Electric Potential

Charges are induced on the inner walls of the conductor due to the charge q.

The net induced charge is zero due to Gauss Theorem.(Since electric field inside a conductor is always 0).

Since it is a conducting sphere,
potential at any point on the sphere (V)= potential at the center

V = potential at the center due to q + that due to induced charges
=q4πε₀r+Σq_i4πε₀R

Where the second term is due to induced charges.
Since these charges are all at a distance of R from the center and net induced charge is 0 (or Σq_i=0)

Σq_i4πε₀R=0

Therefore,

V = q4πε₀r

B.