Question

Which of the following statements is correct with regards to a spherical capacitor

• A. If surface $1$ is earthed, $\overrightarrow{E}$ exists only in region III.
• B. If surface $1$ is earthed, $\overrightarrow{E}$ exists both in region II and region III .
• C. If surface $2$ is earthed, $\overrightarrow{E}$ exists only in region II.
• D. If surface $2$ is earthed, $\overrightarrow{E}$ exists only in region I.

Answer 1

Answer: (B), (C)

The correct options are
B If surface $1$ is earthed, $\overrightarrow{E}$ exists both in region II and region III .
C If surface $2$ is earthed, $\overrightarrow{E}$ exists only in region II.



When $1$ is earthed, two capacitors are formed one between $1$ and $\infty$ , and the other between $1$ and $2$, so the $\overrightarrow{E}$ exists in region - II and region III.

Similarly. when surface $2$ is earthed, $\overrightarrow{E}$ lies only in region - II $[\because \overrightarrow{E}$ inside the shell (region-I) is zero and net charge enclosed within the imaginary gaussian surface in region III will be zero.$]$

Hence, options (b) and (c) are the correct answers.