Practice Faraday's Law in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The induced EMF in a circuit equals the negative rate of change of magnetic flux through the circuit.

The faster you change the magnetic field through a loop, the bigger the voltage you get. Faraday's law tells you exactly how much.

Showing a random 20 of 50 problems.

Example 1

easy
What law gives the direction of the induced current opposing the change in flux?

Example 2

challenge
A circular conducting loop of radius 0.05 m0.05 \text{ m} and resistance 0.02Ω0.02 \Omega lies perpendicular to a magnetic field that decreases at dB/dt=−3 T/sdB/dt = -3 \text{ T/s}. Find the induced current and the power dissipated.

Example 3

hard
A 2525-turn circular coil of radius 0.10 m0.10 \text{ m} lies in a field that changes uniformly from 0.30 T0.30 \text{ T} to 0.90 T0.90 \text{ T} in 0.5 s0.5 \text{ s}. Find the magnitude of the induced EMF.

Example 4

medium
A loop's flux is Φ(t)=3t\Phi(t) = 3t (in Wb, tt in s). Find the EMF in a single loop.

Example 5

easy
A 2020-turn coil, flux changes by 0.50.5 Wb in 11 s. Find the EMF.

Example 6

easy
A 55-turn coil's flux per turn changes at 1.2 Wb/s1.2 \text{ Wb/s}. Find the magnitude of the induced EMF.

Example 7

medium
A 1.0 m21.0 \text{ m}^2 single-loop coil sits in a vertical field. The field changes from +0.20 T+0.20 \text{ T} (upward) to −0.20 T-0.20 \text{ T} (downward) uniformly in 0.5 s0.5 \text{ s}. Find ∣E∣|\mathcal{E}|.

Example 8

easy
Faster flux change gives a bigger or smaller EMF?

Example 9

medium
A coil produces 1212 V with flux changing at 0.60.6 Wb/s. Find the number of turns.

Example 10

easy
If the magnetic flux through a coil does not change, what is the induced EMF?

Example 11

hard
A square coil with 200 turns and side length 0.1 m0.1 \text{ m} is in a magnetic field that decreases uniformly from 0.5 T0.5 \text{ T} to 0 T0 \text{ T} in 0.2 s0.2 \text{ s}. Calculate the induced EMF. In which direction does the induced current flow (clockwise or anticlockwise, if the field points into the page)?

Example 12

medium
A 100100-turn coil of area 0.020.02 m2^2 sits in a field rising at 33 T/s (perpendicular). Find the EMF.

Example 13

easy
What quantity does NΦN\Phi represent?

Example 14

easy
A 55-turn coil has flux changing at 44 Wb/s. Find the EMF.

Example 15

challenge
A square loop of side 0.30.3 m and 1010 turns rotates at ω=20\omega = 20 rad/s in a 0.40.4 T field. Find the peak EMF.

Example 16

medium
A bar of length L=0.3 mL = 0.3 \text{ m} slides at v=4 m/sv = 4 \text{ m/s} perpendicular to a 0.5 T0.5 \text{ T} field through rails completing the circuit. Find the motional EMF.

Example 17

easy
What is the unit of magnetic flux ΦB\Phi_B?

Example 18

medium
A coil with N=80N = 80 has flux Φ=(0.005 Wb/s2) t2\Phi = (0.005 \text{ Wb/s}^2)\, t^2 per turn. Find the induced EMF magnitude at t=2 st = 2 \text{ s}.

Example 19

medium
A coil of 5050 turns has an area of 0.01 m20.01 \text{ m}^2. The magnetic field through it decreases from 0.8 T0.8 \text{ T} to 0.2 T0.2 \text{ T} in 0.5 s0.5 \text{ s}. What is the average induced EMF?

Example 20

challenge
A coil rotates so its flux is Φ(t)=0.5cos⁡(10t)\Phi(t) = 0.5\cos(10t) Wb per turn, with N=20N=20 turns. Find the peak EMF.
← Back to Faraday's Law Worked Examples Formula Explained