Q:

Electric field and electric potential due to induced charges on the inner surface of cavity at outside point is?

In the shown figure the conductor is uncharged and a charge q is
  placed inside a spherical cavity at a distance a from the
  centre(C).Point $P$ and a charge $+Q$ are shown.

I want to find electric field due to induced charges on the inner
 surface of cavity at point $P$.
I feel the $q$ charge inside the shell will induce $-q$ charge on the inner surface of the shell.So the inner surface of the shell will induce an electric field of magnitude $\dfrac{q}{4 \pi \epsilon_o c^2}$ at point $P$.Is my assumption correct?
Also,I want to find the electric potential due to charges on the inner surface of the cavity and $q$ at $P$.
I think it should be $\dfrac{k(-q)}{c}+\dfrac{k(q)}{x}$ where $x$ is distance between charge $q$ and point $P$.But the answer given in my textbook is $0$.I've no idea why!Its seems very strange.Can someone clarify?

A:

Electric field due to induced charge$(-q)$ on the inner cavity surface 'alone' cannot be calculated as the charge distribution is not known(since $q$ is not at the centre). 

(If you want to find out the net electric field at $P$, then it is not due to the charge $q$ and the induced charges in the inner surface of the cavity(They cancel each other out; this is a property of conductors). It is actually due to $+q$ induced on the outer surface of the conductor due to the induced charge $-q$ on the spherical cavity. Also, you have to consider the charge induced to $Q$ on the outer surface of the conductor to find the net electric field at $P$)

Potential is zero(due to $q$ and the induced $(-q$) because of the property of the conductor I mentioned(the charges inside a cavity inside the conductor are virtually hidden from the outer world; their field is always zero outside the conductor; their effect is seen only due to induced charges on the outer surface of the conductor)

