Why Does a Conducting Shell Show Zero Electric Flux Despite an Internal Charge?

[JamesL]

Here is the problem:

Consider an uncharged, conducting hollow spherical shell. The electric field on the inside of the surface of the spherical shell is measured to be directed towards the inner shell wall and varies in magnitude over the shell's inside surface. It is known that the only charge in the hollow cavity inside the spherical shell is a point charge with magniuted q.

---------------------------

I've already concluded that the sign of point charge q is positive, and that the charge is not located at the center of the spherical shell.

Now the two next questions kind of stump me.

1) What is the net electric flux through the sherical shell?

a)flux = q/(2*Epsilon)
b)flux = 0
c)flux = (2*q)/epsilon
d)flux = q/epsilon
e)flux = 2*q
f)flux = q/2
g)flux = q

According to my physics textbook, "the net flux through any closed surface surrounding a point charge q is given by q/epsilon and is independent of the shape of that surface."

So naturally my first answer was d (flux = q/epsilon)... but my online homework service counted this incorrect.

What am i missing guys?

------------------------

The next question i am not really sure how to go about solving.

2)What can you say about the charge distribution on the outside surface of the spherical shell?

a)The charge distribution is negative and is not uniform.
b)The charge distribution is 0.
c)The charge distribution is negative and is uniform.
d)The charge distribution is positive and is not uniform.
e)The charge distribution is positive and is uniform.

Any help would be greatly appreciated.

 

[Wong]

1) The question is tricky. The spherical shell is not a "surface" It has thickness and so it has "volume". I think the question may want to ask you what is the flux into/out of this volume?

2) Presumably there will be some negative charges on the inner surface, and so there will be some positive charges on the outer wall. Can the positive charge in the spherical shell and the negative charges on the inner wall exert any *net* force on the positive charges on the outer wall? It may help if you think about whether there can be any electric field inside a conductor (in static case).

 

[M98Ranger]

For the first question, the correct answer is actually b) flux = 0. This is because the electric field inside the shell is directed towards the inner wall, meaning it is perpendicular to the surface of the shell. Therefore, the electric flux through the surface is 0 since the dot product of the electric field and the surface normal is 0.

For the second question, it is not possible to determine the charge distribution on the outside surface of the shell with the given information. This is because the electric field inside the shell is dependent on the distribution of the point charge inside the cavity. Without knowing the exact location and magnitude of the point charge, we cannot determine the charge distribution on the outside surface.