Two charged spherical conductors of radius R₁ and R₂are connected by a wire. Then the ratio of surface charge densities of the spheres $(σ_{1} / σ_{2})$ is:

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$\frac{R_{1}^{2}}{R_{2}^{2}}$

$\frac{R_{2}}{R_{1}}$

$\frac{R_{1}}{R_{2}}$

$\sqrt{(\frac{R_{1}}{R_{2}})}$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{Q_{1}}{4 {πε}_{0} R_{1}} = \frac{Q_{2}}{4 {πε}_{0} R_{2}} = V \\ ∴ \frac{Q_{1}}{Q_{2}} = \frac{R_{1}}{R_{2}} \\ ∴ \frac{σ_{1}}{σ_{2}} = \frac{Q_{1} / 4 {πR}_{1}^{2}}{Q_{2} / 4 {πR}_{2}^{2}} = \frac{Q_{1}}{Q_{2}} {(\frac{R_{2}}{R_{1}})}^{2} = (\frac{R_{1}}{R_{2}}) {(\frac{R_{2}}{R_{1}})}^{2} \\ \Rightarrow \frac{σ_{1}}{σ_{2}} = \frac{R_{2}}{R_{1}} \end{array}$