Practice Magnetic Force in Physics

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

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Quick Recap

The force exerted on a moving charge or current-carrying conductor by a magnetic field.

A moving charge in a magnetic field feels a sideways push — perpendicular to both its motion and the field. It's like a cross-wind deflecting a moving ball.

Showing a random 20 of 50 problems.

Example 1

medium

A positive charge moves in the

+x

direction through a region with

\vec{B}

in the

+y

direction. In which direction is the magnetic force, and what happens to the speed of the charge?

Example 2

medium

Two long parallel wires

0.05 \text{ m}

apart carry currents

I_1 = 4 \text{ A}

and

I_2 = 6 \text{ A}

in opposite directions. Find the force per unit length between them. Use

\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}

Example 3

medium

A velocity selector uses crossed

\vec{E}

and

\vec{B}

fields. With

E = 2.0 \times 10^4 \text{ V/m}

and

B = 0.10 \text{ T}

, what speed passes through undeflected?

Example 4

easy

A proton (

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

) moves at

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

perpendicular to a

0.3 \text{ T}

magnetic field. What is the magnetic force on the proton?

Example 5

medium

A charge

q=4

C at

v=3

m/s makes

30°

with

B=2

T. Find the force. (

\sin30°=0.5

Example 6

hard

A rectangular loop with sides

a = 0.20 \text{ m}

and

b = 0.10 \text{ m}

carries

I = 3.0 \text{ A}

. The loop's normal makes

30°

with a uniform

\vec{B} = 0.40 \text{ T}

. Find the magnitude of the torque on the loop.

Example 7

hard

An electron moves in a circle in a

0.10 \text{ T}

field with kinetic energy

K = 1.0 \times 10^{-15} \text{ J}

. Find the radius. (

m_e = 9.11\times 10^{-31} \text{ kg}

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

, non-relativistic.)

Example 8

medium

A charge

q=3

C moving at

v=4

m/s at

90°

feels

6

N. Find the field.

Example 9

challenge

A particle (

q = +2.0\times 10^{-19} \text{ C}

m = 4.0\times 10^{-26} \text{ kg}

) enters a uniform

B = 0.30 \text{ T}

field at speed

v = 5.0\times 10^5 \text{ m/s}

perpendicular to the field. Find (a) the cyclotron radius and (b) the cyclotron frequency.

Example 10

hard

Two long parallel wires carry equal currents

I

in the same direction. The wires are

0.10 \text{ m}

apart, and the force per meter is

2.0 \times 10^{-5} \text{ N/m}

(attractive). Find

I

. Use

\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}

Example 11

easy

2

C charge at

5

m/s perpendicular to

B=0.3

T. Find the force.

Example 12

medium

A wire of length

0.30 \text{ m}

carries

I = 6.0 \text{ A}

at an angle of

30°

to a

0.50 \text{ T}

magnetic field. Find the force on the wire.

Example 13

easy

Find the angle

\theta

between

\vec{v}

and

\vec{B}

if a charge

q = 1 \text{ C}

moving at

v = 2 \text{ m/s}

in a

B = 3 \text{ T}

field experiences

F = 3 \text{ N}

Example 14

easy

Does a magnetic force do work on a charged particle moving freely in a static magnetic field?

Example 15

medium

A proton (

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

) moves at

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

perpendicular to a

0.5 \text{ T}

magnetic field. Find the magnetic force.

Example 16

easy

A charge of

0.20 \text{ C}

moves at

v = 50 \text{ m/s}

perpendicular to a

B = 0.40 \text{ T}

magnetic field. Find the force.

Example 17

hard

A wire carrying

I = 10 \text{ A}

has length vector

\vec{L} = (0.20\hat{x} + 0.10\hat{y}) \text{ m}

in a uniform field

\vec{B} = 0.30\hat{z} \text{ T}

. Find the force vector on the wire.

Example 18

hard

A mass spectrometer uses a

0.50 \text{ T}

field. A singly ionized particle (

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

) is accelerated through

1000 \text{ V}

and travels in a circle of radius

0.10 \text{ m}

. Find the particle's mass.

Example 19

medium

A wire of length

0.4

m carries

5

A at

90°

to a field and feels

2

N. Find the field strength.

Example 20

challenge

A charged particle enters a field region perpendicular to

B=0.2

T and follows a semicircle of radius

0.5

m before exiting. If

q/m = 10

C/kg, find its speed.

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