomic magnetic moments are aligned. Random alignment leads to no net magnetization, while alignment in one direction creates a strong magnet.</p> Signup and view all the answers

<p>The force is repulsive. Each wire creates a magnetic field that exerts a force on the other. Because the currents are anti-parallel, the forces are directed away from each other.</p> Signup and view all the answers

<p>The particle moves with constant velocity. The equal &amp; opposite forces cancel, resulting in zero net force and therefore no acceleration according to Newton's first law.</p> Signup and view all the answers

<p>A galvanometer is converted to an ammeter by connecting a low-resistance shunt resistor in parallel with the galvanometer coil. This bypasses most of the current, allowing the ammeter to measure larger currents.</p> Signup and view all the answers

<p>Electromagnetic induction is when a changing magnetic field induces a voltage (EMF) in a conductor. Generators use mechanical energy to rotate coils in a magnetic field, inducing a continually changing magnetic flux and thus generating electricity.</p> Signup and view all the answers

<p>The magnetic field within the toroid is given by $B(r) = \frac{\mu_0 I N}{2 \pi r}$, where $I$ is the current, $N$ is the total number of turns, and $r$ is the radial distance. Relativistic effects can be accounted for by modifying the current distribution using Lorentz transformations, leading to a more complex integral expression for $B(r)$.</p> Signup and view all the answers

<p>The metamaterial will cause the magnetic field to bend and focus in unusual ways, potentially leading to regions of enhanced or reversed magnetic field. This can result in forces on the conductor that are opposite to what would be expected in free space, and potentially lead to instability.</p> Signup and view all the answers

<p>The model involves solving the diffusion equation for the magnetic field, taking into account the skin depth $\delta = \sqrt{\frac{2}{\omega \mu \sigma}}$ and the complex frequency-dependent permeability $\mu(\omega)$. The solution will involve Bessel functions and Fourier analysis to describe the time-dependent field distribution.</p> Signup and view all the answers

<p>The fractal wire will generate a highly complex, non-uniform magnetic field due to its intricate geometry. Calculating the magnetic field at a point requires integrating the Biot-Savart law over the fractal's path, which can be approximated numerically using computational electromagnetics techniques or fractal calculus.</p> Signup and view all the answers

<p>QED corrections introduce virtual particle-antiparticle pairs that screen the charge, modifying the magnetic field at short distances. The magnitude of these corrections is proportional to the fine-structure constant $\alpha \approx \frac{1}{137}$ and becomes significant at relativistic speeds, requiring a full QED treatment.</p> Signup and view all the answers

<p>The equilibrium position is determined by balancing the magnetic forces due to the Meissner effect and flux pinning. The stability analysis involves considering the free energy of the system, including the kinetic energy of the superconducting condensate, and analyzing the effects of thermal fluctuations using statistical mechanics.</p> Signup and view all the answers

<p>For $r &lt; a$, $B = 0$. For $a &lt; r &lt; b$, $B = \frac{\mu_0 I}{2\pi r} \frac{r^2 - a^2}{b^2 - a^2}$. For $r &gt; b$, $B = \frac{\mu_0 I}{2\pi r}$. With skin effect, Ampère's Law directly applied becomes problematic because the symmetry assumptions are violated; a more complex analysis considering displacement current and frequency-dependent current distribution is required.</p> Signup and view all the answers

<p>The constitutive relations are modified to include chiral parameters, e.g., $\mathbf{D} = \epsilon \mathbf{E} + i \chi \mathbf{H}$ and $\mathbf{B} = \mu \mathbf{H} - i \chi \mathbf{E}$, where $\chi$ is the chirality parameter. This coupling leads to phenomena like optical activity and circular dichroism, causing polarization rotation and differential absorption of left- and right-circularly polarized waves.</p> Signup and view all the answers

<p>The setup involves a split-ring resonator with a controllable magnetic flux threading the loop. Challenges include maintaining phase coherence in the presence of decoherence mechanisms, shielding from external electromagnetic fields using superconducting enclosures, and operating at cryogenic temperatures to minimize thermal noise. Sensitivity must be on the order of $\Phi_0 = \frac{h}{2e}$ (the flux quantum).</p> Signup and view all the answers

<p>Relativistic MHD equations must account for the relativistic equation of state and Lorentz transformations of the electromagnetic fields. Key parameters include the magnetization parameter $\sigma = \frac{B^2}{\mu_0 \rho c^2}$, the plasma beta $\beta = \frac{P}{B^2/2\mu_0}$, and the Lundquist number $S = \frac{\mu_0 L V_A}{\eta}$ (where $\eta$ is resistivity). These parameters influence the growth rates of various MHD instabilities, such as the kink instability or the tearing mode.</p> Signup and view all the answers

<p>The direction of the force is reversed.</p> Signup and view all the answers

<p>The forefinger.</p> Signup and view all the answers

<p>The second finger or middle finger.</p> Signup and view all the answers

<p>The thumb.</p> Signup and view all the answers

<p>They are at right angles to each other.</p> Signup and view all the answers

<p>Electric motor, electric generator, loudspeakers, microphones, or measuring instruments.</p> Signup and view all the answers

<p>It is opposite to the direction of electron motion.</p> Signup and view all the answers

<p>The direction of the magnetic field, the direction of the current, and the direction of the force.</p> Signup and view all the answers

<p>To the left.</p> Signup and view all the answers

<p>The magnitude increases.</p> Signup and view all the answers

<p>The direction of the current and the direction of the magnetic field.</p> Signup and view all the answers

<p>When the direction of the current is at right angles to the direction of the magnetic field.</p> Signup and view all the answers

<p>Stretch the thumb, forefinger, and middle finger of your left hand such that they are mutually perpendicular. If the forefinger points in the direction of the magnetic field and the middle finger in the direction of the current, then the thumb will point in the direction of motion or the force acting on the conductor.</p> Signup and view all the answers