Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

Two charged spherical conductors of radii $R_1$ and $R_2$ are connected by a wire. The ratio of surface charge densities of spheres $(\sigma_1/\sigma_2)$ is:

\sqrt{\frac{R_1}{R_2}}

\frac{R_1^2}{R_2^2}

\frac{R_1}{R_2}

\frac{R_2}{R_1}

Step-by-Step Solution

Common Potential: When two charged conductors are connected by a wire, charge flows between them until they reach the same electrostatic potential ( $V$ ). Thus, $V_1 = V_2$ .
Formula for Potential: The potential of a charged sphere of radius $R$ and charge $Q$ is $V = \frac{1}{4\pi\varepsilon_0} \frac{Q}{R}$ .
Equating Potentials: $\frac{Q_1}{R_1} = \frac{Q_2}{R_2} \implies \frac{Q_1}{Q_2} = \frac{R_1}{R_2}$ .
Surface Charge Density ( $\sigma$ ): $\sigma = \frac{\text{Charge}}{\text{Area}} = \frac{Q}{4\pi R^2}$ . Thus, $Q = \sigma(4\pi R^2)$ .
Substitute and Solve: $\frac{\sigma_1(4\pi R_1^2)}{\sigma_2(4\pi R_2^2)} = \frac{R_1}{R_2}$ $\frac{\sigma_1}{\sigma_2} \cdot \frac{R_1^2}{R_2^2} = \frac{R_1}{R_2}$ $\frac{\sigma_1}{\sigma_2} = \frac{R_1}{R_2} \cdot \frac{R_2^2}{R_1^2} = \frac{R_2}{R_1}$ .

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