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+x direction through a region with B⃗\vec{B} in the +y+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 m0.05 \text{ m} apart carry currents I1=4 AI_1 = 4 \text{ A} and I2=6 AI_2 = 6 \text{ A} in opposite directions. Find the force per unit length between them. Use μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}.

Example 3

medium
A velocity selector uses crossed E⃗\vec{E} and B⃗\vec{B} fields. With E=2.0×104 V/mE = 2.0 \times 10^4 \text{ V/m} and B=0.10 TB = 0.10 \text{ T}, what speed passes through undeflected?

Example 4

easy
A proton (q=1.6×10−19 Cq = 1.6 \times 10^{-19} \text{ C}) moves at 5×106 m/s5 \times 10^6 \text{ m/s} perpendicular to a 0.3 T0.3 \text{ T} magnetic field. What is the magnetic force on the proton?

Example 5

medium
A charge q=4q=4 C at v=3v=3 m/s makes 30°30° with B=2B=2 T. Find the force. (sin⁡30°=0.5\sin30°=0.5.)

Example 6

hard
A rectangular loop with sides a=0.20 ma = 0.20 \text{ m} and b=0.10 mb = 0.10 \text{ m} carries I=3.0 AI = 3.0 \text{ A}. The loop's normal makes 30°30° with a uniform B⃗=0.40 T\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 T0.10 \text{ T} field with kinetic energy K=1.0×10−15 JK = 1.0 \times 10^{-15} \text{ J}. Find the radius. (me=9.11×10−31 kgm_e = 9.11\times 10^{-31} \text{ kg}, e=1.6×10−19 Ce = 1.6\times 10^{-19} \text{ C}, non-relativistic.)

Example 8

medium
A charge q=3q=3 C moving at v=4v=4 m/s at 90°90° feels 66 N. Find the field.

Example 9

challenge
A particle (q=+2.0×10−19 Cq = +2.0\times 10^{-19} \text{ C}, m=4.0×10−26 kgm = 4.0\times 10^{-26} \text{ kg}) enters a uniform B=0.30 TB = 0.30 \text{ T} field at speed v=5.0×105 m/sv = 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 II in the same direction. The wires are 0.10 m0.10 \text{ m} apart, and the force per meter is 2.0×10−5 N/m2.0 \times 10^{-5} \text{ N/m} (attractive). Find II. Use μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}.

Example 11

easy
A 22 C charge at 55 m/s perpendicular to B=0.3B=0.3 T. Find the force.

Example 12

medium
A wire of length 0.30 m0.30 \text{ m} carries I=6.0 AI = 6.0 \text{ A} at an angle of 30°30° to a 0.50 T0.50 \text{ T} magnetic field. Find the force on the wire.

Example 13

easy
Find the angle θ\theta between v⃗\vec{v} and B⃗\vec{B} if a charge q=1 Cq = 1 \text{ C} moving at v=2 m/sv = 2 \text{ m/s} in a B=3 TB = 3 \text{ T} field experiences F=3 NF = 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=1.6×10−19 Cq = 1.6 \times 10^{-19} \text{ C}) moves at 3×106 m/s3 \times 10^6 \text{ m/s} perpendicular to a 0.5 T0.5 \text{ T} magnetic field. Find the magnetic force.

Example 16

easy
A charge of 0.20 C0.20 \text{ C} moves at v=50 m/sv = 50 \text{ m/s} perpendicular to a B=0.40 TB = 0.40 \text{ T} magnetic field. Find the force.

Example 17

hard
A wire carrying I=10 AI = 10 \text{ A} has length vector L⃗=(0.20x^+0.10y^) m\vec{L} = (0.20\hat{x} + 0.10\hat{y}) \text{ m} in a uniform field B⃗=0.30z^ T\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 T0.50 \text{ T} field. A singly ionized particle (q=1.6×10−19 Cq = 1.6\times 10^{-19} \text{ C}) is accelerated through 1000 V1000 \text{ V} and travels in a circle of radius 0.10 m0.10 \text{ m}. Find the particle's mass.

Example 19

medium
A wire of length 0.40.4 m carries 55 A at 90°90° to a field and feels 22 N. Find the field strength.

Example 20

challenge
A charged particle enters a field region perpendicular to B=0.2B=0.2 T and follows a semicircle of radius 0.50.5 m before exiting. If q/m=10q/m = 10 C/kg, find its speed.
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