# Electric Field at the Surface of a Conductor

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Physik
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Electric Field at the Surface of a Conductor

### Nächstes Video23.11: Electric Field of a Non Uniformly Charged Sphere

Consider a metallic earth wire placed on the top of an electric transmission tower. When an electrostatically charged cloud looms over this transmission tower, the metallic wires develop an induced surface charge.

The electrostatic equilibrium of the conductor ensures that the electric field outside the conductor is perpendicular to its surface; while it vanishes within the conductor.

The electric field on the surface of this conductor can be calculated, assuming an infinitesimal cylindrical Gaussian surface through the conductor.

Along the curved surface, the flux is zero, whereas, at the flat end, the flux equals electric field times area.

Under the assumption that surface charge density is constant, the total charge enclosed by the flat Gaussian surface equals the surface charge density times the surface area.

Applying Gauss' Law, the total flux equals the charge enclosed divided by the permittivity of the vacuum.

Rearranging the terms, the magnitude of electric field at the conductor's surface is obtained.

Hence, the electric field at the surface of the conductor is dependent only on its surface charge density.

## Electric Field at the Surface of a Conductor

Consider a conductor in electrostatic equilibrium. The net electric field inside a conductor vanishes, and extra charges on the conductor reside on its outer surface, regardless of where they originate.

In the 19th century, Michael Faraday conducted the famous ice pail experiment to prove that the charges always reside on the surface of a conductor. The experimental set-up consists of a conducting uncharged container mounted on an insulating stand. The outer surface of the container is connected to an electroscope. The electroscope deflects when a positively charged metal ball with an insulating thread is lowered into the container without touching its walls. The electroscope's deflection suggests that negative and positive charges are induced on the container's inner and outer surfaces. The negative charges in the metal container are attracted to the positive charges of the metal ball, and they move to the inner surface of the container. In contrast, the positive charges are repelled by the positive charges of the metal ball and move to the outer surface. The electric field due to the induced charges cancels the electric field due to the metal ball inside the container, causing zero electric field.

When the metal ball touches the container's inner wall, the electroscope remains in a deflected position. All the charges on the metal ball flow out and neutralize the induced negative charges. Thus, the inner walls of the container and the metal ball remain uncharged, while positive charges reside on the container's outer surface.

The electric field at the surface of a conductor in electrostatic equilibrium does not have a component parallel to the surface. If the electric field had a component parallel to the surface of a conductor, free charges on the surface would move, a situation contrary to the assumption of electrostatic equilibrium. Therefore, the electric field is always perpendicular to the surface of a conductor. At any point just above a conductor's surface, the electric field's magnitude is directly proportional to the surface charge density.