MHT CET202520 Apr 2025Morning ShiftPhysicsElectrostaticsActual
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 [ ₀= permittivity of free space]
Options
- Azero and Q 4 ₀ R
- BQ 4 ₀ R^2 and zero
- CQ 4 ₀ R and Q 4 ₀ R^2
- Dzero and zero
Correct answer
A. zero and Q 4 ₀ R
Step-by-step solution
Electric Field at the Center For a conducting sphere in electrostatic equilibrium, all charge resides on its outer surface. Consider a Gaussian surface with radius r Electric Potential at the Center The potential is constant throughout a conductor. On the surface, V_ surface = Q / (4 ₀ R) , so the potential at the center is identical: V_ center = Q / (4 ₀ R) . The electric field is zero and the potential is Q / (4 ₀ R) , corresponding to option A .