# Do electric fields in a conductor go to zero in all instances?

• BucketOfFish

#### BucketOfFish

In the absence of external forces, the electric field inside a conductor is supposed to go to zero. This is because if any field were to exist, then the charges in the conductor would experience force and continue moving until they canceled the field.

However, is it true that for any system a certain charge distribution always exists which can successfully cancel all electric field? Could it not be the case that no such configuration exists, forcing the surface charges to remain in constant motion?

Are you aware of any experimental, physical, or mathematical explanation as to why field should always be cancelled?

## Answers and Replies

As far as I understand, such a charge distribution (a) always exists; and (b) is unique. This is a boundary value problem for Poisson's equation and existence and uniqueness of solutions (given completely specified boundary conditions) is a theorem.

If the charges in constant motion accelerated, they would radiate away energy, causing their motion to eventually dampen down. Therefore, particles in perpetual constant motion would need to have constant velocities, which is impossible in a real, finite, material.

In principle, you could have an electric field that was so strong, there simply weren't enough charges available to fully cancel it out. This would be a stationary equilibrium. In practice, I'd imagine you'd have some sort of ionization or breakdown in the material, although that's just a shot in the dark.

1 person
Thanks for the answers! Leveret, you say that it's not physical to have particles in constant motion in a material, but from what I know about superconductors, they can hold constantly circulating currents for very long periods of time without any energy input. Do you know what is happening in that instance?

More accurately: The electric field in a perfect conductor at equilibrium is zero. There are no perfect conductors in real life, so the field always pokes in a bit. But this is an excellent approximation for many conductors. Also, you have to have perfect equilibrium to give all the excess charge time to migrate to the surface.

"However, is it true that for any system a certain charge distribution always exists which can successfully cancel all electric field?" That's the definition of a perfect conductor. If it couldn't provide the free charge to cancel the fields it would not be a conductor.