All Tools

Magnetic Force Calculator

Calculate the magnetic force on a current-carrying wire or a moving charge in a magnetic field. Adjust the current, wire length, field strength, and angle to see how the force changes. A diagram shows the right-hand rule in action, and every step of the formula is worked out for you.

Force Diagram

BI90°FF = 0.5 NRight-hand rule: fingers along I, curl toward B, thumb points in F direction

Parameters

A
m
T
0° (parallel)90° (perpendicular)180°

Results

Magnetic force (F)
0.5 N
sin(θ)
1.0000
Force direction
Out of the page (using right-hand rule)
F / L (force per unit length)
1 N/m
The wire is perpendicular to the field, producing maximum force.

Step-by-Step Calculation

1. Magnetic force on a current-carrying wire

F=BILsin⁡θF = BIL\sin\theta
F=(0.2)(5)(0.5)sin⁡(90∘)F = (0.2)(5)(0.5)\sin(90^\circ)
F=(0.2)(5)(0.5)(1)F = (0.2)(5)(0.5)(1)

2. Final result

F=0.5 NF = 0.5 \text{ N}
sin⁡(90∘)=1  ⟹  F=BIL (maximum force when perpendicular)\sin(90^\circ) = 1 \implies F = BIL \text{ (maximum force when perpendicular)}
F=0.5 NF = 0.5 \text{ N}

3. Direction (right-hand rule)

F⃗=IL⃗×B⃗\vec{F} = I\vec{L} \times \vec{B}
Point fingers along I, curl toward B\text{Point fingers along } I\text{, curl toward } B
Out of the page (using right-hand rule)\text{Out of the page (using right-hand rule)}

Reference Guide

Force on a Current-Carrying Wire

When a wire carrying current II sits in a magnetic field BB, it experiences a force that depends on the angle between them.

F=BILsin⁡θF = BIL\sin\theta

The force is maximum when the wire is perpendicular to the field (θ=90∘\theta = 90^\circ) and zero when they are parallel (θ=0∘\theta = 0^\circ).

Force on a Moving Charge

A single charge qq moving with velocity vv through a magnetic field also feels a force.

F=qvBsin⁡θF = qvB\sin\theta

This force is always perpendicular to the velocity, so it changes direction but not speed. That is why charged particles move in circles in a uniform magnetic field.

Right-Hand Rule

To find the force direction, use the right-hand rule. Point your fingers in the direction of current (or velocity for a positive charge). Curl them toward the magnetic field direction. Your thumb points in the direction of the force.

F⃗=IL⃗×B⃗\vec{F} = I\vec{L} \times \vec{B}

For a negative charge, the force is in the opposite direction.

Real-World Applications

This force principle is the basis of electric motors, where current-carrying coils rotate in magnetic fields. Loudspeakers use a voice coil in a permanent magnet's field to produce sound.

Rail guns use extremely high currents and strong fields to accelerate projectiles. MRI machines use the force on moving charges (protons) in strong magnetic fields to create detailed images of the body.