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. If magnitudes of the electric fields at point P at a distance R from the centre of sphere 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 $E_2>E_1>E_3$

For sphere 1:

Point P is outside the sphere and using Gauss's law, $E_1.4\pi R^2=\frac{Q_{en}}{{ϵ}_0}=\frac{Q}{{ϵ}_0}$
or $E_1=\frac{1}{4\pi {ϵ}_0}\frac{Q}{R^2}$

For sphere 2:

Point P is on the surface of the sphere and using Gauss's law, $E_2.4\pi R^2=\frac{Q_{en}}{{ϵ}_0}=\frac{2Q}{{ϵ}_0}$
or $E_2=\frac{1}{4\pi {ϵ}_0}\frac{2Q}{R^2}$

For sphere 3:

Point P is inside the sphere and using Gauss's law
$E_3.4\pi R^2=\frac{Q_{en}}{{ϵ}_0}=\frac{\rho .\frac{4}{3}\pi R^3}{{ϵ}_0}$ and here $4Q=\rho .\frac{4}{3}\pi (2R{)}^3$
now, $E_3.4\pi R^2=\frac{Q/2}{{ϵ}_0}$
or $E_3=\frac{1}{4\pi {ϵ}_0}\frac{Q}{2R^2}$
thus, $E_2>E_1>E_3$