Charges Q, 2Q and 4Q are uniformly distributed in three dielectri… - Vidyadip

MCQ

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
$E_3 > E_1 > E_2$
✓
$E_2 > E_1 > E_3$
D
$E_3 > E_2 > E_1$

✓

Answer

Correct option: C.

$E_2 > E_1 > E_3$

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

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

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

$E_3 < E_1 < E_2$

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