Magnetic Force on a Moving Charge
Magnetic forces only exist on charged particles while they are moving. This section explains the nature of this force.
- An electric charge moving in a magnetic field experiences a force proportional to the magnitude and velocity of the charge, as well as the magnetic field strength:
- The magnitude of the magnetic force can be calculated using the angle, 𝜃, between the velocity and magnetic field vectors:
- The direction of the magnetic force is found with the right-hand rule.
More Properties of Magnetic Force
- If the velocity of the particle is parallel or anti-parallel to the magnetic field, then the magnetic force is zero.
- Uncharged particles do not feel a force produced by the magnetic field.
- If a charged particle is experiencing both an electric field and a magnetic field, then the total force is the vector sum of the two forces.
Example: Magnetic Force Direction
Consider the following experiment. A charge enters a magnetic field and collides with a sensor as shown in the diagram. If the particle takes the trajectory shown, what is the sign of the charge?
Hint: The magnetic field is pointing into the page. We know this because of the X symbols. If the field was pointing out of the page, there would instead be dots instead.
Use the right-hand rule with v and B as given, and your thumb will point upward. This means that if the charge is positive, then the force should point upward.
Since the trajectory shows acceleration in the upward direction, we know that the magnetic force on this particle is upward.
Since our right-hand rule and the drawn trajectory result in the same force, we know that the charge must be positive.
(If our right-hand rule had given the opposite result of the drawn trajectory, then the charge would have been negative.)
Example: Electron Moving Through Uniform Magnetic Field
An electron moves perpendicular to a uniform magnetic field which exerts a magnetic force on the electron shown in the figures below. In each case, find the direction of the magnetic field?
For the diagram on left side:
Right hand rule (RHR) for positive charge is
If the charge is negative, the final answer should be flipped.
Thus, if this was a positive charge, the F would have been along +Y axis. This mean, RHR indicated that B must be into the page or -X axis.
For the diagram on right side:
Right hand rule (RHR) for positive charge is
If the charge is negative, the final answer should be flipped.
Thus, if this was a positive charge, the F would have been along +Y axis. This mean, RHR indicated that B must be into the page or -Z axis.