# Electrostatic Fields inside Charged Conductors

Homework Helper
Gold Member
Hi,

I'm having a little trouble understanding why the field inside a charged conductor must be zero. I understand that when the charge is put on the conductor, they spread out to the surface such that the surface becomes an equipotential. But why does that mean the field inside must be zero?

## Answers and Replies

Hootenanny
Staff Emeritus
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What would happen (to the free charges) if there was a net electric field inside the conductor?

(I'm assuming that the charged conductor is in equilibrium here).

Homework Helper
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all the free charges are on the surface right? so any fields within the conductor wouldnt affect the charges?

Hootenanny
Staff Emeritus
Science Advisor
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all the free charges are on the surface right?
Correct, but what about the conduction charges?

Homework Helper
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They would move. But we assumed equilibrium, therefore there can be no fields inside in equilibrium?

Hootenanny
Staff Emeritus
Science Advisor
Gold Member
They would move. But we assumed equilibrium, therefore there can be no fields inside in equilibrium?
Sounds good to me I think of a charged conductor as a capacitor's plate. If capacitance is zero, electrons in the plate have zero energy. (U=CV^2)

If a capacitor has capacitance and a charge of one volt: an external electron that passes through the capacitor's voltage field gains an electron volt and the capacitor's energy decreases by one volt. Did the external electron decrease energy per point charge in the capacitor w/o decreasing the number of point charges in the capacitor? How?

Could you also argue that if there was charge on the inside you'd have electrons constantly accelerating creating a bigger and bigger current, thus infinitely heating the conductor, which cannot be the case?