The Force on a Moving Charge in a Time-Changing Field.

SUBJECT: The Force on a Moving Charge in a Time-Changing Field

DESCRIPTION: A positive point charge moves out of the page rigin in a time-changing external field. This external field is uniform in space but varies in time with a period T as indicated by the blue vector in the animation.We assume that the variation of the external field is so rapid that the charge moves only a negligible distance in one period of this field.

When the external magnetic field is zero, we see only the magnetic field of the moving charge. Since the charge is moving out of the page, its field circulates counter-clockwise. When the vertically downward external magnetic field is at its maximum, we see to the left of the charge an enhancement of the the magnetic field. This enhancement arises because the field of the charge is in the same direction as the external magnetic field (downward) on that side. To the right of the charge, where the field of the charge is opposite that of the external magnetic field, we see a reduction in the total magnetic field.

This overall field configuration indicates a net force to the right on the moving charge. This occurs because the pressure of the magnetic field is much higher on the left as compared to the right. Note that if the charge had been moving into the page instead of out of the page, the force would have been to the left, because the magnetic pressure would have been higher on the right.

The animation shows dramatically the inflow of energy into the neighborhood of the charge as the external magnetic field grows, with a resulting build-up of stress that transmits a sideways force to the moving positive charge. The white vector indicates direction and magnitude of this force.