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Three concentric conducting spherical shells of radii R, 2R and 3R carry charges Q, –2Q and 3Q, respectively compute the electric field at $r = \frac{5}{2} R$

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$\frac{- Q}{5 {πε}_{0} R^{2}} \hat{r}$

$\frac{- Q}{{πε}_{0} R^{2}} \hat{r}$

$\frac{- Q}{3 {πε}_{0} R^{2}} \hat{r}$

$\frac{- Q}{25 {πε}_{0} R^{2}} \hat{r}$

answer is B.

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Detailed Solution

$\begin{array}{l} E = \frac{q_{in}}{ϵ_{0} A} (∵ r = 5 / 2 R) \\ E = \frac{- Q}{4 {πϵ}_{0} (5 / 2 R)^{2}} \\ \Rightarrow E = \frac{- Q}{25 {πϵ}_{0} R^{2}} \end{array}$

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