Three Charges inside a Metal Sphere

[student49]

Homework Statement

Three fixed point charges of +2 nC, −3 nC and +4 nC are located inside a thin un-
charged metal spherical shell of radius R = 2 cm. Calculate the strength and direction of the electric field at position P, being 10 cm from
the centre of the shell.
Hint
Think Gauss’s Law and carefully consider the conditions within the thickness of the
metal shell and what this tells you about the charge enclosed. Think about concentric
spherical Gaussian surfaces at various radii, and what you can conclude about the net
charge within them. Do NOT simply try and sum up the E~ -fields from the charges,
this does not work here since there is a spherical metal shell in the way.

Relevant Equations

E = Q/(4πE0r^2)

E0 is air permittivity

I know that for a conductor the charge is uniformly distributed and the electric field is zero inside the shell. However, I am not sure how to calculate the charge inside the shell so I can know the electric field.

 

[TSny]

Welcome to PhysicsForums

I know that for a conductor the charge is uniformly distributed

The charge on a conductor does not have to be uniformly distributed.

and the electric field is zero inside the shell.

Yes. E = 0 at each point within the conducting material of the shell. Can you use this fact to deduce the net charge on the inside surface of the shell?

 

[kuruman]

Yes. E = 0 at each point within the conducting material of the shell. Can you use this fact to deduce the net charge on the inside surface of the shell?

Did you mean to say "... to deduce the net charge on the outside surface of the shell?"

 

[TSny]

Did you mean to say "... to deduce the net charge on the outside surface of the shell?"

I was thinking of first deducing the net charge on the inner surface and then using that to deduce the net charge on the outer surface.

 

[kuruman]

I was thinking of first deducing the net charge on the inner surface and then using that to deduce the net charge on the outer surface.

Yes, as a first step, that would be the way to proceed. Finding the charge on the outer surface is very easy in this case because the shell carries zero net charge and can be done in one step. Not saying where you were headed with your suggestion made me wonder. All is good.