Magnetic Fields

Motion of a Particle

in a Magnetic Field

  F = q v x B

The magnetic force on a moving electric charge is perpendicular to the velocity of the charge. That means no work is done. This is like a centripetal force in that it changes the direction of the velocity but does not change the magnitude of the speed. So the kinetic energy remains the same and no work is done to the charge.

If the charge is initially moving perpendicular to the magnetic field then it will move in a circle in a plane perpendicular to the magnetic field.

If the charge is not moving perpendicular to the magnetic field, it will continue to move in the direction of the magnetic field with constant speed in that direction — while moving in a circular path around the magnetic field. This trajectory is called a helix.

Torque on a Current-Carrying Loop


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(c) Doug Davis, 2002; all rights reserved