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Q.

Charges Q, 2Q and 4Q are uniformly distributed in three dielectrics 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 spheres 1,2 and 3 are E₁, E₂ and E₃ respectively, then

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a

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

b

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

c

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

d

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

answer is C.

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Detailed Solution

$E_{1} = \frac{1}{4 π ε_{0}} \frac{Q}{R^{2}}; E_{2} = \frac{1}{4 π ε_{0}} \frac{2 Q}{R^{2}}$

$E_{3} = \frac{1}{4 π ε_{0}} \frac{Q^{'}}{R^{2}} = \frac{1}{4 π ε_{0}} \frac{Q / 2}{R^{2}}$

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

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Charges Q, 2Q and 4Q are uniformly distributed in three dielectrics 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 spheres 1,2 and 3 are E1, E2 and E3 respectively, then