What is the electric field inside a conductor in electrostatic equilibrium?

What is the electric field inside a conductor in electrostatic equilibrium?

• A. E = ∇φ
• B. E = 0
• C. E = constant nonzero
• D. E = σ/ε0

Answer: (B)

The key idea is that free charges in a conductor rearrange themselves so that the interior feels no electric force. If there were any electric field inside, the charges would move under that field, creating currents until the field is canceled. This rearrangement leaves the interior with a constant electric potential, so the gradient of the potential is zero and the electric field, which is E = -∇φ, vanishes inside. A nonzero constant field would mean continuous movement of charges, which can’t happen in electrostatic equilibrium. The statement saying the field equals the gradient of the potential is not appropriate here, and inside a conductor the potential is constant, making any interior field zero.

The key idea is that free charges in a conductor rearrange themselves so that the interior feels no electric force. If there were any electric field inside, the charges would move under that field, creating currents until the field is canceled. This rearrangement leaves the interior with a constant electric potential, so the gradient of the potential is zero and the electric field, which is E = -∇φ, vanishes inside. A nonzero constant field would mean continuous movement of charges, which can’t happen in electrostatic equilibrium. The statement saying the field equals the gradient of the potential is not appropriate here, and inside a conductor the potential is constant, making any interior field zero.