Electric Field Work on Moving Charge

[david84]

Homework Statement

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?

Homework Equations

W=Fd

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.

 

[Andrew Mason]

Homework Statement

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?

Homework Equations

W=Fd

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.

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