# Change in potential energy/work formula for electric charges.

1. ### theBEAST

372
I have the following formula on my formula sheet:
ΔU = U_a - U_b = q(V_a - V_b)

I was wondering if 'a' is final and 'b' is initial or is it the other way around? Also when I plug in my charge q into the formula, if it was a negative charge do I plug the negative sign into the formula? I realize that some formulas assume that you plug in the magnitude of the charge so I am not so sure about this formula... Thanks!

2. ### ehild

12,383
The change of potential energy from a to b is Ub-Ua=q(Vb-Va), but the work done by the electric field on a charge q when it moves from a to b is W(ab)=Ua-Ub. If the charge moves in free space the work done by the field increases its kinetic energy: Ub-UA=KE(b)-KE(a), which means that U+KE=const, conservation of energy.

Imagine that the (positive) charge moves across a resistor from a to b. The moving charge constitutes current; the current flows from positive to negative, in the direction of decreasing potential: I=(Va-Vb)/R, and the work done (and dissipated on the resistor) while q charge moves from a to b is q(Va-Vb). Va-Vb sometimes is called "voltage" or "potential drop". Ohm's Law means that Current=potential drop divided by resistance.

The charge q can be either positive or negative, but you can omit the sign when you are interested only in the magnitude of work .

ehild