# Why the negative sign?

1. Sep 18, 2009

### PeterPumpkin

1. The problem statement, all variables and given/known data

Why is the difference in electric potential between points A and B defined as the NEGATIVE of the work done in moving a test charge along the path from A to B and then dividing by the charge q? Why the negative sign? Just wondering.

2. Relevant equations

Delta V = - Work done / q

3. The attempt at a solution

2. Sep 18, 2009

### kuruman

This is more general than charges. The work done by a conservative force is the negative of the change in potential energy. Why the negative sign? Think of it this example. Say I toss an object straight up in the air (no air resistance). The work energy theorem says that the change in kinetic energy is the work done by the net force, in this case gravity. The work done by gravity for an object that moves up is negative. Therefore, ΔK = - mgh. The change in potential energy is positive, ΔU = + mgh so that ΔK = - ΔU or ΔK + ΔU = 0 which is mechanical energy conservation with the work done by the conservative force taken out of the picture.

The minus sign basically says that if you take out Joules from the energy of an object by doing negative work on it with a conservative force, then you'd better store these Joules as an increase in potential energy. Conversely, if you add Joules to an object by doing positive work with a conservative force, then these Joules better come from a decrease in potential energy.

3. Sep 18, 2009

### saunderson

Work done against a force field is signed positive, that's why there is a negative sign!

$$dW = - \vec F \cdot d\vec r$$​

(note that like charges push off each other!)

with best regards!