Magnetic Force Examples in Physics

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

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 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.

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: Magnetic Force 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 force 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 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?

Answer

F=2.4×10−13 NF = 2.4 \times 10^{-13} \text{ N}

First step

1
Use F=qvBsin⁡θF = qvB\sin\theta with θ=90°\theta = 90°.

Full solution

  1. 2
    F=1.6×10−19×5×106×0.3×1F = 1.6 \times 10^{-19} \times 5 \times 10^6 \times 0.3 \times 1
  2. 3
    F=2.4×10−13 NF = 2.4 \times 10^{-13} \text{ N}
The magnetic force on a moving charged particle is perpendicular to both the velocity and the magnetic field. It causes the particle to move in a circular path rather than speeding it up or slowing it down.

Example 2

medium
A wire carrying 8 A8 \text{ A} is 0.5 m0.5 \text{ m} long and placed at 60°60° to a 0.4 T0.4 \text{ T} magnetic field. What force acts on the wire?

Example 3

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 4

medium
A proton (q=1.6×10−19 Cq = 1.6\times 10^{-19} \text{ C}) enters a 0.20 T0.20 \text{ T} field perpendicular to its velocity at v=2.0×106 m/sv = 2.0 \times 10^6 \text{ m/s}. The proton's mass is 1.67×10−27 kg1.67\times 10^{-27} \text{ kg}. Find the radius of its circular path.

Example 5

medium
Find the cyclotron period TT of a proton (m=1.67×10−27 kgm = 1.67\times 10^{-27} \text{ kg}, q=1.6×10−19 Cq = 1.6\times 10^{-19} \text{ C}) in a 1.0 T1.0 \text{ T} magnetic field.

Example 6

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 7

hard
Two long parallel wires 0.40 m0.40 \text{ m} apart carry parallel currents I1=8 AI_1 = 8 \text{ A} and I2=3 AI_2 = 3 \text{ A}. 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 8

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 9

challenge
A rail gun has two parallel rails L=0.50 mL = 0.50 \text{ m} apart connected by a sliding conducting bar of mass m=0.10 kgm = 0.10 \text{ kg}. A uniform vertical B=0.80 TB = 0.80 \text{ T} field is applied. What current is required to accelerate the bar at a=20 m/s2a = 20 \text{ m/s}^2 along the rails (ignore friction)?

Practice Problems

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

Example 1

medium
An electron (q=1.6×10−19 Cq = 1.6 \times 10^{-19} \text{ C}, m=9.11×10−31 kgm = 9.11 \times 10^{-31} \text{ kg}) moves at 2×107 m/s2 \times 10^7 \text{ m/s} perpendicular to a 0.01 T0.01 \text{ T} field. What is the radius of its circular path?

Example 2

hard
Two parallel wires 0.1 m0.1 \text{ m} apart each carry 10 A10 \text{ A} in the same direction. What is the force per meter between them? Is it attractive or repulsive? Use μ0=4π×10−7 T m/A\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}.

Example 3

easy
A charge q=3q=3 C moves at v=2v=2 m/s perpendicular to B=4B=4 T. Find the force.

Example 4

easy
A charge moves parallel to a magnetic field. What is the magnetic force?

Example 5

easy
A wire of length 22 m carries 33 A perpendicular to B=0.5B=0.5 T. Find the force.

Example 6

easy
Is the magnetic force on a moving charge parallel or perpendicular to its velocity?

Example 7

easy
A 55 C charge at 11 m/s perpendicular to a field feels 1010 N. Find the field strength.

Example 8

easy
For an electron versus a proton moving the same way in the same field, do the forces point the same or opposite way?

Example 9

easy
A wire feels force only because charges inside it are doing what?

Example 10

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

Example 11

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 12

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 13

medium
A charge q=2q=2 C, mass m=4m=4 kg, at v=6v=6 m/s perpendicular to B=3B=3 T. Find the radius of circular motion.

Example 14

medium
The maximum force on a charge in a field is 2020 N (when perpendicular). What force results when it moves at 60°60°? (sin⁡60°≈0.866\sin60°\approx0.866.)

Example 15

medium
Two wires: wire 1 in field B=0.5B=0.5 T carries 44 A over 33 m; wire 2 carries 22 A over 33 m in 11 T, both perpendicular. Which feels more force?

Example 16

medium
A charge q=1q=1 C at v=10v=10 m/s feels 55 N in a B=1B=1 T field. Find the angle between velocity and field. (sin⁡θ=0.5\sin\theta=0.5.)

Example 17

medium
A wire carries 66 A over 0.50.5 m perpendicular to BB and feels 99 N. Find BB.

Example 18

challenge
A charge q=2q=2 C, mass m=1m=1 kg, circles at r=5r=5 m in a B=0.4B=0.4 T field. Find its speed.

Example 19

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.

Example 20

challenge
A horizontal wire of mass 0.020.02 kg and length 0.50.5 m carries current II in a 0.40.4 T field so the magnetic force just balances gravity. Find II. (g=10g=10 m/s2^2.)

Example 21

medium
A wire of length 1.51.5 m carries 22 A perpendicular to B=0.4B=0.4 T. Find the force.

Example 22

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

Example 23

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 24

easy
A straight wire of length 0.80 m0.80 \text{ m} carries I=5.0 AI = 5.0 \text{ A} perpendicular to a 0.25 T0.25 \text{ T} field. Find the magnetic force on the wire.

Example 25

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 26

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 27

medium
An electron (q=−1.6×10−19 Cq = -1.6\times 10^{-19} \text{ C}, m=9.11×10−31 kgm = 9.11\times 10^{-31} \text{ kg}) moves in a circle of radius 5.0 mm5.0 \text{ mm} in a 0.02 T0.02 \text{ T} field. Find its speed.

Example 28

medium
A square loop of side 0.10 m0.10 \text{ m} lies in the xyxy-plane and carries 2.0 A2.0 \text{ A} counterclockwise as viewed from +z+z. A uniform B⃗=0.30 T z^\vec{B} = 0.30 \text{ T}\,\hat{z} field is applied. What is the net force on the loop?

Example 29

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 30

medium
A wire of mass per unit length λ=0.030 kg/m\lambda = 0.030 \text{ kg/m} carries current II horizontally in a B=0.40 TB = 0.40 \text{ T} horizontal field perpendicular to the wire. What current is required for the magnetic force to support the wire against gravity? (g=9.8 m/s2g = 9.8 \text{ m/s}^2)

Example 31

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 32

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 33

hard
A proton enters a 0.50 T0.50 \text{ T} magnetic field with velocity v=3.0×106 m/sv = 3.0 \times 10^6 \text{ m/s} at 60°60° to the field. The proton's mass is 1.67×10−27 kg1.67\times 10^{-27} \text{ kg}, charge 1.6×10−19 C1.6\times 10^{-19} \text{ C}. Find the pitch of the resulting helical path.

Example 34

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 35

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 36

hard
A wire segment runs along L⃗=0.50x^ m\vec{L} = 0.50\hat{x} \text{ m} carrying I=4.0 AI = 4.0 \text{ A} in a field B⃗=(0.20y^+0.30z^) T\vec{B} = (0.20\hat{y} + 0.30\hat{z}) \text{ T}. Find the magnitude of the force.

Example 37

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 38

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.
← Back to Magnetic Force Formula Explained Practice Mode

Background Knowledge

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

magnetic fieldelectric currentforce