For a uniformly charged spherical shell, which statement about the potential inside the shell is true?

For a uniformly charged spherical shell, which statement about the potential inside the shell is true?

• A. The potential inside is zero
• B. The potential inside varies with position
• C. The potential inside is a constant equal to kQ/R
• D. The potential inside is undefined

Answer: (C)

Inside a uniformly charged spherical shell, the electric field is zero everywhere inside. When the field is zero, moving anywhere inside does no work, so the electric potential does not change with position—it stays constant throughout the interior. Because potential is continuous at the shell’s boundary, this interior constant must match the potential at the surface. For a shell of radius R carrying total charge Q, the surface (and exterior) potential is kQ/R, where k = 1/(4πε0). So the interior potential is the same constant: V = kQ/R.

Inside a uniformly charged spherical shell, the electric field is zero everywhere inside. When the field is zero, moving anywhere inside does no work, so the electric potential does not change with position—it stays constant throughout the interior. Because potential is continuous at the shell’s boundary, this interior constant must match the potential at the surface. For a shell of radius R carrying total charge Q, the surface (and exterior) potential is kQ/R, where k = 1/(4πε0). So the interior potential is the same constant: V = kQ/R.