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A conductor with a cavity is charged pos...

A conductor with a cavity is charged positively and its surface charge density is `sigma`. If E and V represent the electric field and potential, then inside the cavity

A

E = 0 and V = 0

B

E = 0 and `sigma`- constant

C

V = 0 and `sigma` = constant

D

E = 0 and V = constant

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the behavior of electric fields and potentials in and around a charged conductor with a cavity. ### Step-by-Step Solution: 1. **Understanding the Properties of Conductors**: - In electrostatic equilibrium, the electric field inside a conductor is zero. This is because free charges within the conductor rearrange themselves in response to electric fields until they cancel any internal fields. 2. **Analyzing the Cavity**: - The cavity inside the conductor is a region where we need to determine the electric field (E) and the electric potential (V). Since the conductor is positively charged, the charges reside on the surface of the conductor. 3. **Electric Field Inside the Cavity**: - Since the electric field inside a conductor is zero, and there are no charges present inside the cavity (the cavity is empty), the electric field inside the cavity must also be zero. - Therefore, we conclude that: \[ E = 0 \quad \text{(inside the cavity)} \] 4. **Electric Potential Inside the Cavity**: - The electric potential inside the cavity can be understood by considering that the potential is constant throughout the cavity. This is because the electric field (E) is zero, which implies that there is no change in potential within that region. - The potential inside the cavity (V) will be equal to the potential on the surface of the conductor, as the surface is where the charges are located. - Thus, we have: \[ V = \text{constant} \quad \text{(inside the cavity)} \] 5. **Final Conclusion**: - The electric field inside the cavity is zero, and the potential is constant, equal to the potential on the surface of the conductor. ### Summary: - Electric Field (E) inside the cavity: \( E = 0 \) - Electric Potential (V) inside the cavity: \( V = \text{constant} \)
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