Problem: 1707072: Electrostatics

Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ₁ and ρ₂ 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 ρ₁/ρ₂ is ____.

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Net field at the given point zero
\[\frac{\rho _{1}\frac{4}{3}\pi R^{3}}{(2R)^{2}}+\frac{\rho _{2}\frac{4}{3}\pi (2R)^{3}}{(5R)^{2}}=0\]
\[\therefore \frac{\rho _{1}}{\rho _{2}}=-\frac{32}{25}\]