A uniformly charged solid sphere of radius $R$ has potential $V_{0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4}$ and $\frac{V_{0}}{4}$ have radii $R_{1}, R_{2}, R_{3}$ and $R_{4}$ respectively. then

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$R_{1} = 0$ and $R_{2} > (R_{4} - R_{3})$

$R_{1} \neq 0$ and $(R_{2} - R_{1}) > (R_{4} - R_{3})$

$R_{1} = 0$ and $R_{2} < (R_{4} - R_{3})$

$2 R < R_{4}$

answer is C, D.

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Detailed Solution

$V_{0} = \frac{ρ R^{2}}{3 \in_{0}}$ , $R_{2} m u s t b e l e s s t h a n R a n d R_{2} = R / \sqrt{2},$ , $R_{3} a n d R_{4} m u s t b e g r e a t e r t h a n R .$

$R_{3} = \frac{4 R}{3} a n d R_{4} = 4 R$ .

$R_{1} = 0$ and $R_{2} < (R_{4} - R_{3})$ , $2 R < R_{4}$

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