Basic Properties of Conductors

The substances, through which electric charges or charge carriers are free to move, are called conductors. In metallic solid, these charge carriers are free electrons. In fluids, these charge carriers are generally negative and positive ions. A perfect conductor is a material which contains an unlimited supply of completely free charges.

(i) E = 0 inside a conductor.

Consider a conductor P placed in an external electric field E0 produced by two fixed layers of charges. A conductor possesses free mobile charge (equal number of positive and negative ions). The positive ions are drawn in the directions of the field and the negative ions in the opposite direction. They cannot go farther than the surface of the conductor. Having reached the surface, these induced charges produce a field of their own, E₁, which, is in the opposite direction to the external electric field E₀. The movement of the ions in either direction continues till the original field is cancelled. The final distribution of charges at the surface is such that its field exactly cancels the external electric field so that the field inside conductor is zero.

(ii) ρ = 0 inside a conductor.

By Gauss’s law, ∇. E = ρ/ε₀
E = 0 inside a conductor.
. :    ρ = 0 inside a conductor.

(iii) Any net charge resides on the surface of the conductor.

(iv) V is constant, throughout a conductor.

E = 0 everywhere within a conductor.
V(b) – V(a) = - ∫^b_a E. dl = 0
For any two points within, or at the surface of, the conductor.
    . :    V(a) = V(b).

(v) E is perpendicular to the surface, just outside a conductor.

The electric field E near the surface of a conductor is perpendicular to its surface. This is consistent with the surface of the conductor being an equipotential. As we showed in section 3-1, the electric field is always perpendicular to equipotential surfaces.



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