P20-090 – Electric Field at the Surface of a Conductor

Electric Field at the Surface of a Conductor

Conductors are materials that contains free charges meaning that these charges are free to move freely through the conducting material. Consequently, these charges will respond to an applied electric field and move within the conductor under the effect of the resulting electric force. This charge separation creates an induced electric field inside the conductor that opposes the applied electric field so that the total electric field in the conductor is zero.

Therefore, it follows that

• The electric field is zero inside conducting material in electrostatic equilibrium. For example, if a proton is placed next to a conductor, the electric field it creates separates the charges in the conductor which induces an electric field ${\overrightarrow{E}}_{ind}$. This separation will continue until ${\overrightarrow{E}}_{ind}$ cancels the electric field ${\overrightarrow{E}}_{+}$ so that the electric field inside the conductor is $0$.

• If a conductor in electrostatic equilibrium carries a net charge, then it must reside on its surface. Indeed, the charges will repel and move as far as possible from each other to minimize repulsion. As a consequence, free charges tend to accumulate more in regions where the conductor is pointy (smaller radii of curvature) and less where the conductor is flatter (larger radii of curvature). In the figure below, this can be seen at the left and right edges of the elliptical conductor: the radius of curvature is smaller there than at the top and bottom and therefore the charge density is greater.

• The electric field at a conductor’s surface is perpendicular to the surface and has a magnitude $E=\sigma /{\varepsilon }_0$. Thus, at locations where the conductor curves sharply, the electric field is stronger than at locations where it curves softly.