For a uniformly charged hollow spherical shell, what are the electric field values outside and inside?

For a uniformly charged hollow spherical shell, what are the electric field values outside and inside?

• A. Outside: E = kQ/r^2; Inside: E = 0; Potentials: constant inside
• B. Outside: E = kQ/r^2; Inside: E ≠ 0; Potentials vary inside
• C. Outside: E = 0; Inside: E = kQ/r^2; Potentials: constant inside
• D. Outside: E = kQ/(r+R)^2; Inside: E = 0; Potentials: linear inside

Answer: (A)

The key idea is symmetry and Gauss’s law. For a hollow spherical shell with all charge on its surface, the electric field inside the shell must be zero, because any Gaussian surface drawn inside encloses no charge and thus has zero net flux. Outside the shell, all the charge acts as if it’s concentrated at the center, so the field behaves like a point charge: E outside = kQ/r^2 (radial, outward for positive Q). Since the electric field is zero inside, the electric potential is the same everywhere inside the shell—it’s constant. That constant equals the surface potential, and the potential outside falls off as V(r) = kQ/r with V → 0 as r → ∞. So the correct description is: outside field E = kQ/r^2; inside field E = 0; inside potential is constant. The other statements conflict with Gauss’s law, the zero interior field, or use an incorrect outside-field expression.

The key idea is symmetry and Gauss’s law. For a hollow spherical shell with all charge on its surface, the electric field inside the shell must be zero, because any Gaussian surface drawn inside encloses no charge and thus has zero net flux. Outside the shell, all the charge acts as if it’s concentrated at the center, so the field behaves like a point charge: E outside = kQ/r^2 (radial, outward for positive Q).

Since the electric field is zero inside, the electric potential is the same everywhere inside the shell—it’s constant. That constant equals the surface potential, and the potential outside falls off as V(r) = kQ/r with V → 0 as r → ∞.

So the correct description is: outside field E = kQ/r^2; inside field E = 0; inside potential is constant. The other statements conflict with Gauss’s law, the zero interior field, or use an incorrect outside-field expression.