# Equipotential surfaces

1. Sep 8, 2006

### FlipStyle1308

Problem:

A given system has the equipotential surfaces shown below, where Vo = 12.0 V.

(a) What are the magnitude and direction of the electric field?
(b) What is the shortest distance one can move to undergo a change in potential of 5.00 V?

I am not too sure on what equations I can use to solve this, but I have a feeling one of them will be delta V = -W/qo, and I have no other ideas on how to approach this problem.

2. Sep 9, 2006

### Tomsk

You need trig to figure out the distance between the equipotentials. The electric field is always going to be orthogonal to equipotential surfaces. Do you know the relationship between E, V and r? Use that to find E, then use the E that you got from part a) for the last part.

3. Sep 9, 2006

### FlipStyle1308

Okay, so for part (a), I use E = - V/r = - 12/4 = -3? Did I interpret your post correctly?

4. Sep 9, 2006

### Tomsk

Not quite, you need the distance between two equipotential lines, which would be along a line perpendicular to them. I think you've gone along the x axis, which is at an angle to the red lines. Use the triangle formed by the x and y axes and the line V=V0, split it into two smaller right angled triangles and look for similar angles.

5. Sep 9, 2006

### FlipStyle1308

Okay, I determined how to split the triangle into two smaller right triangles and found the smiliar angles, but what exactly is this telling me?

6. Sep 9, 2006

### Tomsk

You should be able to get the distance between the equipotentials, which is your r in E=-V/r. Also, one of the angles gives you the direction of the E field.

7. Sep 9, 2006

### FlipStyle1308

Oh, okay, so the distance between the lines is 1.78885 m, so this is my r. So plugging this into E = -V/r = -12/1.78885 = -6.7082 V/m?

Edit: I just tried submitting this answer (both negative and positive), and both were incorrect.

Last edited: Sep 9, 2006
8. Sep 10, 2006

### Tomsk

That's odd, that's the answer I got. Have you added the direction? Does it say how many s.f. to give?

9. Sep 10, 2006

### FlipStyle1308

I found my mistake. The units in the chart are in cm, so I converted all values into m. This gave me a value of 670.82, which is a correct answer. I also calculated the correct answer for the direction, which is 243 degrees counterclockwise from the +x axis. I also solved part (b). Thank you for your help!

Last edited: Sep 10, 2006