# Is the electric field within a cavity of a conductor affected only by other charges within the cavity?

The following exercise below confuses me:

I don't understand why the answer is (A). I seem to be realizing empirically that the electric field at points inside a cavity in a conductor such as this is only affected by charge inside the cavity like $$+q_c$$ rather than charges outside of it like $$+q$$. However, I can't justify this physically.

If my assumption is correct, why is this? If it's not, what's the proper thinking here? If our point of observation wasn't along a line between the two charges, how would this change things?

• Gauss law might be able to help if you are already able to prove spherical symmetry of field – Aditya Garg May 1 at 17:37
• Is this a n exercise from a text book? – my2cts May 1 at 22:07
• No, it is not - to my knowledge. – sangstar May 2 at 9:17

Because of superposition the effect of both charges can be discussed separately. The correct answer is indeed A. The presence of the conductor does not affect the contribution of $$q_C$$ to the field, although it induces a charge $$-q_C$$ on the inner surface and $$+q_C$$ on the outer. The outer charge, $$q$$, induces a charge distribution $$\rho$$ on the outer surface of the conductor such that inside the conductor the field is cancelled. The surface integral of $$\rho$$ sums vanishes. Its value can be found from Gauss's law, $$\vec \nabla \cdot \vec E = \rho / \epsilon_0$$. Inside the conductor the field is zero, no charge distribution is induced on the inner surface and no field contribution exists in the inner cavity.
Consider this situation: there is no cavity and no $$q_C$$, only a copper sphere and an external point charge $$q$$.
You know that in this situation the charges in the conductor rearrange so that the field in the conductor becomes zero. This is done by means of a non-uniform surface charge density $$\sigma$$, whose generated field in the inner of the conductor cancels with $$q$$'s field. This charge is located only on the surface of the sphere and its total is zero (we' re supposing a neutral conductor).
Finally, the effect of adding $$q_C$$ in the cavity can be simply figured out by means of the principle of superposition.