# Homework Help: Work on an electric charge

1. Feb 19, 2015

### david84

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

An electric field does 40 J of work on a charge moving from point A to point B in a straight line at a distance, d. If the charge moves through a different path from point C to point D at a distance of 2d, what is the work done on the charge?

2. Relevant equations

W=Fd

3. The attempt at a solution

I figure that because the distance is doubled, the work done will be doubled as well according to the work equation. So the total work done will be 40 J x 2 = 80 J. I'm not completely sure though cause I feel like I'm missing something. Is the question really this simple, and do I have the right answer? Thanks.

2. Feb 19, 2015

### Andrew Mason

Welcome to PF David!

You do not have enough information to answer the question. We need to know the direction of the paths relative to the field E at all points in the path. This is because:

$$Work = W = \int \vec{F}\cdot d\vec{s} = \int |\vec{F}| |d\vec{s}|\cos\theta$$

over a given path, where $\theta$ is the angle between the Force and the path.

AM