Question

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

• A. \(\frac{Q}{4\pi \epsilon_oR}\) and Zero
• B. \(\frac{Q}{4\pi \epsilon_oR}\;and\;\frac{Q}{4\pi \epsilon_oR^2}\)
• C. Both are zero
• D. Zero and \(\frac{Q}{4\pi \epsilon_oR^2}\)

Answer 1

The Correct Option is A

To solve the problem regarding the electric potential and electric field at the center of a conducting sphere with radius \(R\) and charge \(Q\), let's break it down using physics concepts for electric fields and potentials:

1. When a charge \(Q\) is given to a conducting sphere, the charge is uniformly distributed on the surface of the sphere. According to the properties of conductors in electrostatic equilibrium, the electric field inside a conductor is zero. This implies that the electric field at the center or any point inside the sphere is zero.
2. The electric potential inside a conductor is constant and is equal to the potential on the surface of the conductor. The potential \(V\) on the surface of a sphere of radius \(R\) and charge \(Q\) is given by: V = \frac{Q}{4\pi \epsilon_o R}
3. Since the electric field inside the sphere is zero, there is no potential difference between any two points inside the sphere, including the center. Thus, the potential at the center is the same as that on the surface, which is: \frac{Q}{4\pi \epsilon_o R}
4. Therefore, the electric field at the center is zero, and the electric potential at the center is: \frac{Q}{4\pi \epsilon_o R}

Thus, the correct answer is:

\(\frac{Q}{4\pi \epsilon_oR}\) (Electric Potential at the center) and Zero (Electric Field at the center).