Two charged spherical conductors of radius R_1 and R_2 are connected by a wire. Then the ratio of surface charge densities of the sphere (σ_1 / σ_2) i - Physics MCQ NEET 2021 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

When two conductors are connected by a wire, they reach the same potential (V_{1} = V_{2}). V = \frac{k Q}{R} So, \frac{k Q _{1}}{R _{1}} = \frac{k Q _{2}}{R _{2}} \Rightarrow \frac{Q _{1}}{Q _{2}} = \frac{R _{1}}{R _{2}} Surface charge density σ = \frac{Q}{4 π R ^{2}} . \frac{σ _{1}}{σ _{2}} = \frac{Q _{1} /4 π R _{1}^{2}}{Q _{2} /4 π R _{2}^{2}} = \frac{Q _{1}}{Q _{2}} \times \frac{R _{2}^{2}}{R _{1}^{2}} Substituting \frac{Q _{1}}{Q _{2}} = \frac{R _{1}}{R _{2}} : \frac{σ _{1}}{σ _{2}} = \frac{R _{1}}{R _{2}} \times \frac{R _{2}^{2}}{R _{1}^{2}} = \frac{R _{2}}{R _{1}}

Try it yourself before checking the explanation above.

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

\frac{R _{1}}{R _{2}}

\frac{R _{2}^{2}}{R _{1}^{2}}

\frac{R _{1}^{2}}{R _{2}^{2}}

\frac{R _{2}}{R _{1}}

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