Electromagnetic Induction Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Electromagnetic Induction.

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 process by which a changing magnetic flux through a conducting loop produces a voltage (electromotive force, EMF) across the conductor, which can drive a current around a closed circuit.

Push a magnet into a coil and current flows — the changing magnetic field 'induces' electricity. Pull it out and current flows the other way.

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: Electromagnetic Induction starts by naming the source, the object affected, and how the field or potential changes through space.

Common stuck point: Students often know a formula related to electromagnetic induction but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I using a field or potential to explain how one object influences another across space?

Worked Examples

Example 1

easy
A single loop of wire with area 0.05 m20.05 \text{ m}^2 is in a magnetic field that changes from 0.8 T0.8 \text{ T} to 0.2 T0.2 \text{ T} in 0.3 s0.3 \text{ s}. What is the induced EMF?

Answer

E=0.1 V\mathcal{E} = 0.1 \text{ V}

First step

1
Change in magnetic flux: ΔΦ=ΔB×A=(0.2−0.8)×0.05=−0.03 Wb\Delta\Phi = \Delta B \times A = (0.2 - 0.8) \times 0.05 = -0.03 \text{ Wb}.

Full solution

  1. 2
    Induced EMF (Faraday's law, N=1N = 1): E=−ΔΦΔt=−−0.030.3=0.1 V\mathcal{E} = -\frac{\Delta\Phi}{\Delta t} = -\frac{-0.03}{0.3} = 0.1 \text{ V}
  2. 3
    The magnitude of the induced EMF is 0.1 V0.1 \text{ V}.
Electromagnetic induction occurs whenever the magnetic flux through a conducting loop changes. The induced EMF is proportional to the rate of change of flux, as stated by Faraday's law.

Example 2

medium
A coil with 200200 turns and area 0.02 m20.02 \text{ m}^2 is rotated from perpendicular to parallel to a 0.5 T0.5 \text{ T} magnetic field in 0.1 s0.1 \text{ s}. What is the average induced EMF?

Example 3

medium
A loop of area 0.04 m20.04\,\text{m}^2 sits perpendicular to a field that grows from 0.2 T0.2\,\text{T} to 1.0 T1.0\,\text{T} in 0.4 s0.4\,\text{s}. Find the EMF.

Example 4

medium
A coil with area 0.02 m20.02\,\text{m}^2 and 100100 turns is rotated from parallel to perpendicular to a 0.3 T0.3\,\text{T} field in 0.05 s0.05\,\text{s}. Find the average EMF.

Example 5

hard
A 5050-turn coil of area 0.01 m20.01\,\text{m}^2 rotates at ω=60 rad/s\omega = 60\,\text{rad/s} in a 0.2 T0.2\,\text{T} field. Find the peak EMF.

Practice Problems

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

Example 1

medium
A bar magnet is pushed into a coil of 100100 turns, increasing the flux through each turn from 00 to 0.004 Wb0.004 \text{ Wb} in 0.2 s0.2 \text{ s}. What is the induced EMF? If the coil has resistance 5 Ω5 \text{ } \Omega, what current flows?

Example 2

hard
A rectangular loop (0.1 m×0.2 m0.1 \text{ m} \times 0.2 \text{ m}) moves at 5 m/s5 \text{ m/s} into a region with a uniform 0.3 T0.3 \text{ T} magnetic field. What EMF is induced as the loop enters the field?

Example 3

easy
What must change through a coil to induce a current?

Example 4

easy
Write the formula for magnetic flux through a flat loop.

Example 5

easy
Pushing a magnet into a coil induces a current. Pulling it out does what?

Example 6

easy
A coil with constant flux through it. What is the induced EMF?

Example 7

easy
Name one way to change the flux through a fixed loop.

Example 8

easy
Induction converts what kind of energy into electrical energy in a generator?

Example 9

easy
A single loop has flux changing by 66 Wb in 22 s. Find the average EMF magnitude.

Example 10

easy
Does a stationary coil in a strong, steady magnetic field carry an induced current?

Example 11

medium
A loop's flux goes from 22 Wb to 88 Wb in 33 s. Find the average EMF.

Example 12

medium
Field B=0.5B=0.5 T through a 0.20.2 m2^2 loop drops to zero in 0.10.1 s (perpendicular). Find the average EMF.

Example 13

medium
A 5050-turn coil has flux per turn changing by 0.40.4 Wb in 0.20.2 s. Find the EMF.

Example 14

medium
A loop area shrinks from 0.50.5 m2^2 to 0.10.1 m2^2 in 0.40.4 s in a steady 22 T field (perpendicular). Find the EMF.

Example 15

medium
A coil's flux changes by 0.30.3 Wb and induces 66 V in a single loop. Find the time interval.

Example 16

medium
A rod of length 0.50.5 m moves at 44 m/s perpendicular to B=2B=2 T. Find the motional EMF.

Example 17

medium
Why does a coil in a constant field produce no current even if the field is enormous?

Example 18

challenge
A square loop of side 0.20.2 m enters a 1.51.5 T field region at 33 m/s, with one edge crossing the boundary. Find the EMF while entering.

Example 19

challenge
A circular loop of area 0.10.1 m2^2 sits in a field that increases uniformly from 00 to 44 T in 0.50.5 s. The loop has 2020 turns. Find the EMF.

Example 20

challenge
A rod of length 0.40.4 m slides at 55 m/s on rails in a 0.50.5 T field, with a 2 Ω2\,\Omega resistor closing the circuit. Find the induced current.

Example 21

medium
A single loop's flux changes from 11 Wb to 55 Wb in 22 s. Find the average EMF.

Example 22

medium
A 2525-turn coil has flux per turn changing by 0.20.2 Wb in 0.50.5 s. Find the EMF.

Example 23

easy
State Faraday's law in words for a single loop.

Example 24

easy
A loop has flux changing by 0.5 Wb0.5\,\text{Wb} in 0.25 s0.25\,\text{s}. Find the average induced EMF magnitude.

Example 25

easy
A coil has N=80N = 80 turns and flux per turn changes by 0.01 Wb0.01\,\text{Wb} in 0.04 s0.04\,\text{s}. Find the EMF.

Example 26

easy
A coil's flux changes uniformly from 00 to 0.6 Wb0.6\,\text{Wb} in 0.3 s0.3\,\text{s}. Find the EMF in a single loop.

Example 27

medium
A 3030-turn coil of area 0.05 m20.05\,\text{m}^2 sits in a field that drops from 0.4 T0.4\,\text{T} to 00 in 0.1 s0.1\,\text{s} (perpendicular). Find the EMF.

Example 28

medium
A rod L=0.6 mL = 0.6\,\text{m} slides at v=3 m/sv = 3\,\text{m/s} perpendicular to B⃗=0.5 T\vec B = 0.5\,\text{T}. Find the motional EMF.

Example 29

medium
In the previous problem, the rod is part of a circuit with total resistance R=3 ΩR = 3\,\Omega. Find the induced current.

Example 30

medium
A circular loop of radius 0.1 m0.1\,\text{m} sits perpendicular to a field changing at dB/dt=0.8 T/sdB/dt = 0.8\,\text{T/s}. Find the EMF.

Example 31

medium
A rod 0.3 m0.3\,\text{m} long slides on rails in a 1.2 T1.2\,\text{T} field at 2 m/s2\,\text{m/s}. Total circuit resistance is 0.6 Ω0.6\,\Omega. Find the induced current.

Example 32

medium
A 4040-turn coil has flux per turn going from 0.05 Wb0.05\,\text{Wb} to 0.20 Wb0.20\,\text{Wb} in 0.3 s0.3\,\text{s}. Find the EMF.

Example 33

medium
A square loop of side 0.25 m0.25\,\text{m} enters a 0.8 T0.8\,\text{T} field region at 4 m/s4\,\text{m/s} (one edge inside). Find the EMF while entering.

Example 34

medium
A flat loop of area 0.1 m20.1\,\text{m}^2 sits at 60∘60^\circ to a 0.5 T0.5\,\text{T} field (angle between B⃗\vec B and normal is 60∘60^\circ). Find the flux through it.

Example 35

hard
A circular coil (N=200N = 200, radius 5 cm5\,\text{cm}) lies perpendicular to a field that varies as B(t)=0.04 t2 TB(t) = 0.04\,t^2\,\text{T} (with tt in seconds). Find the EMF at t=3 st = 3\,\text{s}.

Example 36

hard
A square loop of side 0.4 m0.4\,\text{m}, resistance 2 Ω2\,\Omega, enters a 0.6 T0.6\,\text{T} field at 5 m/s5\,\text{m/s}. Find the power dissipated while entering.

Example 37

hard
A rod of length 0.5 m0.5\,\text{m} slides at 6 m/s6\,\text{m/s} on rails in a 0.4 T0.4\,\text{T} field. Circuit resistance is 1.5 Ω1.5\,\Omega. Find the magnetic drag force on the rod.

Example 38

hard
A circular loop of radius R=0.2 mR = 0.2\,\text{m} sits perpendicular to a uniform field B(t)=(0.5+0.3t) TB(t) = (0.5 + 0.3t)\,\text{T}. Find the induced EMF magnitude.

Example 39

challenge
A 1 m1\,\text{m} rod slides at v=8 m/sv = 8\,\text{m/s} on horizontal rails in a vertical B=0.5 TB = 0.5\,\text{T} field, closing a circuit of total resistance 4 Ω4\,\Omega. Find the external force needed to keep the rod at constant velocity (ignore friction).
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Background Knowledge

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

magnetic fieldmagnetic force