Practice a College Board-style free response question on Magnetism & Electromagnetism. Write your response, then reveal the model answer to see exactly what earns each point.
Free Response Question · Unit 4 · Electromagnetic Induction
A circular loop of wire with area 0.05 m² lies flat on a table, with a uniform magnetic field pointing straight up through the loop (perpendicular to the loop's plane). The magnetic field strength changes over time as shown below.
Time (s)
Magnetic field strength (T)
0
0.40
2.0
1.20
The field increases uniformly (at a constant rate) from t = 0 to t = 2.0 s, then remains constant after that.
A
Calculate the magnitude of the EMF induced in the loop between t = 0 and t = 2.0 s.
✓ Model answer (earns the point)
First find the change in flux. Since the field is perpendicular to the loop (θ = 0°, cosθ = 1), Φ = B·A. Initial flux: Φᵢ = (0.40 T)(0.05 m²) = 0.02 Wb. Final flux: Φf = (1.20 T)(0.05 m²) = 0.06 Wb. ΔΦ = 0.06 − 0.02 = 0.04 Wb.
Using Faraday's law: |EMF| = ΔΦ/Δt = 0.04 Wb / 2.0 s = 0.02 V.
Why it scores: Correctly calculates flux at both times using Φ = BA (recognizing θ = 0° since the field is perpendicular to the loop), correctly finds ΔΦ, AND correctly applies Faraday's law to find the EMF magnitude.
B
What is the induced EMF in the loop after t = 2.0 s (once the field becomes constant)? Justify your answer.
✓ Model answer (earns the point)
After t = 2.0 s, the EMF is zero. Since the magnetic field is now constant, the magnetic flux through the loop (Φ = BA) is also constant, so ΔΦ/Δt = 0. By Faraday's law, a constant flux induces no EMF, regardless of how strong the field is.
Why it scores: States the correct value (zero) AND justifies it by connecting the constant field to zero rate of flux change, rather than just asserting the answer without the underlying Faraday's law reasoning.
C
The magnetic field is directed upward (out of the table) through the loop, and it is increasing in magnitude between t = 0 and t = 2.0 s. Using Lenz's law, determine the direction of the induced current in the loop (clockwise or counterclockwise, as viewed from above) and explain your reasoning.
✓ Model answer (earns the point)
The induced current flows clockwise as viewed from above. Since the upward flux through the loop is increasing, Lenz's law requires the induced current to create a magnetic field that opposes this increase — meaning the induced field inside the loop must point downward (into the table). Using the right-hand rule in reverse (curl fingers in the current direction, thumb points in the field direction the current creates), a current that creates a downward-pointing field inside the loop must flow clockwise when viewed from above.
Why it scores: Correctly identifies that the induced field must oppose the increasing upward flux (so the induced field points downward), AND correctly applies the right-hand rule to translate that required field direction into the correct current direction (clockwise), rather than just stating a direction without the reasoning chain.
How to score points on AP Physics 2 FRQs
Always state the equation before substituting numbers. Φ = BA cosθ and EMF = ΔΦ/Δt should appear explicitly, not just the final numeric answer.
Separate magnitude (Faraday's law) from direction (Lenz's law) into distinct reasoning steps. Trying to get both from one calculation often leads to errors or incomplete explanations.
For Lenz's law direction questions, explicitly state what direction the induced field must point before converting that to a current direction. This two-step reasoning (oppose the change → find the field → find the current) is what graders look for.
Recognize when flux is constant. A loop with no change in field, area, or angle has zero EMF — a very common "trick" part of FRQs.
Watch your angle assumption. Only use Φ = BA (with cosθ = 1) when the field is explicitly perpendicular to the loop; otherwise include the cosθ factor.