Question: The definition of resistivity$\left(\mathbf{\rho }\mathbf{=}\frac{\mathbf{E}}{\mathbf{J}}\right)$ implies that an electrical field exist inside a conductor. Yet we saw that in chapter there can be no electrostatic electric field inside a conductor. Is there can be contradiction here? Explain.

The term resistivity is opposition offered by the particular electric conductor to the flow the charges. It depends on the type of material used, while the resistance will depend on the length and the area of the conductor.

The expression for the resistance is,

$\mathbf{R}\mathbf{=}\frac{\mathbf{\rho L}}{\mathbf{A}}$

Here, is the resistivity, Ris the resistance, L is the length and A is the area of the cross section.

As the electric field applied, the charges align themselves with respect to the filed and an opposing filed is developed in the direction to which the field is applied.

Both the filed cancel each other due to the acceleration of the electrons and there is no filed left. The electric filed in the conductors connected to the supply will develop a electric field within the wire that is sustained.

Hence, there is no any contradiction because when the charges are in an electrostatic instant the electric field is neutral.