Question

A conducting sphere of radius 'R' is given a charge 'Q' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ε₀ = permittivity of free space] ______.

Options

• zero and \[\frac{Q}{4\pi\varepsilon_{0}R}\]

• \[\frac{Q}{4\pi\varepsilon_{0}R^2}\] and zero

• \[\frac{Q}{4\pi\varepsilon_{0}R}\] and \[\frac{Q}{4\pi\varepsilon_{0}R^2}\]

• zero and zero

Answer 1

A conducting sphere of radius 'R' is given a charge 'Q' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ε₀ = permittivity of free space] zero and \[\frac{Q}{4\pi\varepsilon_{0}R}\].

Explanation:

For a conducting sphere, all charge resides on the surface, so the electric field inside (including the centre) is zero by Gauss's Law, while the potential everywhere inside equals the surface potential \[\frac {Q}{4πε_0R}\]​ since no work is done moving a charge inside a conductor.