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What is the electric field between two parallel plates with charge Q and area A, according to the provided text?
What is the electric field between two parallel plates with charge Q and area A, according to the provided text?
What is the capacitance of a parallel plate capacitor with plate area A, plate separation d, and permittivity ε₀?
What is the capacitance of a parallel plate capacitor with plate area A, plate separation d, and permittivity ε₀?
Which of the following is TRUE about the electric field between two parallel plates based on the provided content?
Which of the following is TRUE about the electric field between two parallel plates based on the provided content?
How does the capacitance of a parallel plate capacitor change if the plate separation is increased?
How does the capacitance of a parallel plate capacitor change if the plate separation is increased?
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What is the relationship between the charge stored on a capacitor and the voltage across it?
What is the relationship between the charge stored on a capacitor and the voltage across it?
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When two capacitors are connected in parallel, what is the same for both capacitors?
When two capacitors are connected in parallel, what is the same for both capacitors?
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What is the equivalent capacitance (Ceq) of two capacitors C1 and C2 connected in parallel?
What is the equivalent capacitance (Ceq) of two capacitors C1 and C2 connected in parallel?
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What is the value of the magnetic flux that passes through a sphere if the sphere is placed in a constant uniform magnetic field, $B$?
What is the value of the magnetic flux that passes through a sphere if the sphere is placed in a constant uniform magnetic field, $B$?
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Faraday's law of electromagnetic induction states that:
Faraday's law of electromagnetic induction states that:
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Suppose you have two capacitors, one with capacitance C1 and the other with capacitance C2, where C1 > C2. Which of these capacitors will store more charge when connected in parallel to a battery with voltage V?
Suppose you have two capacitors, one with capacitance C1 and the other with capacitance C2, where C1 > C2. Which of these capacitors will store more charge when connected in parallel to a battery with voltage V?
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If a coil has N turns, what is the induced emf in the coil when the magnetic flux through it changes at a rate of $dΦ_B/dt$?
If a coil has N turns, what is the induced emf in the coil when the magnetic flux through it changes at a rate of $dΦ_B/dt$?
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Which of the following actions can change the magnetic flux through a coil?
Which of the following actions can change the magnetic flux through a coil?
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In the example provided about the flexible loop, what is the initial flux through the loop before it's stretched?
In the example provided about the flexible loop, what is the initial flux through the loop before it's stretched?
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What is the final flux through the flexible loop in the example after it's stretched?
What is the final flux through the flexible loop in the example after it's stretched?
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What is the final flux through the wire loop in the second example when the magnetic field changes from +0.30T to -0.20T?
What is the final flux through the wire loop in the second example when the magnetic field changes from +0.30T to -0.20T?
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What is the average induced emf in the second example when the magnetic field changes from +0.30T to -0.20T in 1.5s?
What is the average induced emf in the second example when the magnetic field changes from +0.30T to -0.20T in 1.5s?
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What is the average value of an alternating current (AC)?
What is the average value of an alternating current (AC)?
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What is the relationship between the average value of the square of an AC wave and the peak value of the AC wave?
What is the relationship between the average value of the square of an AC wave and the peak value of the AC wave?
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What happens to the magnetic field produced by an induced current when the magnetic field decreases?
What happens to the magnetic field produced by an induced current when the magnetic field decreases?
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What does Lenz's Law describe?
What does Lenz's Law describe?
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What is the key factor that determines the direction of the induced current in Lenz's Law?
What is the key factor that determines the direction of the induced current in Lenz's Law?
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What happens to the induced EMF in a coil if the magnetic field decreases?
What happens to the induced EMF in a coil if the magnetic field decreases?
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What happens to the magnetic field created by the induced current in a coil if the magnetic field decreases?
What happens to the magnetic field created by the induced current in a coil if the magnetic field decreases?
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What is the significance of the average value being zero for an AC waveform?
What is the significance of the average value being zero for an AC waveform?
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Which of the following statements accurately describes the inconsistency Ampere's Law faced when applied to the gap between two capacitor plates?
Which of the following statements accurately describes the inconsistency Ampere's Law faced when applied to the gap between two capacitor plates?
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Why is the changing electric field between the capacitor plates considered a source of the magnetic field?
Why is the changing electric field between the capacitor plates considered a source of the magnetic field?
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What is the significance of Maxwell's modification to Ampere's Law in the context of electromagnetic theory?
What is the significance of Maxwell's modification to Ampere's Law in the context of electromagnetic theory?
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What happens to the magnetic field between the capacitor plates when the capacitor is charging?
What happens to the magnetic field between the capacitor plates when the capacitor is charging?
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Which of the following statements is TRUE about the displacement current in the gap between two capacitor plates?
Which of the following statements is TRUE about the displacement current in the gap between two capacitor plates?
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Why does a magnetic field not increase or decrease the energy of a particle?
Why does a magnetic field not increase or decrease the energy of a particle?
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What determines the radius of the circular orbit of a charged particle in a magnetic field?
What determines the radius of the circular orbit of a charged particle in a magnetic field?
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How does a stronger magnetic field affect the radius of the circular orbit of a charged particle?
How does a stronger magnetic field affect the radius of the circular orbit of a charged particle?
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What is the relationship between the magnetic field strength and the angular frequency of a charged particle in a circular orbit?
What is the relationship between the magnetic field strength and the angular frequency of a charged particle in a circular orbit?
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Why is a magnetic field able to bend a charged particle's path but not change its speed?
Why is a magnetic field able to bend a charged particle's path but not change its speed?
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Which of the following statements is NOT true about the interaction of a charged particle with a magnetic field?
Which of the following statements is NOT true about the interaction of a charged particle with a magnetic field?
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What is the formula for the radius of the circular orbit of a charged particle in a uniform magnetic field?
What is the formula for the radius of the circular orbit of a charged particle in a uniform magnetic field?
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What is the relationship between the electric field at a point P due to a charged ring and the distance from the center of the ring to the point P?
What is the relationship between the electric field at a point P due to a charged ring and the distance from the center of the ring to the point P?
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What is the expression for the electric field at a point on the axis of a uniformly charged ring, where the distance from the center of the ring to the point is much greater than the radius of the ring?
What is the expression for the electric field at a point on the axis of a uniformly charged ring, where the distance from the center of the ring to the point is much greater than the radius of the ring?
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What is the direction of the electric field at any point on the axis of a uniformly charged ring?
What is the direction of the electric field at any point on the axis of a uniformly charged ring?
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What is the expression for the electric field at a point on the y-axis due to a uniformly charged wire lying along the z-axis?
What is the expression for the electric field at a point on the y-axis due to a uniformly charged wire lying along the z-axis?
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What is the significance of the angle θ in the calculation of the electric field due to the charged wire?
What is the significance of the angle θ in the calculation of the electric field due to the charged wire?
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What is the correct expression for the component of the electric field along the y-axis due to a small charge element dq on the charged wire?
What is the correct expression for the component of the electric field along the y-axis due to a small charge element dq on the charged wire?
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Why is the electric field due to a charged wire only along the y-axis, and not in other directions?
Why is the electric field due to a charged wire only along the y-axis, and not in other directions?
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How does the electric field due to a charged wire vary with the distance from the wire?
How does the electric field due to a charged wire vary with the distance from the wire?
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Flashcards
Gauss's Law
Gauss's Law
The flux of electric field through a closed surface equals the charge enclosed divided by the permittivity of free space.
Electric Field (E)
Electric Field (E)
The force per unit charge experienced by a test charge in an electric field.
Capacitance (C)
Capacitance (C)
The ability of a system to store charge per unit voltage.
Potential Difference (V)
Potential Difference (V)
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Charge (q) in Capacitors
Charge (q) in Capacitors
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Parallel Capacitors
Parallel Capacitors
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Capacitor Geometry
Capacitor Geometry
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Electric Flux (Φ)
Electric Flux (Φ)
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Electric field of a ring
Electric field of a ring
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Coulomb's law
Coulomb's law
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Continuous charge distribution
Continuous charge distribution
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Symmetry in electric field
Symmetry in electric field
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Component of electric field
Component of electric field
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Integration in electric field
Integration in electric field
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Charge element (dq)
Charge element (dq)
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Cosine angle in fields
Cosine angle in fields
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Power Dissipation
Power Dissipation
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Force on a Wire
Force on a Wire
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Formula for Power
Formula for Power
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Lenz's Law
Lenz's Law
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Induced Current
Induced Current
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Alternating Current (AC)
Alternating Current (AC)
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Average Value of AC
Average Value of AC
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Square of AC Wave
Square of AC Wave
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Magnetic Flux
Magnetic Flux
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Faraday's Law
Faraday's Law
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Induced EMF
Induced EMF
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Rate of Change of Flux
Rate of Change of Flux
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Coil Changes
Coil Changes
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Area of Coil
Area of Coil
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Average Induced EMF Calculation
Average Induced EMF Calculation
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Magnetic Field Strength
Magnetic Field Strength
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Ampere's Law
Ampere's Law
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Displacement Current (ID)
Displacement Current (ID)
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Magnetic Field Sources
Magnetic Field Sources
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Capacitor Charge (Q)
Capacitor Charge (Q)
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Maxwell's Modification
Maxwell's Modification
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Work done by a magnetic field
Work done by a magnetic field
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Magnetic force and displacement
Magnetic force and displacement
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Circular orbit in a magnetic field
Circular orbit in a magnetic field
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Equilibrium of forces
Equilibrium of forces
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Radius of orbit formula
Radius of orbit formula
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Angular frequency
Angular frequency
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Perpendicular forces
Perpendicular forces
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Effects of strong magnetic fields
Effects of strong magnetic fields
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Study Notes
Lecture 23 - Electrostatics II
- Calculating electric fields from continuous charge distributions involves dividing the region into small pieces that behave like point charges. The total electric field is the sum of the fields from each piece.
- Charge density is used to describe charge distribution. Linear, surface, and volume charge densities are defined.
- Example: Electric field calculated from a uniform ring of charge at a point.
Lecture 24 - Electric Potential Energy
- Electrostatic force is conservative.
- Electric potential is defined as the work done bringing a unit positive charge from infinity to the point.
- Potential energy for two point charges q, and q₂: U(r) = q₁q₂/(4πε₀r).
- Gravitational potential energy.
- Relationship to forces with F = -dU/dr
Lecture 25 - Capacitors and Currents
- A capacitor is formed by two conductors isolated from their surroundings.
- Capacitance is defined as the ratio of the amount of charge Q to the potential difference (voltage) V between the conductors. C = Q/V
- Capacitance of parallel plates is proportional to the area of the plates and inversely proportional to the distance between them.
- Energy stored in a capacitor.
Lecture 26 - Electric Potential Energy
- Electric current is the flow of charge; i = dq/dt.
- The unit of current is the ampere (A); 1A = 1C/1s.
- EMF is the difference in potential between two points in a circuit which causes current to flow.
- Ohm's Law relates voltage, current and resistance; I = V/R.
Lecture 27 - The Magnetic Field
- A moving charge in a magnetic field experiences a force perpendicular to both the velocity of the charge and the magnetic field direction. F = qvB sin θ.
- The unit of magnetic field is the Tesla.
- The Lorentz Force describes the force due to both electric and magnetic fields simultaneously; F = qE + qv × B.
Lecture 28 - Electromagnetic Induction
- Magnetic flux is a measure of the amount of magnetic field passing through a surface. Ф=∫B.dĀ
- Faraday's Law states that a changing magnetic flux induces an EMF(electro-motive force)
- The direction of the induced current is given by Lenz's Law, which opposes the change in flux.
Lecture 29 - Alternating Current
- Alternating current (AC) is current that changes direction periodically, often sinusoidally.
- The root mean square (rms) value of an AC current is related to its peak value by a factor of 1/√2.
- Transformers step up or down voltage using the ratio of turns on the primary and secondary coils.
Lecture 30 - Electromagnetic Waves
- Maxwell's equations describe electromagnetic waves, showing that changing electric fields create changing magnetic fields, and vice versa, which allows propagation through empty space.
- The speed of electromagnetic waves in a vacuum is a constant, c = 3 × 10⁸ m/s.
- Electromagnetic waves have both electric and magnetic field components that oscillate perpendicular to each other and the direction of travel.
Lecture 31 - Light
- Light is a form of electromagnetic radiation with different frequencies corresponding to different colours.
- The electromagnetic spectrum encompasses various types of electromagnetic radiation from radio waves to gamma rays, distinguished by their frequencies and wavelengths.
Lecture 32 - Interaction of Light with Matter
- Light interacts with matter in four key ways: emission, absorption, transmission and reflection.
- Blackbody radiation is the continuous spectrum of electromagnetic radiation emitted by any object with a temperature above absolute zero.
- The wavelength of maximum intensity in blackbody radiation is inversely proportional to its temperature (Wien's Law).
Lecture 33 - Interference and Diffraction
- Interference is the superposition of two or more waves resulting in either constructive or destructive interference, depending on the relative phases of the waves.
- Diffraction is the bending of waves around obstacles or through openings; it results in interference patterns.
Lecture 34 - The Particle Nature of Light
- Light has a wave-particle duality, exhibiting properties of both waves and particles.
- The photoelectric effect demonstrates the particle nature of light, where light knocks electrons out of a material, and the energy of the emitted electrons depends on the frequency of light, not the intensity.
- A photon is a quantum of light with energy proportional to its frequency (E = hv)
- Einstein's explanation of the photoelectric effect, introducing the concept of the photon as a particle of light.
Lecture 35 - Geometrical Optics
- Light travels in straight lines, called rays, in many circumstances.
- Reflection: the angle of incidence equals the angle of reflection.
- Refraction: light bends as it passes from one medium to another.
- Lenses and mirrors form images.
Lecture 36 - Thermal Physics I
- Heat is a form of energy that flows from higher to lower temperatures.
- Temperature is a measure of the average kinetic energy of the constituent particles of a substance.
- Thermal equilibrium is the state where there is no net heat flow between objects.
- Thermometric properties are physical properties that change with temperature and can be used to measure it.
- Specific heat describes the amount of heat required to change the temperature of a unit mass of a substance by one degree.
- Heat of transformation (latent heat) is the heat required for a change of phase such as melting or boiling.
Lecture 37 - Thermal Physics II
- Internal energy E is the total energy of a system (not just kinetic)
- First Law of Thermodynamics: ∆E = Q + W , where ∆E is the change in internal energy, Q is heat and W is work.
- Concepts of work done during thermal expansion/compression
- Equations of state for ideal gases: PV= Nk_B T.
Lecture 38 - Thermal Physics III
- Statistical mechanics describes the macroscopic properties of matter in terms of the microscopic behavior of its constituent particles.
- The average kinetic energy of a particle.
Lecture 39 - Special Relativity I
- Historical context of special relativity
- Time dilation and length contraction as consequence special relativity.
- Coordinate transformations (Galilean and Lorentz).
Lecture 40 - Special Relativity II
- Lorentz transformations.
- Spacetime intervals (timelike, spacelike, lightlike).
- Relativistic velocity addition.
Lecture 41 - Waves and Particles
- Wave-particle duality describes the dual nature of light and matter
- Photoelectric effect.
- Planck's constant, h.
- Photon.
Lecture 42 - Quantum Mechanics
- Quantum mechanics describes the behavior of matter at the atomic and subatomic levels.
- The principle of quantization
- Quantum numbers (n, l, ml).
- Electron in a hydrogen atom as matter wave
- Uncertainty principle and the implications for quantum behavior.
Lecture 43 - Introduction to Atomic Physics
- Historical developments in atomic theory, including the work of Democritus, Lavoisier, and Dalton
- Avogadro's hypothesis and Avogadro's number.
- Size of atoms.
Lecture 44 - Introduction to Nuclear Physics
- The nucleus of an atom and the composition of the nucleus.
- Isotopes, atomic number & mass number
- Nuclear forces.
- Radioactive decay.
Lecture 45 - Physics of the Sun
- Basic properties of the sun
- Nuclear fusion as the energy source of the sun.
- Thermal equilibrium of the sun and the hydrostatic principle.
- The role of the greenhouse effect.
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Test your knowledge on the principles of electromagnetism and capacitors with this quiz. Explore topics such as electric fields between parallel plates, capacitance, and electromagnetic induction. Challenge yourself with questions on connections of capacitors and their fundamental relationships.