Work
The work done to move a charge is the force, F, exerted on the charge, multiplied by the
displacement, d, of the charge in the direction of the force. As we saw earlier, the
magnitude of the force exerted on a charge q in an electric field E is = qE. Thus, we can
derive the following equation for the work done on a charge:
Remember that d is not simply the displacement; it is the displacement in the direction
that the force is exerted. When thinking about work and electric fields, keep these three
rules in mind:
- When the charge moves a distance r parallel to the electric field lines, the work
done is qEr. - When the charge moves a distance r perpendicular to the electric field lines, no
work is done. - When the charge moves a distance r at an angle to the electric field lines, the
work done is qEr cos.