# Equipotential Surfaces and Conductors

JoVE Core
Physik
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JoVE Core Physik
Equipotential Surfaces and Conductors

### Nächstes Video24.10: Determining Electric Field From Electric Potential

Consider a spherical conductor of radius R in which all charges are at rest. The electric field inside the conductor is zero, and it varies inversely with the square of the radial distance outside it.

Now imagine that the electric field has a tangential component outside the conductor's surface.

Such a tangential component would mean that there is also a tangential component of the electric field inside the conductor, causing charges to move in a rectangular loop. This would violate the electrostatic nature of the system.

Therefore no tangential component of the electric field is possible outside the conductor's surface. The electric field can only be perpendicular to the conductor's surface, making it an equipotential surface.

Consider two spherical conductors, with different radii, surface charge densities, and charges, connected by a thin conducting wire.

Here, the complete system is equipotential, and both spheres are at the same potential. Expressing the charge in terms of the surface charge density indicates that the surface charge density and electric field are higher for a smaller radius of curvature.

## Equipotential Surfaces and Conductors

For a conductor in which all charges are at rest, the conductor's surface is equipotential. The electric field is always perpendicular to equipotential surfaces. Therefore, in a conductor with static charges, the electric field just outside the conductor is always perpendicular to the conductor's surface. Any tangential component of the electric field will cause charges to move inside the conductor, which will violate the electrostatic nature of the system. In an electrostatic situation, if a conductor has a cavity with no charges inside it, then there can be no charge anywhere on the surface of the cavity. This means that inside a charged metallic enclosure, with no charges inside the enclosure, one can touch the walls of the enclosure from inside without getting an electrical shock.

Consider two conducting spheres of different radii having different surface charge densities and different amounts of static charges. If a thin conducting wire connects these conductors, the whole system becomes equipotential. The potential of each sphere is the same, and the surface charge density and the electric field are higher on the conductor with a smaller radius of curvature. A practical application of this phenomenon is a lightning rod—a grounded metal rod with a sharp end pointing upward. As positive charge accumulates in the ground due to a negatively charged cloud overhead, the electric field around the sharp point becomes very large. When the field reaches a value of approximately 3.0 × 106 N/C (the dielectric strength of the air), the free ions in the air are accelerated to such high energies that their collisions with air molecules ionize the molecules. The resulting free electrons in the air then flow through the rod to Earth, thereby neutralizing some of the positive charges. This keeps the electric field between the cloud and the ground from becoming large enough to produce a lightning bolt in the region around the rod.