What is the formula for the magnetic force on a moving charge?

F = qvB sin θ, where q is the charge, v is the speed, B is the magnetic field strength, and θ is the angle between v and B. The force is perpendicular to both.

What is the motor effect?

The force on a current-carrying wire in a magnetic field, F = BIL sin θ. The same physics as the force on a moving charge, summed over all the charges in the wire.

How do I find the direction?

Use the right-hand slap rule (or the right-hand rule for cross products). For a positive charge moving with velocity v in field B, F is in the direction of v × B. For a negative charge, the force is opposite.

When is the force zero?

When v (or I) is parallel or antiparallel to B (sin θ = 0). Maximum force occurs when v is perpendicular to B (sin θ = 1).

← HSC Physics calculators

NSW · HSCModule 6

Lorentz force / motor effect calculator

F = qvB sin θ for a moving charge, F = BIL sin θ for a current-carrying wire. Switch mode to compute either.

Inputs

Force onCharge q (C)Electron charge ≈ 1.602e-19Speed v (m/s)Magnetic field B (T)Angle θ between v (or I) and B (degrees)

Result

Force F

8.010e-14N

F = qvB sin θ. The force is perpendicular to both v (or I) and B.

How this calculator works

For a moving charge, the calculator multiplies q × v × B × sin θ. For a current-carrying wire, it multiplies B × I × L × sin θ. The angle θ is between the velocity (or current) and the magnetic field.

Common questions

What is the formula for the magnetic force on a moving charge?: F = qvB sin θ, where q is the charge, v is the speed, B is the magnetic field strength, and θ is the angle between v and B. The force is perpendicular to both.
What is the motor effect?: The force on a current-carrying wire in a magnetic field, F = BIL sin θ. The same physics as the force on a moving charge, summed over all the charges in the wire.
How do I find the direction?: Use the right-hand slap rule (or the right-hand rule for cross products). For a positive charge moving with velocity v in field B, F is in the direction of v × B. For a negative charge, the force is opposite.
When is the force zero?: When v (or I) is parallel or antiparallel to B (sin θ = 0). Maximum force occurs when v is perpendicular to B (sin θ = 1).