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Q.

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 magnitudes of the electric fields at point P at a distance R from the center of spheres 1, 2 and 3 are E₁ , E₂ and E₃ respectively, then

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a

E₂ > E₁ > E₃

b

E₃ > E₂ > E₁

c

E₃ =E₂ > E₁

d

E₁ > E₂ > E₃

answer is C.

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Detailed Solution

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$\begin{array}{l} E_{1} = \frac{KQ}{R^{2}}; E_{2} = \frac{K 2 Q}{R^{2}}, E_{3} = \frac{K (4 Q) R}{(2 R)^{3}} \\ E_{3} = \frac{KQ}{2 R^{2}} \\ E_{2} > E_{1} > E_{3} \end{array}$

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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 magnitudes of the electric fields at point P at a distance R from the center of spheres 1, 2 and 3 are E1 , E2 and E3 respectively, then