Question

A conductor with an air core cavity inside, is charged to attain the surface charge density of \(\sigma\). If E is the magnitude of electric field and V is the potential, then inside the cavity

• A. \(E \neq 0\)
• B. \(V = 0\)
• C. \(E \neq 0\) and \(V = 0\)
• D. \(V \neq 0\) and \(E = 0\)
• E. \(\sigma = 0\) and \(E = 0\)

Hint:

For a charged conductor with a cavity, the electric field inside the cavity is zero in electrostatic equilibrium.

Answer 1

The Correct Option is D

Step 1:
In electrostatic equilibrium, electric field inside a conductor is $E = 0$.


Step 2:
For an empty cavity inside a conductor with no charge inside, $E = 0$ in the cavity.


Step 3:
Since $E = -\dfrac{dV}{dr} = 0$, potential remains constant inside the cavity.


Step 4:
The constant potential inside the cavity is equal to the surface potential of the conductor, hence $V \neq 0$.
Final Answer:
Option D: $V \neq 0 \text{ and } E = 0$.