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Magnetism and the Lorentz Force

by Ron Kurtus (revised 15 September 2006)

When an electric charge moves through a magnetic field, there is a force on the charge, perpendicular to the direction of the charge and perpendicular to the direction of the magnetic field. This force is called the Lorentz Force. This also applies to electric current in a wire. 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 work when current flows in a wire?
• What is the right-hand rule?

This lesson will answer those questions. There is a mini-quiz near the end of the lesson.

Useful tools: Metric-English Conversion | Scientific Calculator.

Moving charged particle in magnetic field

A moving particle with an electric charge--such as a proton or electron--creates a magnetic field. If that charge is moving through an external magnetic field there will be an attraction or repulsion force, as the magnetic fields interact.

(See Magnetism for more information.)

There is a relationship between the movement of the particle through the magnetic field, the strength of that magnetic field and the force on the particle. The following equation describes the force:

F = qvB

where:

• F is the force in Newtons
• q is the electric charge in Coulombs
• v is the velocity of the charge in meters/second
• B is the strength of the magnetic field in Teslas
• qvB is q times v time B

Current through wire

If instead of a moving charge, such as an electron or proton, there was electric current moving through a wire, the force would be a result of the current and the magnetic field:

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
• BIL is B times I times L

Force on wire with current flowing

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.

Force on moving charge through magnetic field (Right Hand Rule)

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.

Question on direction

A good question about the directions of things in this example is: "Why are they using a positive (+) charge moving through the field instead of an electron, which has a negative (-) charge?"

The reason has to do with the unfortunate convention that electricity in a wire travels from (+) to (-), when in reality the electrons go through the wire in the opposite direction. Saying that a positive (+) charge travels through the magnetic field in one direction is the same as saying the electric current goes in that same direction.

It is just a confusing convention that you have to remember.

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.

Answers to Readers' Questions

Do excellent work

Resources

The following resources provide information on this subject:

Websites

Explanation of Magnetism - from NASA

Magnetism - from South Dakota School District

Physical Science Resources

Books

Top-rated books on Magnetism

Miscellaneous

Mini-quiz to check your understanding

1. Why is a moving electron affected by a magnetic field?

2. What is the force on a wire carrying current in a magnetic field called?

3. What is the direction of the force of an electron moving through a magnetic field?

If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.

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Magnetism and the Lorentz Force