Question

Charge $Q,2Q$ 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 field 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

The correct option is C $E_2>E_1>E_3$

Gauss law

$E.s=\frac{q}{e_w}$

Sphere $1$

$E_{1}4\pi R^2=\frac{Q}{e_w}$

$E_1=\frac{q}{4\pi e_w{R}^2}$

Sphere $2$

$E_2.4\pi R^2=\frac{2Q}{e_w}$

$E_2=\frac{2Q}{4\pi e_w{R}^2}$

Sphere $3$

$E_3\times 4\pi R^2=\frac{O}{e_w}$

$E_3=O$

On comparing

$E_2>E_1>E_3$