Electromagnetic Induction Examples: 44 Problems with Answers

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 \text{ m}^2

is in a magnetic field that changes from

0.8 \text{ T}

0.2 \text{ T}

0.3 \text{ s}

. What is the induced EMF?

Answer

E = 0.1 V

First step

Change in magnetic flux:

\Delta\Phi = \Delta B \times A = (0.2 - 0.8) \times 0.05 = -0.03 \text{ Wb}

Full solution

2
Induced EMF (Faraday's law, $N = 1$ ): $E = - \frac{Δ Φ}{Δ t} = - \frac{- 0.03}{0.3} = 0.1 V$
3
The magnitude of the induced EMF is $0.1 \text{ V}$ .

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

200

turns and area

0.02 \text{ m}^2

is rotated from perpendicular to parallel to a

0.5 \text{ T}

magnetic field in

0.1 \text{ s}

. What is the average induced EMF?

Example 3

medium

A loop of area

0.04\,\text{m}^2

sits perpendicular to a field that grows from

0.2\,\text{T}

1.0\,\text{T}

0.4\,\text{s}

. Find the EMF.

Example 4

medium

A coil with area

0.02\,\text{m}^2

and

100

turns is rotated from parallel to perpendicular to a

0.3\,\text{T}

field in

0.05\,\text{s}

. Find the average EMF.

Example 5

hard

50

-turn coil of area

0.01\,\text{m}^2

rotates at

\omega = 60\,\text{rad/s}

in a

0.2\,\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

100

turns, increasing the flux through each turn from

0

0.004 \text{ Wb}

0.2 \text{ s}

. What is the induced EMF? If the coil has resistance

5 \text{ } \Omega

, what current flows?

Example 2

hard

A rectangular loop (

0.1 \text{ m} \times 0.2 \text{ m}

) moves at

5 \text{ m/s}

into a region with a uniform

0.3 \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

6

Wb in

2

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

2

Wb to

8

Wb in

3

s. Find the average EMF.

Example 12

medium

Field

B=0.5

T through a

0.2

^2

loop drops to zero in

0.1

s (perpendicular). Find the average EMF.

Example 13

medium

50

-turn coil has flux per turn changing by

0.4

Wb in

0.2

s. Find the EMF.

Example 14

medium

A loop area shrinks from

0.5

^2

0.1

^2

0.4

s in a steady

2

T field (perpendicular). Find the EMF.

Example 15

medium

A coil's flux changes by

0.3

Wb and induces

6

V in a single loop. Find the time interval.

Example 16

medium

A rod of length

0.5

m moves at

4

m/s perpendicular to

B=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

0.2

m enters a

1.5

T field region at

3

m/s, with one edge crossing the boundary. Find the EMF while entering.

Example 19

challenge

A circular loop of area

0.1

^2

sits in a field that increases uniformly from

0

4

T in

0.5

s. The loop has

20

turns. Find the EMF.

Example 20

challenge

A rod of length

0.4

m slides at

5

m/s on rails in a

0.5

T field, with a

2\,\Omega

resistor closing the circuit. Find the induced current.

Example 21

medium

A single loop's flux changes from

1

Wb to

5

Wb in

2

s. Find the average EMF.

Example 22

medium

25

-turn coil has flux per turn changing by

0.2

Wb in

0.5

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\,\text{Wb}

0.25\,\text{s}

. Find the average induced EMF magnitude.

Example 25

easy

A coil has

N = 80

turns and flux per turn changes by

0.01\,\text{Wb}

0.04\,\text{s}

. Find the EMF.

Example 26

easy

A coil's flux changes uniformly from

0

0.6\,\text{Wb}

0.3\,\text{s}

. Find the EMF in a single loop.

Example 27

medium

30

-turn coil of area

0.05\,\text{m}^2

sits in a field that drops from

0.4\,\text{T}

0

0.1\,\text{s}

(perpendicular). Find the EMF.

Example 28

medium

A rod

L = 0.6\,\text{m}

slides at

v = 3\,\text{m/s}

perpendicular to

\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\,\Omega

. Find the induced current.

Example 30

medium

A circular loop of radius

0.1\,\text{m}

sits perpendicular to a field changing at

dB/dt = 0.8\,\text{T/s}

. Find the EMF.

Example 31

medium

A rod

0.3\,\text{m}

long slides on rails in a

1.2\,\text{T}

field at

2\,\text{m/s}

. Total circuit resistance is

0.6\,\Omega

. Find the induced current.

Example 32

medium

40

-turn coil has flux per turn going from

0.05\,\text{Wb}

0.20\,\text{Wb}

0.3\,\text{s}

. Find the EMF.

Example 33

medium

A square loop of side

0.25\,\text{m}

enters a

0.8\,\text{T}

field region at

4\,\text{m/s}

(one edge inside). Find the EMF while entering.

Example 34

medium

A flat loop of area

0.1\,\text{m}^2

sits at

60^\circ

to a

0.5\,\text{T}

field (angle between

\vec B

and normal is

60^\circ

). Find the flux through it.

Example 35

hard

A circular coil (

N = 200

, radius

5\,\text{cm}

) lies perpendicular to a field that varies as

B(t) = 0.04\,t^2\,\text{T}

(with

t

in seconds). Find the EMF at

t = 3\,\text{s}

Example 36

hard

A square loop of side

0.4\,\text{m}

, resistance

2\,\Omega

, enters a

0.6\,\text{T}

field at

5\,\text{m/s}

. Find the power dissipated while entering.

Example 37

hard

A rod of length

0.5\,\text{m}

slides at

6\,\text{m/s}

on rails in a

0.4\,\text{T}

field. Circuit resistance is

1.5\,\Omega

. Find the magnetic drag force on the rod.

Example 38

hard

A circular loop of radius

R = 0.2\,\text{m}

sits perpendicular to a uniform field

B(t) = (0.5 + 0.3t)\,\text{T}

. Find the induced EMF magnitude.

Example 39

challenge

1\,\text{m}

rod slides at

v = 8\,\text{m/s}

on horizontal rails in a vertical

B = 0.5\,\text{T}

field, closing a circuit of total resistance

4\,\Omega

. Find the external force needed to keep the rod at constant velocity (ignore friction).

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Related Concepts

Magnetic Field Magnetic Force Faraday's Law Lenz's Law Generator

Background Knowledge

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

magnetic fieldmagnetic force