AP Physics – Electromagnetic Induction (Faraday’s Law, Lenz’s Law)

AP Physics – Electromagnetic Induction (Faraday’s Law, Lenz’s Law)

AP Physics: Electromagnetic Induction (Faraday’s Law & Lenz’s Law) – Exam-Ready Study Guide

What This Is

Electromagnetic induction is the process of generating an electric current (or voltage) in a conductor by changing the magnetic field around it. This is the foundation of how power plants, electric generators, and transformers work—essentially, how we get most of the electricity we use every day! On the AP exam, you’ll need to predict the direction of induced currents (Lenz’s Law) and calculate induced voltages (Faraday’s Law). Real-world example: When you pedal a bike with a dynamo light, the spinning wheel moves a magnet near a coil, inducing a current that powers the light—no batteries needed!

Key Terms & Concepts

• Magnetic Flux (?_B): The "amount" of magnetic field passing through a loop of wire. Formula: ?_B = B·A·cos?, where:
• B = magnetic field strength (T, tesla)
• A = area of the loop (m²)

• ? = angle between B and the normal (perpendicular) to the loop.

• Faraday’s Law of Induction: A changing magnetic flux induces an electromotive force (emf, ?) in a loop. Formula:-= –N(_B/?t), where:

• N = number of loops

• _B/?t = rate of change of magnetic flux (Wb/s or T·m²/s).

• Lenz’s Law: The induced current flows in a direction that opposes the change in magnetic flux that created it. (Think: "Nature hates change!")

• Induced emf (?): The voltage generated by a changing magnetic flux. Units: volts (V).

• Motional emf: A special case of Faraday’s Law where a conductor moves through a magnetic field, inducing an emf. Formula:-= B·L·v, where:

• L = length of the conductor (m)

• v = velocity of the conductor (m/s).

• Eddy Currents: Loops of induced current in bulk conductors (e.g., metal sheets) that create magnetic fields opposing motion (used in magnetic braking).

• Self-Inductance (L): A coil’s ability to oppose changes in current through it. Formula:-= –L(?I/?t), where L = inductance (H, henry).

• Transformer: A device that uses induction to step up or step down AC voltages. Formula: V_s/V_p = N_s/N_p, where:

• V_s, V_p = secondary/primary voltage

• N_s, N_p = number of turns in secondary/primary coils.

• Right-Hand Rule for Induced Current (Lenz’s Law):

• Point thumb in the direction of the external magnetic field (B).
• If flux is increasing, the induced field opposes B (thumb points opposite).
• Curl fingers to find the direction of the induced current.

Step-by-Step: Solving Induction Problems

1. Identify the change in flux:
2. Is the magnetic field (B) changing?
3. Is the area (A) of the loop changing?

4. Is the angle (?) between B and the loop changing?

5. Calculate the flux (?_B = B·A·cos?):

6. If B or A is changing, find the initial and final flux.

7. Apply Faraday’s Law (? = –N_B/?t):

8. Plug in the change in flux (_B) and time interval (?t).

9. The negative sign indicates direction (Lenz’s Law).

10. Determine the direction of the induced current (Lenz’s Law):

11. Ask: "Is the flux increasing or decreasing?"

12. The induced current creates a magnetic field that opposes this change.

13. For motional emf (? = B·L·v):

14. Use when a conductor moves through a constant magnetic field.

15. The direction of the induced current is given by the right-hand rule (thumb = velocity, fingers = B, palm = force on positive charges).

16. Check units and signs:

17. Flux (?_B) is in webers (Wb) = T·m².
18. emf (?) is in volts (V).

Common Mistakes

• Mistake: Forgetting the negative sign in Faraday’s Law. Correction: The negative sign is Lenz’s Law—it tells you the direction of the induced emf opposes the change in flux.

• Mistake: Mixing up the direction of the induced magnetic field. Correction: If flux is increasing, the induced field points opposite the external field. If flux is decreasing, it points in the same direction.

• Mistake: Using B·A without cos? for flux. Correction: Flux depends on the angle between B and the normal to the loop. If the loop is parallel to B, flux = 0!

• Mistake: Assuming a stationary magnet near a loop induces a current. Correction: No change in flux = no induced emf. The magnet must be moving or the loop must be changing size/orientation.

• Mistake: Confusing motional emf with Faraday’s Law. Correction: Motional emf (? = B·L·v) is a special case of Faraday’s Law for moving conductors in a constant B field.

AP Exam Insights

• FRQ Hot Topics:
• Calculating induced emf in a loop with changing B, A, or ?.
• Determining the direction of induced current (Lenz’s Law) in a loop near a moving magnet.

• Motional emf problems (e.g., a rod sliding on rails in a magnetic field).

• Multiple-Choice Traps:

• Tricky distinction: "A magnet is held near a loop—is there an induced current?" Answer: No, unless the magnet is moving or the loop is changing.
• Sign errors: The negative sign in Faraday’s Law is often tested—remember it’s Lenz’s Law in disguise!

• Units: Flux is in webers (Wb), not tesla (T). 1 Wb = 1 T·m².

• Lab-Based Questions:

• You might be asked to design an experiment to measure induced emf (e.g., moving a magnet through a coil and measuring voltage with a voltmeter).

Quick Check Questions

1. A loop of wire is placed in a uniform magnetic field pointing into the page. If the area of the loop decreases, what is the direction of the induced current?
2. (A) Clockwise
3. (B) Counterclockwise
4. (C) No current

5. (D) Depends on the speed of the change Answer: (A) Clockwise. The flux into the page is decreasing, so the induced current creates a field into the page to oppose this (right-hand rule: curl fingers clockwise).

6. A 0.5 m long conductor moves at 4 m/s perpendicular to a 0.2 T magnetic field. What is the induced emf?

7. (A) 0.4 V
8. (B) 0.8 V
9. (C) 1.0 V

10. (D) 1.6 V Answer: (A) 0.4 V.-= B·L·v = (0.2 T)(0.5 m)(4 m/s) = 0.4 V.

11. A coil with 50 turns has a magnetic flux that changes from 0.02 Wb to 0.05 Wb in 0.1 s. What is the magnitude of the induced emf? Answer: 15 V.-= N(_B/?t) = 50 × (0.05 – 0.02)/0.1 = 15 V.

Last-Minute Cram Sheet

1. Faraday’s Law:-= –N(_B/?t) Negative sign = Lenz’s Law!
2. Magnetic Flux: ?_B = B·A·cos? (Wb = T·m²).
3. Lenz’s Law: Induced current opposes the change in flux.
4. Motional emf:-= B·L·v (for a rod moving in B).
5. Right-Hand Rule: Thumb = B, fingers = current direction (for induced fields).
6. Transformer Equation: V_s/V_p = N_s/N_p.
7. Self-Inductance:-= –L(?I/?t) (opposes current changes).
8. Eddy Currents: Oppose motion (used in magnetic braking).
9. No change in flux = no induced emf! Stationary magnet near a loop = 0 V.
10. Units: 1 Wb = 1 T·m², 1 H (henry) = 1 V·s/A.