Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities 1 and 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 centres of the spheres, is zero. The ratio can be

Engineering

Physics

Electric Field and Charged Particle in Electric Field

Question

Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities $ρ$ ₁ and $ρ$ 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 centres of the spheres, is zero. The ratio $\frac{ρ_{1}}{ρ_{2}}$ can be

$- \frac{32}{25}$

– 4

$\frac{32}{25}$

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$\frac{K (ρ_{1} \frac{4}{3} {πR}^{3})}{{(2 R)}^{2}} = \frac{K [ρ_{2} \frac{4}{3} π {(2 R)}^{2}]}{{(5 R)}^{2}}$

$\frac{ρ_{1}}{ρ_{2}} = \frac{8 \times 4}{25}$

$\frac{ρ_{2} R}{3 ε_{0}} = \frac{1}{4 {πε}_{0}} \frac{(ρ_{1} \frac{4}{3} {πR}^{3})}{{(2 R)}^{2}}$

$\frac{ρ_{1}}{ρ_{2}} = 4$