Verified Solution • 2025–26 Session moderate

QJEEM20Ph10cd: JEE Main 2020 Physics - Class 12 JEEM20Ph10cd Solution: Consider two charged metallic spheres S 1 and S 2 of radii R 1…

Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1) and E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1 (on S1) / V2 (on S2) of the electrostatic potentials on each sphere is :

Multiple Choice Options

  • A (R1/R2)2
  • B (R2/R1)
  • C (R1/R2)3
  • D R1/R2

Step-by-Step Verified Solution

We know,

E1 = KQ1R12{{K{Q_1}} \over {R_1^2}} and E2 = KQ2R22{{K{Q_2}} \over {R_2^2}}

Given

E1E2=R1R2{{{E_1}} \over {{E_2}}} = {{{R_1}} \over {{R_2}}}

⇒\Rightarrow KQ1R12KQ2R22=R1R2{{{{K{Q_1}} \over {R_1^2}}} \over {{{K{Q_2}} \over {R_2^2}}}} = {{{R_1}} \over {{R_2}}}

⇒\Rightarrow Q1Q2=R13R23{{{Q_1}} \over {{Q_2}}} = {{R_1^3} \over {R_2^3}}

Now V1V2=KQ1R1KQ2R2{{{V_1}} \over {{V_2}}} = {{{{K{Q_1}} \over {{R_1}}}} \over {{{K{Q_2}} \over {{R_2}}}}} = R12R22{{R_1^2} \over {R_2^2}}

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