Work done by Electric Fields

When work is done by a conservative electric field on a test charge, then the charge will lose EPE and gain KE. This is written mathematically as

W_{E field} = - DEPE = DKE
Since E is a conservative field, this is merely a restatement
of the Law of Conservation of Energy.

Remember that work is calculated according to the formula: W = Fs cos q

fieldAB.gif (1705 bytes)

If a positive test charge, +q, is moved from point B to point A, along the direction of a field line, then the angle between F=qE and s equals 0º and the field does positive work on +q. This is evidenced by the fact that the point charge would gain KE as it reaches A. But the charge has lost electric potential energy since position B sits on a higher potential surface than position A.

fieldABvoltage.gif (2014 bytes)

The change in EPE equals +q (DV) = +q (V_A - V_B) = (+)(-) < 0

Suppose instead that a negative point charge is moved by the field from A to B. Does this work done by the field also represent a loss of EPE?

Remember that in uniform fields, field lines point from the positive plate to the negative plate. Therefore, equipotential surface A is closer to the negative plate and therefore represents a position of higher potential energy for a negative charge. The field would naturally accelerate a negative test charge from surface A to surface B, so F and s point in the same direction, making q = 0º.

W = Fs cos q > 0, but DEPE = -q (V_B - V_A) = (-)(+) < 0