General Physics 2: Magnetism and Electromagnetism PDF

GENERAL PHYSICS MAGNETISM and ELECTROMAGNETISM 2 1. Magnetism 2. Magnetic Forces 3. Magnetic Field and Flux 4. Ampére’s Law...

GENERAL PHYSICS MAGNETISM and ELECTROMAGNETISM 2 1. Magnetism 2. Magnetic Forces 3. Magnetic Field and Flux 4. Ampére’s Law 5. Biot-Savart Law 6. Electromagnetic Induction 7. Faraday’s Law 8. Lenz’s Law 9. Electric Fields and Different Circuits 10.Inductance and LC Liam Troy Dimitui Circuits John Gabriel Pineda Lance Vincent Soriano  Magnetism and 01 Magnetic Forces LANCE SORIANO 1.1Magnetism Recall that electric force arises in two stages: (1) A charge produces an electric field around it, and (2) A second charge responds to this field. Electric force is produced. Magnetic forces act similarly: (1) A moving charge or a collection of such (current) produces a magnetic field around it, and (2) A second moving charge or current responds to this field. Magnetic force is produced. 1.2Magnetic Field - Magnetic fields can be represented by magnetic field lines. - These lines are tangent to the magnetic field vector at that certain point. - Field lines never intersect. 1.2Magnetic Field - Magnetic field lines are continuous loops. - Outside of the magnet, these point out of the North pole and into the South pole. - Inside the magnet, these are straight towards the north pole again. - The denser the lines, the stronger the field. - The closer to the source, the stronger the field.  1.3Magnetic Poles - Magnets are the strongest at their poles. - Poles always exist in pairs; there is no such thing as a magnetic monopole. - If a magnet is broken, a new pole is generated, and two magnets are yielded, not two isolated poles. - Unlike poles attract, like poles repel. - The further away from the pole something is, the weaker of the magnetic field and force. 1.4Magnetization - Magnetic properties can wear out with the passage of time or through demagnetization. - Such techniques include hammering, heating, or being exposed to alternating currents. - This mixes up the arrangement of molecules to cancel the polarity of the entire material. - Demagnetized magnets can be magnetized again by exposing it to another magnet with a strong magnetic field. 1.4Magnetization - We can thus infer from magnetization that the magnetic forces between two objects are fundamentally due to interactions between moving electrons in the atoms of the objects. - Inside a magnetized object, the motion of electrons is coordinated, while in unmagnetized objects they are not coordinated. 1.5Magnetic Forces - The magnetic force is a consequence of the - The induction of a magnetic force is electromagnetic force, caused by the motion described as such: of charges. - Two objects containing charge with the same 1. A moving charge or current creates a direction of motion are attracted to each magnetic field in addition to its electric other. Conversely, charges moving in field 𝑬𝑬. opposite directions are repulsed by each 2. The magnetic field exerts a force 𝑭𝑭 on any other. other moving charge present. 1.5Magnetic Forces - There are four characteristics of a magnetic force on a moving charge: 𝐹𝐹 = 𝑞𝑞 𝑣𝑣𝑣𝑣 = 𝑞𝑞 𝑣𝑣𝑣𝑣 sin 𝛷𝛷 (1) Its magnitude is proportional to the magnitude of the charge; Where F is magnetic force in N; (2) Its magnitude is proportional to the and q is the magnitude of the charge in C; magnitude of the field; and 𝜱𝜱 is the angle measured from the direction (3) It depends on the particle’s velocity of velocity v in m/s to the direction of magnetic field B in T (4) The magnetic force 𝑭𝑭 is perpendicular to magnetic field 𝑩𝑩 and velocity 𝒗𝒗. 1.5Magnetic Forces - There are four characteristics of a magnetic force on a moving charge: 𝐹𝐹 = 𝑞𝑞 𝑣𝑣𝑣𝑣 = 𝑞𝑞 𝑣𝑣𝑣𝑣 sin 𝛷𝛷 (1) Its magnitude is proportional to the Where F is magnetic force in N; magnitude of the charge; and q is the magnitude of the charge in C; (2) Its magnitude is proportional to the and 𝜱𝜱 is the angle measured from the direction magnitude of the field; of velocity v in m/s to the direction of (3) It depends on the particle’s velocity magnetic field B in T (4) The magnetic force 𝑭𝑭 is perpendicular to * F is also called the Lorentz Force magnetic field 𝑩𝑩 and velocity 𝒗𝒗. 1.5Magnetic Forces - The right-hand rule can be used to determine the direction of the magnetic force; (a) the thumb is the direction of the force 𝐹𝐹𝑚𝑚 (b) the index finger is the direction of the current or moving charge 𝑣𝑣 (c) the middle finger is the direction of the magnetic field 𝐵𝐵 1.5Magnetic Forces - When placing a current-carrying conductor in a magnetic field, the conductor as a whole particle experiences a magnetic force. This is quantified by: 𝐹𝐹 = 𝐼𝐼𝐼𝐼𝐼𝐼 = 𝐼𝐼𝐼𝐼𝐼𝐼 sin 𝛷𝛷 Where F is magnetic force in N; and I is the magnitude of the current in A; and 𝜱𝜱 is the angle measured from the segment of wire l in m to the direction of magnetic field B in T 1.5Magnetic Forces - Another method, the palm method, can be used to determine the direction of the magnetic force: (a) the palm is the direction of the force 𝐹𝐹 (b) the thumb is the direction of the current 𝐼𝐼 (c) the 4 remaining fingers are the direction of the magnetic field 𝐵𝐵 CHECKPOINT Magnetism (a) A positive charged particle is moving to the left and the magnetic field it is in is towards the outside. What would be the direction of the magnetic force? (b) A positive charged particle is moving up and the magnetic field it is in is towards you. What would be the direction of the magnetic force? (c) Charge – Positive ; Force – North ; Magnetic Field – into the page ; Velocity – ? (d) Charge – Positive ; Force – North ; Magnetic Field – out the page ; Velocity – ? (e) Charge – Positive ; Magnetic Field – into the page; Velocity – South ; Force – ? CHECKPOINT Magnetism A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. In this region there is a horizontal magnetic field toward the northeast (that is, 45° north of east) with magnitude 1.20 T. (a) Find the magnitude and direction of the force on a 1.00 m section of rod. (b) While keeping the rod horizontal, how should it be oriented to maximize the magnitude of the force? What is the force magnitude in this case? CHECKPOINT Magnetism A 6.4 x 10^−11 C charged proton with a velocity of 9.7 x 10^4 m/s is moving through a space with a magnetic field strength of 1.2 T. From the magnetic field pointing to the east, how much force would the force feel? CHECKPOINT Magnetism An electron is moving at right angles to a magnetic field of strength B=1.0T at a speed of v=1.0ms^−1. What is the magnitude of the Lorentz force acting upon it? CHECKPOINT Magnetism A wire of length 30cm carrying a current of 1.0A lies perpendicular to a magnetic field of strength 30mT. What is the size of the Lorentz force on the wire?  02 Magnetic Field and Flux LIAM DIMITUI 2.1Magnetic Field - The right-hand grip rule can be used to determine the direction of the field and current, where: (a) the thumb denotes the direction of the current; (b) the 4 remaining fingers denote the direction of the magnetic field 2.1Magnetic Field - The movement of charge when placed in a magnetic field is circular in nature. - The motion of a charged particle under the action of a magnetic field alone is always constant in speed. 2.1Magnetic Field - The radius of a particle can be quantified by: 𝑚𝑚𝑚𝑚 𝑅𝑅 = 𝑞𝑞 𝐵𝐵 Where R is the radius in m; and m is the mass of the particle in kg; and v is the speed of the particle in m/s; and q is the charge of the particle in C; and B is the magnitude of the magnetic field in T. 2.1Magnetic Field - If the charged particle is negative, it moves clockwise around the orbit. - If the direction of the initial velocity is perpendicular to the magnetic field, it experiences a force at a right angle and will be steered into a circular path. - If the direction of the initial velocity is not perpendicular to the magnetic field, the velocity parallel to the field is constant and so it moves in a helix. 2.1Magnetic Field - The number of revolutions per unit time in a magnetic field can be quantified as: 𝑞𝑞 𝐵𝐵 𝑓𝑓 = 2𝜋𝜋𝜋𝜋 Where f is the frequency in Hz; and q is the charge in C; and B is the magnitude of the magnetic field in T; and m is the mass of the particle in kg 2.2Magnetic Flux - The magnetic flux through a surface 𝛷𝛷𝐵𝐵 is defined as the total number of magnetic field lines passing through a given coil or area. This can be quantified as: 𝛷𝛷𝐵𝐵 = 𝐵𝐵𝐵𝐵 = 𝐵𝐵𝐵𝐵 cos 𝜙𝜙 Where 𝛷𝛷𝐵𝐵 is the magnetic flux in Wb, and B is the magnetic field in T; and A is the area of the surface in m²; and 𝝓𝝓 is the angle between the direction of B and a line perpendicular to the surface 2.2Magnetic Flux - If the surface or the coil is perpendicular to the magnetic field lines, the flux is maximum and the angle 𝜃𝜃 can be either 0° or 180°. - If the surface of the coil is at a certain angle to the magnetic field lines, the flux is less than maximum but not zero. - If the surface of the coil is parallel to the magnetic field lines, the flux is zero and the angle 𝜃𝜃 is 90°. 2.2Magnetic Flux 2.3Biot-Savart’s Law - Determines the magnetic field at any given point due to a current. - Applied in most problems with asymmetrical elements. 𝜇𝜇0 𝐼𝐼𝐼𝐼𝑙𝑙 sin 𝜃𝜃 𝑑𝑑𝑑𝑑 = 4𝜋𝜋 𝑟𝑟 2 Where dB is the magnetic field due to a point charge; and 𝝁𝝁𝟎𝟎 is the magnetic constant 4𝜋𝜋 × 10−7 Tm/A; and I is the current in A; and dl is the length of the wire segment in m; and r is the distance from the wire segment to field; and 𝜽𝜽 is the angle between wire segment and an element of the charge. 2.3Biot-Savart’s Law - Determines the magnetic field at any given point due to a current. - Applied in most problems with asymmetrical elements. 𝜇𝜇0 𝐼𝐼𝐼𝐼𝑙𝑙 sin 𝜃𝜃 𝑑𝑑𝑑𝑑 = 4𝜋𝜋 𝑟𝑟 2 Where dB is the magnetic field due to a point charge; and 𝝁𝝁𝟎𝟎 is the magnetic constant 4𝜋𝜋 × 10−7 Tm/A; and I is the current in A; and dl is the length of the wire segment in m; and r is the distance from the wire segment to field; and 𝜽𝜽 is the angle between wire segment and an element of the charge. 2.3Biot-Savart’s Law - Determines the magnetic field at any given point due to a current. - Applied in most problems with asymmetrical elements. 𝜇𝜇0 𝐼𝐼𝐼𝐼𝑙𝑙 sin 𝜃𝜃 𝑑𝑑𝑑𝑑 = 4𝜋𝜋 𝑟𝑟 2 Where dB is the magnetic field due to a point charge; and 𝝁𝝁𝟎𝟎 is the magnetic constant 4𝜋𝜋 × 10−7 Tm/A; and I is the current in A; and dl is the length of the wire segment in m; and r is the distance from the wire segment to field; and 𝜽𝜽 is the angle between wire segment and an element of the charge. 2.3Biot-Savart’s Law - Suppose we have an infinitely long, straight wire 𝜇𝜇0 𝐼𝐼 𝑑𝑑𝑑𝑑 = 2𝜋𝜋𝑎𝑎 Where dB is the magnetic field due to a point charge; and 𝝁𝝁𝟎𝟎 is the magnetic constant 4𝜋𝜋 × 10−7 Tm/A; and I is the current in A; and a is the distance from the wire segment to field. 2.3Biot-Savart’s Law - Suppose we have a magnetic field at the center of a circular current loop 𝜇𝜇0 𝑁𝑁𝐼𝐼 𝑑𝑑𝑑𝑑 = 2𝑎𝑎 Where dB is the magnetic field due to a point charge; and N is the number of turns; and 𝝁𝝁𝟎𝟎 is the magnetic constant 4𝜋𝜋 × 10−7 Tm/A; and I is the current in A; and a is the distance from the wire segment to field. 2.4Ampere’s Law For any closed loop, the dot product of the magnetic field and the total distance (length elements) around the loop is equal to the product of the permeability constant and current enclosed by the loop. - High symmetry 𝐵𝐵 ⋅ 𝑑𝑑𝐼𝐼 = 𝜇𝜇0 𝐼𝐼 2.4Ampere’s Law Given the summation of all the current-carrying elements around a circle, we get its circumference; and so the magnetic field generated by any point on a current is the same and constant; 𝜇𝜇0 𝐼𝐼 𝑑𝑑𝑑𝑑 = 2𝜋𝜋𝑎𝑎 Where dB is the magnetic field due to a point charge; and 𝝁𝝁𝟎𝟎 is the magnetic constant 4𝜋𝜋 × 10−7 Tm/A; and I is the current in A; and a is the distance from the wire segment to field. 2.4Ampere’s Law - Suppose we have a magnetic field at the center of a very long solenoid; 𝜇𝜇0 𝑁𝑁𝑁𝑁 𝑑𝑑𝑑𝑑 = L Where dB is the magnetic field due to a point charge; and 𝝁𝝁𝟎𝟎 is the magnetic constant 4𝜋𝜋 × 10−7 Tm/A; and N is the number of turns in a coil; and I is the current in A; and L is the length of the wire in m. CHECKPOINT Magnetic Flux BIOT-SAVART AMPERE Calculates the magnetic field caused Used to find the magnetic field by a steady current element (very around a closed loop due to the small segment of wire) current passing through it Applied to any current distribution Solves problems with high symmetry; even without symmetry magnetic field is perfectly cylindrical or axial CHECKPOINT Magnetic Flux The dimensions of a rectangular loop is given as 0.051 m and 0.068 m. B and θ are 0.02T and 47° respectively. Calculate the magnetic flux through the given surface. CHECKPOINT Magnetic Flux A current of 20 A flows East through a 50 cm long wire. A magnetic field of 4.0 T is directed into the page. What is the magnitude and direction of the magnetic force acting on the wire? CHECKPOINT Magnetic Flux A short wire of length 1.0 cm carries a current of 2.0 A in the vertical direction. The rest of the wire is shielded so it does not add to the magnetic field produced by the wire. Calculate the magnetic field at point P, which is 1 meter from the wire in the x-direction. CHECKPOINT Magnetic Flux A long straight wire has a current of 800 A. At what distance a from the wire is the magnitude of the magnetic field equal to 2 T? CHECKPOINT Magnetic Flux A wire is shaped into a coil of 300 turns, each with a radius of 2.5 cm. If the current in the wire is 6 mA, find the magnitude of the magnetic field at the center of the coil. CHECKPOINT Magnetic Flux A wire is shaped into a coil of 1,600 turns, each with a radius of 30 cm. If the current in the wire is 3A, find the magnitude of the magnetic field at the center of the coil. CHECKPOINT Magnetic Flux A 1 m wire is shaped into a coil of 300 turns. If the current in the wire is 6 mA, find the magnitude of the magnetic field at the center of the coil.  Electromagnetic 03 Induction JOHN PINEDA  3.1Induced emf - Magnetic flux through a solenoid causes a current to be induced, which is in turn caused by an electromotive force (emf). We can observe this phenomenon through the following experiments: (i) A stationary magnet is put near or in a solenoid. No current is induced. (ii) A magnet moving either away or towards a solenoid will generate some amount of energy. (iii) A second solenoid that is charged with a current can induce emf in another solenoid; given that one of them is in motion.  3.1Induced emf - This is all due to the changing magnetic flux through the solenoid. - The induced emf is proportional to this rate of change of magnetic flux, and its direction depends on whether the flux increases or decreases. 3.1Induced emf  3.2Faraday’s Law d𝛷𝛷𝐵𝐵 𝜀𝜀 = −𝑁𝑁 d𝑡𝑡 - The induced emf varies proportionally to: Where 𝜺𝜺 is the induced emf in V; (a) the number of turns in the solenoid, and N is the number of turns in the solenoid; (b) the diameter or area oof the solenoid, and B is the magnetic field in T; (c) the change in the angle 𝜃𝜃 between the and A is the area of the solenoid in m²; magnetic field and the solenoid, and t is the time in s. (d) the change in magnetic field, (e) the change in time. The induced electromotive force in a closed loop is equal to the negative times rate of change of magnetic flux inside the loop. 3.2Lenz’s Law  3.2Lenz’s Law NORTH POLE NORTH POLE SOUTH POLE SOUTH POLE TO LOOP AWAY FROM TO LOOP AWAY FROM LOOP LOOP Magnetic Field, B Increase Decrease Increase Decrease Direction of B Same direction Opposite Same Opposite Induced Magnetic Oppose Field Current Flow Downwards Upwards Upwards Downwards  3.2Lenz’s Law - Derived from Faraday’s Law, Lenz posited that the direction of any magnetic induction - Lenz’s Law is also related to the principle of effect is such as to oppose the cause of the conservation of energy; if the induced effect. current goes along with the changing flux, - Wherein “cause” refers to the changing then the magnetic force on the object would flux. accelerate it to a speed near infinity without - Within the area bounded by a circuit, any external energy source; this is a the magnetic field of an induced current violation of energy conservation. is opposite to the original field if the - The induced magnetic field always tries to original is increasing but is in the same keep the flux in a solenoid constant. direction of the original field if the latter is decreasing. CHECKPOINT Electromagnetic Induction A circular coil with a radius of 0.15m consists of 10 loops and is placed in a uniform magnetic field of 0.8T. The plane of the coil is perpendicular to the magnetic field, meaning the field lines pass straight through it. The magnetic field then decreases uniformly from 0.8T to 0.3T in 3 seconds. What is the induced emf in the coil during this time?  Electric Fields 04 and a Recap on Circuits LIAM DIMITUI 4.1Electric Fields - Electrostatic fields are fields that start at positive charges and end at negative charges. - These are conservative in nature. - Induced electric fields go around in loops; they do not start at a charge. - These only require varying magnetic fields. - This can happen with or without free electrons. - These are nonconservative in nature. 4.2AC & DC Circuits AC DC Energy that can Safer to transfer Weaker power, be carried long distance, shorter distance more power Frequency 50-60Hz No frequency Direction Reverses One direction Current Varies with time Constant Electron flow Switch directions One direction Obtained from Generator Cell or battery  05 Inductance JOHN PINEDA 5.1Inductance - Inductance is described as the ratio of induced voltage opposed to the rate of change of current causing it. - Inductance is carried out by an inductor, which is a device in a circuit that opposes a change in current. (1) A current increases through a solenoid, increasing magnetic field. (2) This changing magnetic field induces an emf. (3) This emf then acts to oppose the change that induced it (Lenz). (4) This then slows down the increase of the current, through back emf. 5.1Inductance - Mutual inductance is inductance that requires another inductor to induce back emf. - Self inductance is inductance that (1) Consider two neighboring opposes a flowing solenoids of wire. A current current or generates flowing in coil 1 produces a a back emf by itself. magnetic field and hence a magnetic flux through coil 2. (2) Should the current in coil 1 change, the flux through coil 2 changes as well, inducing an emf in coil 2. 5.2Transformers - Transformers step up or step down voltage. - In step-down transformers, the output voltage is lower than the input voltage. - In step-up transformers, the output voltage is higher than the input voltage. 5.3LC Circuits - LC circuits are so called because they contain an inductor and a capacitor. - When a charged capacitor is connected to an inductor, the energy oscillates from electrical to magnetic, and back and forth. - This is why LC circuits are also called oscillatory circuits. 5.3LC Circuits Consider a capacitor charged to a potential The charges from the capacitor will be depleted difference connected to an inductor. These at some point. The induced emf in the inductor charges will migrate from the positive to the will reverse direction. The inductor then will negative plate. A current then starts to flow generate an induced current to slow down the across the inductor; as it increases, the inductor decrease of the current, reversing the polarity of generates an opposing current, slowing it down. the capacitor. 5.3LC Circuits 5.3LC Circuits: Initial Stages 5.3LC Circuits: Poles Reverse