Shape of equipotential surface in 3d

[Lochikilebor]

Homework Statement

Give answer

Relevant Equations

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We have 2 infinite cylinders, need to find out which shape will equipotential surface be in 3D.

 

[Steve4Physics]

Hi @Lochikilebor. Welcome to Physics Forums.

The way it works here is that we help/direct/advise you so that you can work out the answer for yourself. (Take a look at some of the other threads.) We don't do the problem for you!

Read the forum rules here: https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

So to start, you need to give your own thoughts, e.g. what you've tried, any relevant working, why you're stuck.

By the way, the question is not clear. Do you need to produce a drawing of the equipotentials? Or a description? Or equations? You haven't posted the full original question exactl;y as set, so we can't tell.

[Edited -typo's.]

 

[Lochikilebor]

No, i only need to answer the question - which form will be the equipotential surface in 3d. I tried to imagine this some ways - like cone or spherical elongated circles, but its wrong, so teacher give me the 2d drawing:

Based on this drawing, i just need to give an answer, what shape will the equipotential surface in 3d of two infinite parallel cylinders be? According to the teacher's suggestion, the answer should be too simple, I just can't get to it.

 

[Steve4Physics]

No, i only need to answer the question - which form will be the equipotential surface in 3d. I tried to imagine this some ways - like cone or spherical elongated circles, but its wrong, so teacher give me the 2d drawingBased on this drawing, i just need to give an answer, what shape will the equipotential surface in 3d of two infinite parallel cylinders be? According to the teacher's suggestion, the answer should be too simple, I just can't get to it.

Try a couple of easier questions first:
1) What shape are the equipotential surfaces around a uniformly charged sphere?
2) What shape are the equipotential surfaces around a single uniformly charged infinite cylinder?

 

[Lochikilebor]

Around a uniformly charged sphere it must be sphere shapes surface, so the same single uniformly charged infinite cylinder must have cylinder shape surface...?

 

[Steve4Physics]

Around a uniformly charged sphere it must be sphere shapes surface, so the same single uniformly charged infinite cylinder must have cylinder shape surface...?

Yes. That’s right.

On a (2D) drawing for a charged sphere, we would show equipotential lines which would be circles. In real (3D) life, we actually have spherical equipotential surfaces, (because we have spherical symmetry).

On a (2D) drawing for a charged infinite cylinder, we would show equipotential lines which would also be circles. But in real (3D) life, we now have cylindrical equipotential surfaces (because we have cylindrical symmetry).

Note that for the cylinder, we could pick any 2D equipotential circle and imagine 'sliding' it in the direction parallel to the cylinder's axis. Some 3D imagination is needed. The moving circle then ‘sweeps out’ a cylindrical equipotential surface as it travels along.

(Imagine a hoop laying flat on a table. You move the hoop vertically upwards, keeping its plane parallel to the table. The hoop 'sweeps' along a cylindrical surface.)

If all that makes sense, you can go back to your Post #3 diagram. Imagine sliding the diagram along in the direction parallel to the cylinders' axes. Each dotted line (equipotential line) 'sweeps out' an equipotential surface.

The problem is then how to describe the shape of this surface in suitable words.