Chapter 25, Problem 25.1DQ

The definition of resistivity (ρ = E/J) implies that an electric field exists inside a conductor. Yet we saw in Chapter 21 that there can be no electrostatic electric field inside a conductor. Is there a contradiction here? Explain.

To determine

if there is any contradiction to the statement, there can be no electrostatic electric field inside a conductor.

Explanation of Solution

There is no contradiction to the statement, since that was a situation dealing with electrostatics.

Consider the formula for the resistivity $\left(\rho \right)$.

$\rho =\frac{E}{J}$ (I)

• $E$ is the electric field,
• $J$ is current density.

From equation (I), we have E, which refers to the electric field applied in a closed circuit. This forms a major difference from the electrostatics situation.

The main condition with respect to electrostatics was that the charges involved in the situation were static. That is they were not moving charges. This is because they do not experience any force while in their equilibrium position. In this situation, there is no presence of electric field.

In the given situation of the electric field, we have moving charges as it is a closed circuit with an applied field. There is no such equilibrium as in the case of electrostatics.

Conclusion:

Therefore, there is any contradiction to the statement there can be no electrostatic electric field inside a conductor.