# Electric field outside a conductor

Say there is a conducting cylinder in a uniform external field. The charges on the cylinder surface will distribute and create a surface charge density.

Is there any reason the charge density would generally be uniform across the surface? We know: $$\sigma = \Delta E \cdot \varepsilon_0 \cdot \hat{n}$$ But what physically ensures the electric field just outside the conductor is equal in magnitude all around the encompassing circle?

• Charge density can't be uniform across the surface in this case. If originally the total charge of conductor was 0 it will remain 0 after we put the conductor into external field. Charges can't accumulate inside the conductor, so to total charge of the surface is still zero. And if density is uniform - it must be zero everywhere. – lesnik May 27 at 6:49