# Net electric field inside a conductor

I was reading Electrostatics, and I came across this statement which said that the electric field intensity inside a conductor is zero under electrostatic conditions. Let's take a solid conductor, so obviously it has electrons. Every electron has an electric field around it , due to the charge. So why do they say that the electric field inside a conductor is zero?

Or do they mean 'net' electric field is zero? Most of the sources on the internet just mention it as 'electric field'.

In a conductor, the electrons are free to move. Thus if any field remains inside the conductor, there will be a force on a mobile charge there, and the situation will not be static. If the solution is static, if must be there is no force on any force inside, hence no field. This does not depend on the net charge of the conductor.

Alternatively the electrons will accumulate on the physical surface of the conductor as this minimizes, on average, the distance between any electron and all the others. Again, this does not depend on the overall charge of the conductor.

As result of the reorganization of charges, there is no net field inside a conductor for otherwise the charges would reorganize until there would be no net field inside.

The charges on the surface are described by a surface charge density $\sigma$, which in general will not be constant and will depend in some complicated way on the geometry of the surface and on the external field.

This is to be contrasted with the situation for a dielectric (or insulator) wherein the electrons are fixed and in which a net field can be established by plunging a neutral dielectric in an external field or by placing free charge on the dielectric.

By electrostatic conditions,I am assuming that you mean the charges in the conductor are in electrostatic equilibrium (I also assume the conductor is isolated).

Electrostatic equilibrium implies that there is no current; no motion of charges; the net force exerted by the electric field on the charges is zero. Restated: the net electric field inside the conductor (solid or not) is zero (F = qE). (If it were not, the resulting force imbalance on the free charges, which as you state, are always present in a conductor, would set up perpetual currents, which contradicts our assumption of electrostatic equilibrium.)

Intensity is a scalar quantity, equivalent to the magnitude of the time-averaged Poynting vector (this is a rough description for the purposes of this question). The Poynting vector, in turn, is directly proportional to the square of the magnitude of the electric field. Since this latter quantity is zero, the intensity is zero.

The reason the qualifier 'net' is not required to describe the electric field intensity inside the conductor is because intensity is a scalar quantity. At this point, there are no vector quantities, which include magnitude and direction, to add and subtract; the intensity is the same for any point inside the conductor.

Thus, the statement being discussed is valid.

The net electric field is 0, because you usualy have the same number of electrons as protons in a material. So the electric fields cancel eachother out.

• this is incorrect. A neutral insulator can still have an E-field inside of it even if neutral. The nature of the material, i.e. the difference in charge mobility between conductors and insulators, makes the difference. – ZeroTheHero Feb 3 '17 at 12:17
• He was talking about a conductor, wasn't he? – MaDrung Feb 3 '17 at 12:24