Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1,2 and 3 of radii

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1. Electric Charges and Fields

hard

Charges $Q, 2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres $1,2$ and $3$ of radii $R/2, R$ and $2 R$ respectively, as shown in figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres $1,2$ and $3$ are $E_1 E_2$ and $E_3$ respectively, then

A

$E_1 > E_2 > E_3$

B

$E_3 > E_1 > E_2$

C

$E_2 > E_1 > E_3$

D

$E_3 > E_2 > E_1$

(IIT-2014)

Solution

$E_1=\frac{K Q}{R^2}$

$E_2=\frac{k(2 Q)}{R^2} \quad \Rightarrow \quad E_2=\frac{2 k Q}{R^2}$

$E_3=\frac{k(4 Q) R}{(2 R)^3} \quad \Rightarrow \quad E_3=\frac{k Q}{2 R^2}$

$E_3 < E_1 < E_2$

Standard 12

Physics

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