# Spherical Conducting Shell

• dipolarBear
In summary, a conducting sphere with charge +Q will induce a -Q charge on the inner surface of a surrounding conducting shell, and a +Q charge on the outer surface. If a point charge is placed outside the shell, the net charge on the inner surface of the shell will be -2Q. This can be solved using the equation E=\frac{F}{q} to determine the electric field created by the charges. If the sphere and shell are not concentric, the net charge on the inner surface will remain the same.

## Homework Statement

(1)A conducting sphere w/ charge +Q is surrounded by a spherical conducting shell.
What is net charge on inner surface of the shell?

(2) A charge is placed outside the shell.
What is the net charge on the inner surface now?

(3) What if the shell and sphere are not concentric, will this change your answers?

## Homework Equations

$$E=\frac{F}{q}$$

## The Attempt at a Solution

I've done some reading from 2 different books on the same topic, and I've gotten some info from other similar problems on PF. I still feel like I need work on this section, any help is appreciated. Thanks.

(1) The inner sphere will induce a -Q charge on the interior surface of the shell, and a +Q on the outer surface.

(2) This one has me stumped: I figure that the interior surface of the shell must become -2Q with the introduction of a point charge outside. I think since its a conducting shell, the charge inside must be zero, and as a result it must create an e-field that can counter the fields of both charges, in order to remain neutral. Could I use the equation $$E=\frac{F}{q}$$, to help me solve this problem?

(3) If the sphere and shell are not concentric, the results should be the same since we're dealing with the net charge on the interior surface.

In (2), you seem to assume that the external charge is equal the internal. That is not how the problem is stated.

Sorry, the problem uses q for the point charge outside, and +Q for the charge of the sphere. I'm not exactly sure if they're suppose to be the same, but if we assumed they were not equivalent, would the charge of the interior surface in (2) be -(Q+q)? Thanks

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