Question

Why the answer for (a) (i) is -Q and (ii) is +Q I am so confuse can anyone explain?thanks

Answer 1

Gauss law and the fact that there is no static electric field in the bulk of a conductor gives you (i), while (ii) follows if (and only if) you assume the hollow sphere to be electrically neutral.

Explanation:

The charge on a conductor resides entirely on its surface.

Imagine a sphere passing through the point B and centered at O. Its surface is completely inside the bulk of the conductor, where there can be no electric field (at least in the static condition). So the flux of the electric field across this surface must vanish, and by Gauss law - so must the net charge inside it. Now, the net charge inside this sphere has two contributions - the charge `+q` at O, and the charge on the inner surface of the conducting sphere. Since the net charge here is zero, the charge on the innner surface must be `-q`.

The charge on the outer surface of the conducting sphere is `+q` only if you make the assumption that the hollow sphere is neutral overall.