Electrostatics

JEE Main level, single correct, medium

197 of 311

Question 197 of 311

Consider two charged metallic spheres S1{S}_{1} and S2{S}_{2} of radii R1{R}_{1} and R2,{R}_{2}, respectively. The electric fields E1{E}_{1} (on S1{S}_{1} ) and E2{E}_{2} (on S2{S}_{2} ) on their surfaces are such that E1E2=R1R2.\dfrac{{E}_{1}}{{E}_{2}}=\dfrac{{R}_{1}}{{R}_{2}}. Then the ratio V1{V}_{1} (on S1{S}_{1} )//V2{V}_{2} (on S2{S}_{2} ) of the electrostatic potentials on each sphere is:

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Answer: (B) (R1R2)2{\left(\dfrac{{R}_{1}}{{R}_{2}}\right)}^{2}

Given, E1E2=R1R2\dfrac{{E}_{1}}{{E}_{2}}=\dfrac{{R}_{1}}{{R}_{2}}
Then ratio of potential would be,
V1V2=E1R1E2R2=R1R2×R1R2=(R1R2)2\dfrac{{V}_{1}}{{V}_{2}}=\dfrac{{E}_{1}{R}_{1}}{{E}_{2}{R}_{2}}=\dfrac{{R}_{1}}{{R}_{2}}\times \dfrac{{R}_{1}}{{R}_{2}}={\left(\dfrac{{R}_{1}}{{R}_{2}}\right)}^{2}

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