1
$\begingroup$

Question as written in textbook: "Figure 1 illustrates a nested arrangement of four cylindrical conductors (seen side-on in cross-section) in which the cylinders are separated by electrical insulators. A body carrying a charge of –Q is suspended in the smallest cylinder."

Figure 1

Figure 1

This results in the following charge distribution (answer from textbook):

Figure 2

Figure 2

(note, the charges are meant to be on the surface of the conductor)

My question: How does having insulators between the conducting cylinders affect the problem, and what (if anything) would be different about the answer shown in Figure 2 if the material marked insulator was replaced with a conductor?


My thought process:

  1. I initially thought the insulator would result in only the inside cylinder (separated from the charged sphere without any insulators in the way) becoming charged, and the insulator that separates the first cylinder from the second would stop any polarization of the second cylinder. But due to the answer shown in Figure 2, this is not the case.

  2. If I replaced the conducting cylinders and insulators with one big conductor, I would get the same result as Figure 2.

enter image description here

The insulator behaves as per the image below: But is this any different to how a conductor would behave (i.e. if the insulator in the question was replaced with a conductor?)

  • The picture shows for the conductor the side near the negative charge will become positive, and the side opposite the negative charge will become positive.
  • Similarly, for the insulator, the side near the negative charge will become positive, and the side opposite the negative charge will become positive (however, this occurs in small segments as the electrons are not free to move like in a metal)

Insulator (Image Source)

$\endgroup$
2
$\begingroup$

What the insulator does in this problem is keeping the shells electrically neutral. So that any positive charge built on the inner wall will be balanced with the negative charge on the outer wall. And your figure (unlabeled) of replacing the incubator layers with conductors is correct.

$\endgroup$
1
$\begingroup$

An insulator can be thought of as an extreme form of a dielectric. It does not result in decreasing the net electric field due to displacement of charge/ polarisation. So, the main reason the question mentions insulation is that you don't need to consider cancellation of the electric field in the region at all. Just pure E from the cylinders. Connecting all the cylinders to form a block is correct, but what the question wants you to understand is how each part contributes to net polarisation of a bulk conductor.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.