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'.
Best Answer
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.