Potential on a conducting uncharged sphere due to a ring. [closed]

Question

A thin conducting uniformly charged ring has charge $Q$ ,radius $ R $ is placed co-axially with a conducting uncharged sphere of same radius $R$. The distance between centre of sphere and centre of ring is $d$.($d$ is greater than $R$)

1. Potential of sphere is :
2. The electric potential at centre of sphere due to charges induced on sphere is :

My Approach : According to me the answer to the first question is $$ \frac{kQ}{\sqrt{R^2 + d^2}} $$ as sphere has no charge on it.

For second question I applied the property of conductors that $E_(ext) + E_(ind) =0$ . Hence the answer for it will be $$ -\frac{kQ}{\sqrt{R^2 + d^2}} $$

First of all please tell me whether my answer and approach are correct or not . If not please explain the right approach.

Answer 1

Assuming you are talking about a solid conducting sphere, the total potential at the centre $\phi_o$ = potential due to ring at centre $\phi_r$ + potential due to induced charges on sphere at centre $\phi_s$. Note the $\phi_s$ is zero, since $\phi_s$ =K $\int$ $\frac{dq}{R^2}$, which is clearly zero since the sphere is uncharged. So the answer to your second question is zero. Putting this back into the expression for total potential at centre, $\phi_o$ = $\phi_r$ , i.e: the potential at the centre is due only to the ring. Since the conductor is an equipotential, this must also be the potential at the surface. SO find the potential at the centre due to the charged ring(your job) and that is the answer to the first question.