EJC Physics H217 Electromagnetic Induction - 1. Notes (2024) FULL

9749(2024) H2 Physics H217 Electromagnetic Induction – Notes Page 1 of 20 H2 Topic 17 – Electromagnetic Induction In traditional vehicles, friction is applied at the wheels to slow down the vehicle. Essentially, all of the kinetic energy of a vehicle is converted into heat each time the vehicle comes to a stop. With regenerative braking, about 60% to 70% of kinetic energy can be turned back into useful work in accelerating the vehicle subsequently. Content • Magnetic flux • Laws of electromagnetic induction Learning Objectives: Candidates should be able to: (a) define magnetic flux as the product of an area and the component of the magnetic flux density perpendicular to that area (b) recall and solve problems using Φ = BA (c) define magnetic flux linkage (d) infer from appropriate experiments on electromagnetic induction: i. that a changing magnetic flux can induce an e.m.f. ii. that the direction of the induced e.m.f. opposes the change producing it iii. the factors affecting the magnitude of the induced e.m.f. (e) recall and solve problems using Faraday’s law of electromagnetic induction and Lenz’s law (f) explain simple applications of electromagnetic induction Brake force is distributed by the on -board system between friction and regenerative braking. Some kinetic energy is transferred via the motor shaft; motor acts as a generator electronically. Kinetic energy is converted into electrical energy in the motor. Electrical energy is stored in the battery pack.

9749(2024) H2 Physics H217 Electromagnetic Induction – Notes Page 2 of 20 17.0 Introduction Earlier in electromagnetism, we learnt that (i) an electric current can produc e a magnetic field and (ii) a magnetic field can exert a force on moving charges or current -carrying conductors. As nature is often symmetric, it was later found that magnetic fields can in turn generate electric current. 17.1 E.m.f. from Motion In electromagnetism, we observe electrical energy converted into kinetic energy using an electric motor. In electromagnetism induction, we can observe, explain, and calculate the electrical energy that is converted from mechanical motion. 17.1.1 Electromagnetic Induction of straight conductor To explain why relative motion of a conductor and a magnetic field induces an e.mf., consider a thin straight conductor of length L moving at a constant speed v in a region of uniform magnetic flux density B directed normally into the plane of paper as shown. By Fleming’s left- hand rule, electrons initially experience a downward magnetic force. Negative charges accumulate at the lower end, which results in a corresponding region of positive charge at the upper end. - Inside the conductor, a potential difference is induced and results in an electric field down the length of the conductor. - Outside the conductor, it can be regarded as an induced e.m.f. that can drive current around an external circuit. Steady state is attained when the magnetic force and electric force are balanced. There will be no further charge separation and the induced e.m.f. ( inducedε ) will remain constant: BEFF Bq = sinv θ q= induced induced L BLv E VBv d ε ε = ∆= = Note: The equation is true in general for a straight conductor of length L “cutting” magnetic flux lines but it is not one that we should recall and use. For most questions, we will need to start from basic principles and show how an equation is formed, before applying it. From the equation, magnitude of inducedε depends on the magnitude of the external magnetic flux density, the length of conductor that is inside the magnetic field, and the speed at which the wire is moving across the field. In each of the above, an induced e.m.f. or induced current can be observed via the voltmeter or microammeter. B v FB FE + + + +

9749(2024) H2 Physics H217 Electromagnetic Induction – Notes Page 3 of 20 B θ A N turns axis of solenoid 17.2 Magnetic Flux where Φ represents magnetic flux, B represents magnetic flux density, A represents area, θ represents the angle between B and the normal of the area We can visualise magnetic flux Φ as magnetic field lines piercing an identified area at 90°: The unit for magnetic flux Φ is the Weber (Wb). One Weber is the magnetic flux through an area of one squared metre when the magnetic flux density normal to the area is one tesla. 17.3 Magnetic Flux Linkage Consider a solenoid of N number of turns. We can visualise magnetic flux linkage ( NΦ) as N layers of magnetic flux stacked on each other. The area for magnetic flux need not be a filled area e.g. flat circular sheet of metal; it can be an area of free space that is outlined by a wire loop. magnetic flux is the product of an area and component of magnetic flux density perpendicular to that area Magnetic flux linkage through a loop is product of magnetic flux through the loop and number of turns of wire in the loop. Magnetic flux is the product of an area and component of magnetic flux density perpendicular to that area. B A θ Φθ ⊥= = cosA BAB ( )Φθ ⊥ == cosN A NBANB

9749(2024) H2 Physics H217 Electromagnetic Induction – Notes Page 4 of 20 Example 1 A 100-turn square coil of sides 5.0 cm is placed in a uniform magnetic field of flux density 0.20 T. Find the magnetic flux linkage through the coil when its plane is Example 2 (a) normal to the field, (b) 60° to the field, (c) parallel to the field. 60° 30° 1 2 3 Bout Three loops of wire shown below are placed in a region of uniform magnetic field. Loop 1 swings left and right like a pendulum. Loop 2 rotates about a vertical axis. Loop 3 oscillates vertically on the end of a spring. State which loops experiences a changing magnetic flux. Solution: Loop 2 experiences a changing magnetic flux; orientation relative to magnetic field changes with time as it rotates.

9749(2024) H2 Physics H217 Electromagnetic Induction – Notes Page 5 of 20 17.4 Laws of Electromagnetic Induction Faraday’s Law allows us to find the magnitude of the induced e.m.f. in a conductor. Lenz’s Law gives the direction of the induced e.m.f. (or direction of induced current if there is a closed circuit). Constant of proportionality is 1, hence A negative sign is introduced as a result of Lenz’s Law. As a result of both laws, 17.4 .1 Laws of Electromagnetic Induction Calculations and Graphs Consider a wire of length L moving with velocity v normal to a uniform magnetic field of flux density B. Determine the induced e.m.f.: { } { } ( ) { } ( ) ( ){ } ΦΦ= = = = = induced 1 where A is the area "swept" by th e wire d widt dd dd d d hd N BA BL t BLv EN tt t Note: This is the same equation, as it should be, when we considered the “microscopic” picture of an electron inside the wire being subject to a magnetic force and an electric force. The following scenarios provide a non- exhaustive list of how B, A, and θ can be changed across time to induce an e.m.f. in a conductor: B v L Faraday’s Law states that the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage Lenz’s Law states that the direction of induced e.m.f. produces effects to oppose the change causing it ( ) ( ) θ Φ= − = − induced d d d cosd NE t NBAt ( )Φ∝induced d d NE t ( ) θ=induced d cosdE NBA t

9749(2024) H2 Physics H217 Electromagnetic Induction – Notes Page 6 of 20 taking t sec to move a circular coil totally out of a region of uniform magnetic field taking t sec to straighten a coiled wire in a region of uniform magnetic field rotating a wire coil with angular velocity ω between poles of magnet(s) initial0d d BB