WBJEE · Physics · Electrostatics
Three concentric metallic shells A, B and C of radii \(a, b\) and \(c(a < b < c)\) have surface charge densities \(+\sigma,-\sigma\) and \(+\sigma\) respectively. The potential of shell B is
- A \(\quad(a+b+c) \frac{\sigma}{\varepsilon_0}\)
- B \(\frac{\sigma \mathrm{c}}{\varepsilon_0}\)
- C \(\left(\frac{a^2}{c}-\frac{b^2}{c}+c\right) \frac{\sigma}{e_0}\)
- D \(\left(\frac{a^2}{b}-b+c\right) \frac{\sigma}{e_0}\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{a^2}{b}-b+c\right) \frac{\sigma}{e_0}\)
Step-by-step Solution
Detailed explanation
\(V_b=V_{A, b}+V_{B, b}+V_{C, b}\) \(=\frac{K \sigma 4 \pi a^2}{b}-\frac{K \sigma 4 \pi b^2}{b}+\frac{K \sigma 4 \pi c^2}{c}\) \(=\frac{\sigma}{\varepsilon_0}\left(\frac{a^2}{b}-b+c\right)\)
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