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 smaller sphere is zero. The ratio $\frac{{\rho }_1}{{\rho }_2},$ is

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

Answer 1

The correct option is B $-\frac{32}{25}$ and 4

Case 1 :


$\frac{{\rho }_{1}V}{4R_2}=\frac{{\rho }_2\left(8V\right)}{(5R{)}^2}$
$\frac{{\rho }_1}{{\rho }_2}=\frac{-32}{25}$

Case 2:


$\frac{Q_1}{4R^2}=\frac{Q_{2}R}{8R^3}$
$\frac{Q_1}{Q_2}=\frac{1}{2}$
$\frac{{\rho }_1}{{\rho }_2}=4$