Electrostatics 7 Question 20
22. Two non-conducting solid spheres of radii $R$ and $2 R$, having uniform volume charge densities $\rho_{1}$ and $\rho_{2}$ respectively, touch each other. The net electric field at a distance $2 R$ 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
(2013 Adv.)
(a) -4
(b) $\frac{-32}{25}$
(c) $\frac{32}{25}$
(d) 4
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Answer:
Correct Answer: 22. (b,d)
Solution:
- At point $P$
If resultant electric field is zero, then
$$ \frac{K Q_{1}}{4 R^{2}}=\frac{K Q_{2}}{8 R^{3}} R \quad \Rightarrow \quad \frac{\rho_{1}}{\rho_{2}}=4 $$
At point $Q$
If resultant electric field is zero then
$$ \begin{aligned} \frac{K Q_{1}}{4 R^{2}}+\frac{K Q_{2}}{25 R^{2}} & =0 \\ \frac{\rho_{1}}{\rho_{2}} & \left.=-\frac{32}{25} \quad \text { ( } \rho_{1} \text { must be negative }\right) \end{aligned} $$
