Electrostatics - Metal Shell Question

[Cazicami]

Homework Statement

Consider a thick metal shell with inner radius a = 2cm and b = 4cm. The shell carries no net charge. A point charge of q = 3nC is placed at the centre of the shell. Find the total charged induced on the inner boundary of the shell. Find the total charge induced on the outer boundary of the shell.

5 marks.

Homework Equations

E = q/4∏ ε0 r^2 - I think.

The Attempt at a Solution

My attempt was to use the equation above to work out the charge at each radius. However the answer I get is very wrong. The solutions simply state,
"Obviously, the charge induced on the inner boundary is -3nC, while the charge induced on the outer boundary is 3nC." So this is making me think I have missed something. Considering the value I calculated was E = 67438NC^-1


Any help you can give would be great, as I am studying for my resits.
Thanks

 

[BruceW]

you have calculated the electric field at the inner radius due to just the charge in the middle. But the question does not ask for this. And this is not really important, either. Think about what happens inside a conductor in electrostatic problems. You have probably used this concept before.

 

[Cazicami]

Thanks, Sorry it was such a noob question, but I have now found it in my notes.

Thanks so much for your help.

Cazi