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

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

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

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

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

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Solution

The correct option is C $\frac{R_{2}}{R_{1}}$

When two conductors are connected by a conducting wire, then the two conductors should have the same potential.

So, $V_{1} = V_{2}$

$\Rightarrow \frac{1}{4 π ε_{0}} \frac{Q_{1}}{R_{1}} = \frac{1}{4 π ε_{0}} \frac{Q_{2}}{R_{2}}$

$\Rightarrow \frac{1}{4 π ε_{0}} \frac{Q_{1}}{R_{1}} \times \frac{R_{1}}{R_{1}} = \frac{1}{4 π ε_{0}} \frac{Q_{2}}{R_{2}} \times \frac{R_{2}}{R_{2}}$

$\Rightarrow \frac{Q_{1} R_{1}}{4 π R_{1}^{2}} = \frac{Q_{2} R_{2}}{4 π R_{2}^{2}}$

$\Rightarrow σ_{1} R_{1} = σ_{2} R_{2} (∵ σ = Q / A)$

$∴ \frac{σ_{1}}{σ_{2}} = \frac{R_{2}}{R_{1}}$

Hence, option $(C)$ is correct.

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Two charged spherical conductors of radii R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres (σ1/σ2) is

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