# Using the Lorentz Force Law to Examine Electric & Magnetic Forces

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• 0:03 Things That Go Great Together
• 0:29 Generating a Magnetic Field
• 2:20 Two Forces Acting at Once
• 2:39 Electric Force
• 2:54 Magnetic Force on…
• 5:04 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

Electricity and magnetism are closely related. Electric charges generate electric fields, and moving charges generate magnetic fields. In this lesson, we will learn how to calculate the strength of a magnetic field and use the Lorentz force law, which deals with the two forces on a charge moving through a magnetic field.

## Things That Go Great Together

Pen and paper, peanut butter and jelly, lock and key. These are classic pairs. One classic pair of physics-related phenomenon is electricity and magnetism. With the first set of examples I gave, one can exist without the other, and they definitely do not generate each other, but moving electric charges generate magnetic fields, and changing magnetic fields generate electric fields.

## Generating a Magnetic Field

The magnetic field generated by a moving electric charge can be calculated using Equation 1, shown here:

• Î¼o is a the permeability of free space equal to 4Ï€ x 10-7 Tesla-meter-per-amp (Tm/A)
• q is the magnitude of the charge in coulombs (C)
• v is velocity in meters-per-second (m/s)
• r is the distance from the charge in meters (m)
• Î¸ is the angle between the direction of the charge's velocity and the distance to the point in question

This equation involves the cross-product, which is a way to multiply vectors that results in a vector that is perpendicular to the velocity of the moving charge and distance from it.

The magnitude of the magnetic field is given by Equation 2, shown here:

Since the magnetic field is a vector, there must be a direction attached to its magnitude. We use the right-hand rule to determine the direction of the magnetic field at the point in question.

• The right pointer finger points in the direction of the charged particle's velocity.
• The right middle finger points in towards point where magnetic field is to be calculated.
• The thumb points in the direction of the magnetic field at the point in question.

A dot and an X represent direction.

A representation of the magnetic field generated from a moving positive charge is given in Diagram 1.

If the charge is negative, the magnetic field points in the opposite direction.

#### Example 1

Calculate the magnetic field at point P created by an electron moving at 2 x 104 m/s.

It is always a good idea to draw a diagram of the scenario.

We are now ready to use Equation 2, which was given earlier, to solve the problem:

Using the right-hand rule, we point the finger to the right, the middle finger up, which automatically makes the right thumb point out of the screen. This means the magnetic field at point P points out of the screen.

## Two Forces Acting at Once

We've learned from previous lessons that charges exert forces on other charges via the electric fields they generate. A magnetic field also exerts a force on a charge moving through it as long as the charge is not moving parallel to the magnetic field. When these two forces are added together we get the Lorentz force law.

## Electric Force

The electric force is given by Equation 3.

• F is force in newtons (N)
• q is the electric charge in coulombs (C)
• E is the electric field in newtons-per-coulomb (N/C)

## Magnetic Force on an Electric Charge

The only time an electric charge will not feel a force due to a magnetic field is if it is moving directly parallel to the magnetic field or it isn't moving in the field.

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