# Electric Potentials (4 charges on corners of a rectangle)

## Homework Statement

A rectangle has sides of length 5cm (right and left) and 15cm (top and bottom).

Top left corner has charge (q1) = -5uC
Top right corner has charge A = ?
Bottom left corner has charge B = ?
Bottom right corner has charge (q2) = 2uC

a) What are the electric potentials of A and B
b)How much external work is required to move a third charge (q3 = 3uC) from B to A along the diagonal of the rectangle

## Homework Equations

Not too sure. For part b I'm thinking I would use a line intergral and say that the diagonal path from A to B is equivilent to going from B to q1, then q1 to A.

V = U/Qo

But where will I get U (potential energy) from?

## The Attempt at a Solution

What I really want is part a, once part a is done I can just do some line intergrals to find the work done for part b.

Do I use equipotentials? So potential of A is the same as potential of q1? B is the same as q2?

Any pointers and I'm very grateful.

Calculate the potential due to a point charge as a function of distance. The potentials add at any given point in space. How is the electric field created by a point charge related to the potential?

I'm still confused sorry. Say if I wanted to find the potential of A, which is in the top right corner. It is inbetween two different fields created by charges q1 and q2. I cannot just find the electric field of one, then say 'since A is a distance r from this charge it's potential is this'??? It doesn't make sense. Don't fields superimpose?

And the fact that I'm working with a damn rectangle makes it more harder to interpretate.

Electric field of q1 at B: -1.8E7 Nc-1
Electric field of q1 at A: -2E6 Nc-1
Electric field of q2 at B: 8E5 Nc-1
Electric field of q2 at A: 7.2E6 Nc-1

K so these are the electric fields using the distances on the rectangle. Now to find the potentials of A and B, how to do this?

K, A and B are just corners... Hmm..

Electric fields superimpose and so do potentials. Potentials are scalars so the superposition is straightforward. You should be able to find the potential of a point charge anywhere in space from

$$V=-\int^r_\infty\vec{E}\cdot\mbox{d}\vec{r'}$$

and Gauss's Law can be used to find the E field of a point charge as a function of r. The upper limit r is the distance from the point charge to a corner.