A uniformly charged thin spherical shell of total charge \( q \) and radius \( R \) has an electric potential at an internal point at a distance \( r \) (\( r < R \)) equal to:

For a uniformly charged thin spherical shell of radius \( R \) and total charge \( q \), the electric field inside the shell (\( r < R \)) is zero (\( E = 0 \)). Since the electric field is related to the electric potential by \( E = -\frac{dV}{dr} \), a zero electric field means that the electric potential remains constant throughout the interior region and is equal to its value at the surface. Therefore, the electric potential at any internal point where \( r < R \) is given by \( V = \frac{1}{4\pi\varepsilon_0} \frac{q}{R} \).