Final answer:
Correct option: a. 1/4πε0 Q/R.
The electric potential at a distance 'x' inside a conducting sphere with charge Q is constant and equal to the potential on the surface; thus, the answer is 1/4πε_0 Q/R.
Step-by-step explanation:
The electric potential at a distance x from the centre, inside a conducting sphere having a charge Q and radius R, is due to the spatial distribution of the charge on the conducting sphere. Inside the sphere, the electric field is zero because the charges redistribute themselves on the surface of the conductor to cancel out any internal field. By Gauss's law, when a spherical symmetric charge causes no electric field in a region, the electric potential within this region remains constant and is equal to the potential on the surface of the conductor.
Therefore, the electric potential inside the sphere does not depend on x, and is the same as on the surface of the sphere. The formula for the potential on the surface of a charged conducting sphere is V = 1/4πε0 Q/R. Hence, the correct answer for the electric potential at a distance x from the centre of a conducting sphere with charge Q is option a. 1/4πε0 Q/R.