# Flow of charges in a conductor

in the case of a spherical conductor the charges reside on the surface...the electric field is perpendicular to this surface (radial) and no parallel component exists ,as it leads to the flow of charges across the surface...why is this flow not feasible i.e why does the parallel component vanish??..what is wrong with the charges flowing across the surface?

Because charge flowing through the conductor (electric current) leads to the emission of Joule heat as a dissipative process. This process cannot be supported for indefinite time if no external energy sources compensate the energy loss. Thus, it is a non-equilibrium situation. In equilibrium, there should not be any electric current. According to Ohms law, there should not be a parallel electric field component.

to say the same thing again: if the charges are moving,...wait a moment. They'll reach equilibrium which, presumable, is what you're interested in if its an electrostatics problem.

Because charge flowing through the conductor (electric current) leads to the emission of Joule heat as a dissipative process. This process cannot be supported for indefinite time if no external energy sources compensate the energy loss. Thus, it is a non-equilibrium situation. In equilibrium, there should not be any electric current. According to Ohms law, there should not be a parallel electric field component.

okay....so this happens to avoid the violation of the law of conservation of energy??... if i have some mechanism by which i can compensate the heat loss will there exist a parallel component?

okay....so this happens to avoid the violation of the law of conservation of energy??... if i have some mechanism by which i can compensate the heat loss will there exist a parallel component?

Yes, just attach a battery via two wires connected to two points on the surface of the sphere.

Meir Achuz
Homework Helper
Gold Member
in the case of a spherical conductor the charges reside on the surface...the electric field is perpendicular to this surface (radial) and no parallel component exists ,as it leads to the flow of charges across the surface...why is this flow not feasible i.e why does the parallel component vanish??..what is wrong with the charges flowing across the surface?
The charge will flow until the parallel E field vanishes. This takes about a microsecond.
Then E parallel is zero.

The charge will flow until the parallel E field vanishes. This takes about a microsecond.
Then E parallel is zero.

what causes it to vanish?...i.e is it a field in the opposite direction?

The redistribution of the charges on the surface conductor is such that it makes the field satisfy the following two conditions:

1. There is no electric field in the body of the conductor, which according to Gauss's Law implies that there are no charges in the body of the conductor, i.e. they are all distributed on its surface;

2. There is no tangential component of the electric field to the surface. We know that the equipotential surfaces are always perpendicular to the electric field (because the electric field is the negative gradient of the electric potential and the the gradient of a function is always perpendicular to the level surfaces of the function). Thus, the conducting surface is an equipotential surface, i.e. all point on the surface of a conductor are at the same potential.

thanks..