A conducting sphere A of radius a, with charge Q, is placed concentrically inside a conducting shell B of radius b. B is earthed. C is the common centre of the A and B

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The potential difference between A and B is $\frac{1}{4 π ε_{0}} Q (\frac{1}{a} - \frac{1}{b})$

The potential at a distance r from C, Where $a < r < b, is \frac{1}{4 π ε_{0}} \frac{Q}{r}$

The field is at a distance r from C, Where $a < r < b, is \frac{1}{4 π ε_{0}} \frac{Q}{r^{2}}$

The potential at a distance r from C, Where $a < r < b, is \frac{1}{4 π ε_{0}} Q (\frac{1}{r} - \frac{1}{b})$

answer is A, C, D.

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Detailed Solution

$a < r < b;$ Enclosed charge $= Q$

$E .4 π r^{2} = \frac{Q}{ε_{0}}$

$\Rightarrow E = \frac{Q}{4 π ε_{\circ} r^{2}}$ Option (A) is correct.

Let Q’ be the charge on B

$V_{B} = 0 \Rightarrow Q' = - Q; V_{A} = \frac{1}{4 π ε_{0}} [\frac{Q}{a} - \frac{Q}{b}]$ Option (C) is correct.

$V_{B} = 0 \Rightarrow V_{A} - V_{B} = V_{A}$

$\Rightarrow V_{r} = \frac{1}{4 π ε_{\circ}} [\frac{Q}{r} - \frac{Q}{b}]$ Option (D) is correct. Option (B) is wrong.

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