Magnetic Field Examples: 45 Problems with Answers

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

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

Concept Recap

A vector field around magnets and moving charges that exerts force on other moving charges and magnetic materials.

Moving charges create a swirling force field around them. This field can push on other moving charges or magnets.

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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: Magnetic Field 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 magnetic field 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

medium

A proton (

q = 1.6 \times 10^{-19} \text{ C}

) moves at

3 \times 10^6 \text{ m/s}

perpendicular to a magnetic field of

0.5 \text{ T}

. What force does it experience?

Proton moving perpendicular to B field; find the magnetic force.

Answer

F = 2.4 \times 10^{- 13} N

First step

Force on a moving charge in a magnetic field:

F = qvB\sin\theta

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Example 2

hard

A wire carrying

5 \text{ A}

of current is

0.3 \text{ m}

long and placed perpendicular to a

0.2 \text{ T}

magnetic field. What force acts on the wire?

Wire perpendicular to 0.2 T field; find the force on the wire.

Example 3

medium

A field of

B = 0.4\text{ T}

passes perpendicular to a

0.5\text{ m}\times 0.3\text{ m}

rectangular loop. Find the magnetic flux through the loop.

Example 4

hard

A square loop (

L = 0.1\text{ m}

) carrying

I = 2\text{ A}

sits in a uniform field

B = 0.3\text{ T}

with its plane parallel to

B

. Find the torque magnitude on the loop.

Practice Problems

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

Example 1

medium

An electron moves at

2 \times 10^7 \text{ m/s}

30°

to a

0.1 \text{ T}

magnetic field. What is the magnetic force on the electron? (

|q_e| = 1.6 \times 10^{-19} \text{ C}

)

Electron at 30° to B = 0.1 T; find the magnetic force.

Example 2

hard

A proton (

q = 1.6 \times 10^{-19} \text{ C}

m = 1.67 \times 10^{-27} \text{ kg}

) enters a uniform magnetic field of

0.2 \text{ T}

90°

with a speed of

5 \times 10^6 \text{ m/s}

. Calculate: (a) the magnetic force, (b) the radius of its circular path.

Proton enters B = 0.2 T at 90°; find force and radius of circular path.

Example 3

easy

What are the units of magnetic field strength?

Example 4

easy

Do magnetic field lines start and stop, or form closed loops?

Example 5

easy

Name one source of a magnetic field besides a permanent magnet.

Example 6

easy

In a

0.5

T field, a wire carries

2

A over length

1

m perpendicular to the field. Find the force. (

\sin90°=1

Wire perpendicular to B = 0.5 T; find the force.

Example 7

easy

Is magnetic field a vector or a scalar?

Example 8

easy

The force on a charge is perpendicular to both its velocity and the field. Which rule gives the direction?

Example 9

easy

A wire carries

3

A over

2

m in a

0.2

T field, perpendicular. Find the force.

Wire perpendicular to B = 0.2 T; find the force.

Example 10

easy

A constant magnetic field passes through a stationary coil. Is any current induced?

Example 11

medium

4

m wire in a

0.5

T field carries current and feels

6

N (perpendicular). Find the current.

Example 12

medium

A wire of length

0.5

m carries

4

A at

30°

to a

2

T field. Find the force. (

\sin30°=0.5

Wire at 30° to B = 2 T carrying 4 A; find F

Example 13

medium

A flux of

\Phi = BA

has

B=0.4

T through area

A=0.5

^2

perpendicular. Find the flux.

Example 14

medium

Field

B=0.6

T through area

A=2

^2

\theta=60°

from the normal. Find the flux. (

\cos60°=0.5

Example 15

medium

Two parallel wires each carry current and create fields. The field at a point from one wire is

0.3

T east, from the other

0.4

T north. Find the net field magnitude.

Example 16

medium

A wire feels maximum force

8

N when perpendicular to a field. What force does it feel at

30°

? (

\sin30°=0.5

Example 17

medium

A charge

q=2

C moves at

v=3

m/s perpendicular to

B=0.5

T. Find the force.

Charge q = 2 C moving perpendicular to B = 0.5 T; find the magnetic force.

Example 18

challenge

A charge

q=1

C, mass

m=2

kg, moves at

v=4

m/s perpendicular to

B=0.5

T. Find the radius of its circular path.

Example 19

challenge

Two long parallel wires

0.1

m apart carry currents that produce a field of

4\times10^{-6}

T from one wire at the other. Each wire is

2

m long carrying

2

A. Find the force between them.

Example 20

challenge

A proton (

q=1.6\times10^{-19}

C) moves at

v=2\times10^6

m/s perpendicular to

B=0.1

T. Find the magnetic force magnitude.

Example 21

medium

A charge

q=4

C moves at

v=2

m/s perpendicular to

B=0.25

T. Find the magnetic force.

Example 22

medium

A field

B=0.8

T through a square loop of side

0.5

m at

\theta=0

. Find the flux.

Example 23

easy

A wire

2\text{ m}

long carries

5\text{ A}

perpendicular to a

0.3\text{ T}

field. Find the force.

Wire perpendicular to B = 0.3 T; find the force.

Example 24

easy

A charge of

3\text{ C}

moves at

4\text{ m/s}

perpendicular to a

0.5\text{ T}

field. Find the force.

Charge q = 3 C moving perpendicular to B = 0.5 T; find the magnetic force.

Example 25

easy

A wire

0.4\text{ m}

long carries

8\text{ A}

perpendicular to a

0.25\text{ T}

field. Find the force.

Wire perpendicular to B = 0.25 T; find the force.

Example 26

medium

A wire of length

1.5\text{ m}

in a

0.6\text{ T}

field carries current and feels

0.9\text{ N}

(perpendicular). Find the current.

Example 27

medium

2\text{ m}

wire makes a

30°

angle with a

0.5\text{ T}

field and carries

4\text{ A}

. Find the force on the wire.

Wire at 30° to B = 0.5 T carrying 4 A; find F

Example 28

medium

A circular loop has area

0.2\text{ m}^2

in a field

B = 0.5\text{ T}

60°

from the normal. Find the flux (

\cos60°=0.5

Example 29

medium

2\text{ C}

charge moves at

3\text{ m/s}

30°

to a

1\text{ T}

field. Find the magnetic force (

\sin30°=0.5

Charge q = 2 C at 30° to B = 1 T; find F

Example 30

medium

Earth's magnetic field at the surface is roughly

5\times10^{-5}\text{ T}

. Express in milligauss (use

1\text{ T} = 10^4\text{ G}

1\text{ G} = 10^3\text{ mG}

Example 31

medium

A wire feels

12\text{ N}

when perpendicular to a field. What force does it feel at

45°

to the field (

\sin45° \approx 0.707

Wire at 45° to field; maximum force at 90° is 12 N; find force at 45°.

Example 32

medium

A long straight wire carries current

I

. The field magnitude at distance

r

B = \mu_0 I/(2\pi r)

. For

I = 5\text{ A}

and

r = 0.1\text{ m}

, compute

B

(use

\mu_0 = 4\pi\times10^{-7}

Example 33

hard

A solenoid of

n = 2000

turns per meter carries

0.5\text{ A}

. Find the interior field magnitude (

\mu_0 = 4\pi\times10^{-7}

T·m/A).

Example 34

hard

An electron (

q = -1.6\times10^{-19}\text{ C},\; m = 9.11\times10^{-31}\text{ kg}

) moves at

4\times10^6\text{ m/s}

perpendicular to a

0.2\text{ T}

field. Find the radius of its circular path.

Example 35

hard

Two long parallel wires carry currents

I_1 = 4\text{ A}

and

I_2 = 3\text{ A}

in the same direction, separated by

d = 0.05\text{ m}

. Find the force per unit length between them (

\mu_0/(2\pi) = 2\times10^{-7}

Example 36

hard

A coil of

50

turns and area

0.02\text{ m}^2

sits in a field that changes from

0.4\text{ T}

0

0.1\text{ s}

. Find the induced EMF magnitude.

Example 37

hard

A magnetic field of

0.5\text{ T}

uniform perpendicular passes through a

0.4\text{ m}^2

coil with

200

turns. Find the total flux linkage.

Example 38

hard

Why do magnetic field lines never cross?

Example 39

challenge

A proton (

m = 1.67\times10^{-27}\text{ kg}, q = 1.6\times10^{-19}\text{ C}

) in a cyclotron field of

1.5\text{ T}

has cyclotron frequency

f = qB/(2\pi m)

. Compute

f

Example 40

challenge

A charged particle enters a uniform field with a velocity that has both parallel and perpendicular components. Describe the resulting path.

Example 41

challenge

A magnetic field exerts force only perpendicular to a charge's velocity. Explain why the field can never change the kinetic energy of the charge.

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Related Concepts

Electric Current Electric Field Magnetic Force Electromagnetic Induction

Background Knowledge

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

electric currentelectric field