Drawing Electric Field Lines and Equipotential Lines

[jumbogala]

Homework Statement

You have two metal electrodes, not touching each other. One is a circle and one is like a thin plank. The plank is at a lower electric potential.

Draw electric field lines between them, including direction.

Draw equipotential lines in the space between the electrodes as well.

Homework Equations

The Attempt at a Solution

I'm not sure how to do this because I've never drawn electric field lines for things that are not just charged objects. What does the circle being at a lower potential tell you?

Does it mean that one object will act like a negative charge and the other like a positive charge?

Let's start with that because once I can draw the electric field lines, I think I can draw the equipotential lines (just 90 degrees everywhere to the field lines).

 

[Delphi51]

Yes, the one with the higher potential is positive with respect to the one with the lower potential. Remember that E field lines generally emerge perpendicular to the surface of the electrode.

 

[jumbogala]

So what I'll do is treat the circle electrode as positive and the plank electrode as negative.

The only problem now is figuring out how the electric field lines from each object interact with each other. I can draw them for each object separately, but in the space right between the two objects I'm not sure. Just gradually change the field lines from one type to the other?

Would the charges have equal magnitudes (but opposite signs)?

 

[Delphi51]

Gradual is good, but the basic idea is to draw lines from the circle to the plank. Start with one going straight from the closest point on the circle to the middle of the plank. The others will tend to bulge out as they leave the circle perpendicular to its surface.

 

[jumbogala]

So it should look similar to how 2 point charges would look, then.

Thanks, I think I can do it now!

 

[jumbogala]

I finished drawing it. It seems like the equipotential lines should mimic the shape of the electrode.

The equipotential lines around the circle do, but not around the plank. The ones around the plank look like really elongated ovals: is that okay or should it be more rectangular?

 

[Delphi51]

I'm not sure about the plank. It does seem to me that the lines should emerge perpendicular to it. The E field will be particularly strong at the corners, so the lines will be close together there.