A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the cent

Question

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are:

Accepted Answer

1. **Electric Field:** According to the properties of electrostatics of conductors, the net electrostatic field inside a charged conductor is zero everywhere. This applies to the entire volume, including the centre. Thus, $E_{center} = 0$ [1].
2. **Electric Potential:** Since the electric field inside is zero ($E = -dV/dr = 0$), the potential is constant throughout the volume of the conductor and has the same value as on its surface. The potential on the surface of a conducting sphere of radius $R$ and charge $Q$ is given by $V = \frac{1}{4\pi\varepsilon_0}\frac{Q}{R}$. Therefore, the potential at the centre is also $\frac{Q}{4\pi\varepsilon_0 R}$ [2], [1].

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