# Calculating Induced Charge on a neutral sphere due to a point charge outside

I was able to solve option A conceptually- at centre of sphere, potential due to induced charge on sphere is 0 as left and right hemispheres' induced charge is same and opposite. So only potential due to point charge needs to be calcuated.

But I am not getting how to solve for option D. Do I calcuate the induced charge on the sphere (which is not same throughout), or can I solve using gauss theorem, or any other method which I could not think of?

1) Since, the potential at center of neutral conducting sphere is $$\cfrac{q}{4\pi\epsilon o(d +r)}$$ as you mentioned.
$$V_{q}$$ + $$V_{sphere}$$ $$=$$ $$\cfrac{q}{4\pi\epsilon o(d +r)}$$ ----$$\mathrm{I}$$
since $$V_q$$ at point B is $$\cfrac{q}{4\pi\epsilon o d}$$, putting it in $$\mathrm{I}$$
$$V_{sphere}$$ $$=$$ $$\cfrac{-qr}{4\pi\epsilon o(d + r)d}$$