Question

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 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. $E_3>E_2>E_1$

Answer 1

Answer: (C)

$E_2>E_1>E_3$

For a point outside sphere we have,
$E=\frac{Q}{4\pi {\epsilon }_o{R}^2}$
$1.Q\to Q,R\to R\Rightarrow E_1=E$
$2.Q\to 2Q,R\to R\Rightarrow E_2=2E$
$3.Q\to 0,R\to R\Rightarrow E_3=0$
$\Rightarrow E_2>E_1>E_3$