# Work equation for electrostatics and electricity

1. May 7, 2013

### Benny851

I have a question about the equation for work as it pertains to electrostatics and electricity. One book I read says equation for work done by electric field is W=qV, but another book says W=-PE. However, when I try both equations for the following problem I get different answer. Could someone please explain to me which equation I should use and why? Thanks.

Parallel plate capacitor with 10 V battery. +3 charge is on negative plate and you need to move it to positive plate. calculate work.

w=-pe -> -(3*10) = -30

w=qv -> 3*10= 30

2. May 7, 2013

### collinsmark

Something I like to do is to put myself into the problem.

Imagine for a moment that you are able to shrink yourself down to the size of the charge and physically push it. If the force that you apply on the charge is in the same direction as the charge's displacement, then it can be said that "you have done positive work on the system."

On the other hand, if you are pushing the charge forward, but the charge ends up going backward such that the force that you exert is in the opposite direction as the charge's displacement, then it can be said that "you have done negative work on the system." This is equivalent to saying "the system has done positive work on you."

So the correct answer involves who is doing work on what.

In this problem there are two forces involved: the force that you exert on the system and the equal and opposite force that the system exerts on you (or exerts on the charge if you were not there to keep it from accelerating).

Assuming a constant force, one can define the work as
$$W = \vec F \cdot \vec{\Delta x}$$
If $\vec F$ and $\vec{\Delta x}$ are in the same direction the work is positive, if they are in opposite directions, the work is negative. Of course the answer depends on which force you are talking about!

So let's revisit this problem as it was worded:

The question, as it was worded, is sort of ambiguous. It's not clear if its talking about the work done by the system or the work done by you. But if I had to guess, I would say it wants you give the work done by you, on the system, when you move the charge from the negative plate to the positive plate.

Last edited: May 8, 2013