Lorentz Force from Magnetic Field

by Ron Kurtus (updated 30 May 2023)

The Lorentz Force on an electric charge occurs when the charge moves through a magnetic field. This force is perpendicular to the direction of the charge and also perpendicular to the direction of the magnetic field. It is a vector combination of the two forces.

This Lorentz Force was first formulated by James Clark Maxwell in 1865, then by Oliver Heaviside in 1889, and finally by Hendrick Lorentz in 1891.

Since electrons are moving in a wire, this force also applies to an electric current. The direction of the force is demonstrated by the Right Hand Rule.

Questions you may have include:

What causes the Lorentz force?
How does it apply when current flows in a wire?
What is the right-hand rule?

This lesson will answer those questions. Useful tool: Units Conversion

Cause of Lorentz Force

A magnetic field is created by the motion of an electrically charged particle—such as a proton or electron. If that electrical charge is moving through an external magnetic field, there will be a magnetic attraction or repulsion force, depending on how the two magnetic fields interact.

(See Basics of Magnetism for more information.)

The relationship between the force on the moving particle, the velocity of the particle through the magnetic field, the strength of that magnetic field and the force on the particle, and the angle between the directions of the particle and magnetic field is:

F = qvB*sinθ

where:

F is the force in Newtons
q is the electric charge in Coulombs
v is the velocity of a positive (+) charge in meters/second
B is the strength of the magnetic field in Teslas
sinθ is the sine of the angle between v and B
θ is Greek letter theta

Note: The direction of the magnetic field B is defined as from N to S. Also, the direction of the electrical charge is from (+) to (−). An electron would move in the opposite direction.

The Lorentz Force equation implies that if the velocity of the particle is zero (v = 0), then F = 0. Also, if the particle is moving in a direction parallel to B, again F = 0.

Current through wire

Since an electrical current in a wire consists of moving electrons, the Lorentz Force also applies to a current in a magnetic field. When the current is perpendicular to the direction of the magnetic field, the force equation is:

F = BIL

where:

F is the force in Newtons
B is the strength of the magnetic field in Teslas
I is the electrical current in Amperes
L is the length of the wire through the magnetic field in meters

Note: Remember that the convention for current direction in the wire is opposite the direction of the motion of the electrons.

Lorentz Force on wire in magnetic field

This force on the wire can be measured in an experiment.

Right Hand Rule

The direction of the Lorentz force for a given direction of current and magnetic field can be remembered by the Right Hand Rule. If you took your right hand and stuck your thumb up, your forefinger (first finger) forward and your second finger perpendicular to the other two, then the direction of the force would be as indicated in the drawing below.

Right Hand Rule for force on moving charge through magnetic field

The Right Hand Rule is supposed to help you remember which way things are pointing for the force on a moving charge. But personally, I think it is confusing. Still, you should be aware of it, because some teachers include it in tests.

Summary

The Lorentz Force is applied to an electric charge that moves through a magnetic field. It is perpendicular to the direction of the charge and the direction of the magnetic field. The direction of the force is demonstrated by the Right Hand Rule.

Do excellent work