Question

Questions: A conductor that carries a net charge has a hollow, empty cavity in its interior. Does the potential vary from point to point within the material of the conductor? What about within the cavity? How does the potential inside the cavity compare to the potential within the material of the conductor?

Short answer

Answer

The electric potential not vary from one point to another point within the material of the conductor or with in the cavity. And do not compare potential inside the cavity with the potential within the material of the conductor because electric potential is constant.

Step-by-step solution

Definition of electric potential

The term electric potential is defined as the amount of work done by the unit charge in moving from one point to another against electric field.

The electric field obtained by the relation:

$\overrightarrow{E}=-\overrightarrow{\nabla }V$

Taking integration on side and taking limit from

$$\begin{gathered} {\int }_A^{B}dV=-\int Edr \\ {V}_B-V_A=-\int 0dr+C \\ {V}_B-V_A=C \\ {V}_B-V_A=C \end{gathered}$$

Explain the reasoning of questions

The expression for the potential difference shows the enclosed charge is zero and the field in the conductor is also zero that further defines the potential of the conductor as constant.

Conclude that Potential difference is arbitrary constant.

The electric field and charge within the material of the conductor and within the cavity is zero that’s why the electric potential not vary from one point to another point within the material of the conductor or with in the cavity. And do not compare potential inside the cavity with the potential within the material of the conductor because electric potential is constant in all cases.