WBJEE · Physics · Electrostatics
A metal sphere of radius \(R\) carrying charge \(q\) is surrounded by a thick concentric metal shell of inner and outer radii a and \(\mathrm{b}\) respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surface of the shell is grounded will be
- A \(\frac{\mathrm{q}}{4 \pi \epsilon_{0}}\left(\frac{1}{\mathrm{a}}-\frac{1}{\mathrm{~b}}\right)\)
- B \(\frac{\mathrm{q}}{4 \pi \epsilon_{0}} \frac{1}{\mathrm{a}}\)
- C \(\frac{\mathrm{q}}{4 \pi \epsilon_{0}}\left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{a}}\right)\)
- D \(\frac{\mathrm{q}}{4 \pi \epsilon_{0}} \frac{1}{\mathrm{R}}\)
Answer & Solution
Correct Answer
(C) \(\frac{\mathrm{q}}{4 \pi \epsilon_{0}}\left(\frac{1}{\mathrm{R}}-\frac{1}{\mathrm{a}}\right)\)
Step-by-step Solution
Detailed explanation
\(V_{A}=V_{B}+V_{C}+V_{c}\) \(V_{c}=\frac{1}{4 x \varepsilon_{0}}\left(\frac{-q}{a}\right)+\frac{1}{4 x \varepsilon_{0}}\left(\frac{q}{R}\right)+0\) \(=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{q}{R}-\frac{q}{a}\right)\)…
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