Question

Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ${\rho }_1$ and ${\rho }_2$ respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centre of the spheres is zero. The ratio ${\rho }_1/{\rho }_2$ can be:

• A. -4
• B. $-\frac{32}{25}$
• C. $\frac{32}{25}$
• D. 4

Answer 1

Answer: (B), (D)

The correct options are
B $-\frac{32}{25}$
D 4

$Sol.(B,D)$
At point $P_1,\frac{1}{4\pi {ϵ}_0}\frac{1{\rho }_1\left(4/3\right)\pi R^3}{4R^2}=\frac{{\rho }_{2}R}{3{ϵ}_0}$

$\frac{{\rho }_{1}R}{12}=\frac{{\rho }_{2}R}{3}$

$\frac{{\rho }_1}{{\rho }_2}=4$


At point $P_2$
,
$\frac{{\rho }_1\left(4/3\right)\pi R^3}{(2R{)}^2}+\frac{{\rho }_2\left(4/3\right)\pi 8R^3}{(5R{)}^2}=0$

$.\text{.}\frac{{\rho }_1}{{\rho }_2}=-\frac{32}{25}$