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Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively, as shown in figure . If magnitude of the electric fields at point P at a distance R from the centre of sphere 1,2 and 3 are $E_{1}, E_{2} {and E}_{3}$ respectively, then

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$E_{3} > E_{2} > E_{1}$

$E_{2} > E_{1} > E_{3}$

$E_{1} > E_{2} > E_{3}$

$E_{3} > E_{1} > E_{2}$

answer is C.

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Detailed Solution

$E_{1} = \frac{1}{4 π \in_{0}} . \frac{Q}{R^{2}}; E_{2} = \frac{1}{4 π \in_{0}} . \frac{2 Q}{R^{2}}; E_{3} = \frac{1}{4 π \in_{0}} . \frac{Q / 2}{R^{2}} Clearly E_{2} > E_{1} > E_{3}$

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