Question

A solid sphere of radius $r_1=1cm$ carries charge distributed uniformly over it with densiity ${\rho }_1=-3C/c{m}^3$. It is surrounded by a concentriic spherical shell of radius $r_2=2cm$ carrying uniform charge density ${\rho }_2=\frac{1}{2}C/c{m}^2$. If $E_d$ denotes the magnitude of the electric field at distance $d$ from the common centre of the spheres, then

• A. $E_d=\frac{1}{3{\epsilon }_0{d}^2},d\le 1cm$
• B. $E_d=\frac{1}{{\epsilon }_0{d}^2},d\le -1cm$
• C. $E_d=\frac{d}{3{\epsilon }_0},d\le 1cm$
• D. $E_d=\frac{d}{{\epsilon }_0}d\le 1cm$

Answer 1

Answer: (D)

Electric field at a point inside inner sphere is only due to charge enclosed.
We use Gauss' law to get,
$E=\left(\frac{q}{4\pi {\epsilon }_0{R}^3}\right)r=\frac{{\rho }_R}{3{\epsilon }_0}$
Here, $\rho =-3\left(\frac{C}{c{m}^3}\right)$
So, $E=\frac{-d}{{\epsilon }_0}$ or $|E|=\frac{d}{{\epsilon }_0}$