Faraday's Law Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Faraday's Law.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept 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.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: EMF is proportional to the rate of flux change — more turns or faster change means more voltage.

Common stuck point: The negative sign means the induced EMF opposes the change (Lenz's law) — it's not just a math convention.

Sense of Study hint: When you see a Faraday's law problem, first calculate the magnetic flux \Phi_B = BA\cos\theta at the initial and final times. Then find the rate of change d\Phi_B/dt (or \Delta\Phi_B / \Delta t for constant rates). Finally, multiply by the number of turns N and apply the negative sign to find the induced EMF.

Worked Examples

Example 1

medium
A coil with 100 turns experiences a change in magnetic flux from 0.05 \text{ Wb} to 0.02 \text{ Wb} in 0.1 \text{ s}. What is the induced EMF?

Solution

  1. 1
    Faraday's law: \mathcal{E} = -N\frac{\Delta \Phi}{\Delta t}.
  2. 2
    Change in flux: \Delta \Phi = 0.02 - 0.05 = -0.03 \text{ Wb}.
  3. 3
    \mathcal{E} = -100 \times \frac{-0.03}{0.1} = -100 \times (-0.3) = 30 \text{ V}

Answer

\mathcal{E} = 30 \text{ V}
Faraday's law states that a changing magnetic flux through a coil induces an EMF. More turns and faster flux changes produce larger EMFs. This is the basis of electric generators.

Example 2

hard
A single loop of area 0.04 \text{ m}^2 is in a magnetic field that increases uniformly from 0 to 0.6 \text{ T} in 0.3 \text{ s}. What is the induced EMF?

Example 3

medium
A coil of 50 turns has a magnetic flux that changes from 0.02 \text{ Wb} to 0.08 \text{ Wb} in 0.1 \text{ s}. Find the induced EMF.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A coil of 50 turns has an area of 0.01 \text{ m}^2. The magnetic field through it decreases from 0.8 \text{ T} to 0.2 \text{ T} in 0.5 \text{ s}. What is the average induced EMF?

Example 2

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

These ideas may be useful before you work through the harder examples.

electromagnetic induction