Electric Field induces Surface Charge in Conductor

Physical Law

Let $B$ be a body made out of an electrically conducting substance.

Let $B$ be in the shape of a slab with two parallel surfaces $P_1$ and $P_2$.

Let $B$ be placed in an electric field $\mathbf E$ acting perpendicular to $P_1$ and $P_2$.

Then $B$ will develop a surface charge on both $P_1$ and $P_2$ of a polarity such as to oppose the electric field being applied.

Informal Explanation

When the electric field $\mathbf E$ is first applied, there exists a macroscopic electric field $\mathbf E'$ throughout $B$.

Under the influence of $\mathbf E$, the conduction electrons move by Coulomb's Law towards the positive source of $\mathbf E$ and away from the negative source of $\mathbf E$.

Hence the conduction electrons make $P_1$ and $P_2$ charged in the opposite polarity to the electric field at $P_1$ and $P_2$.

From Distribution of Macroscopic Electric Charge within Conductor, it is not possible for there to be different (macroscopic) electric fields throughout $B$.

Hence, away from the surfaces $P_1$ and $P_2$, there is no difference in electric charge throughout the interior of $B$.

$\blacksquare$

Also see

• Definition:Induced Charge: the name for the surface charge which develops.

Sources

• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.3$ Electric Fields in Matter: $1.3.3$ The macroscopic electric field