Verified Solution • 2025–26 Session moderate

QJEEM20Ph3abe: JEE Main 2020 Physics - Class 12 JEEM20Ph3abe Solution: Concentric metallic hollow spheres of radii R and 4R hold…

Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :

Multiple Choice Options

  • A 3Q24πε0R{{3{Q_2}} \over {4\pi {\varepsilon _0}R}}
  • B 3Q14πε0R{{3{Q_1}} \over {4\pi {\varepsilon _0}R}}
  • C 3Q116πε0R{{3{Q_1}} \over {16\pi {\varepsilon _0}R}}
  • D Q24πε0R{{{Q_2}} \over {4\pi {\varepsilon _0}R}}

Step-by-Step Verified Solution

JEE Main 2020 (Online) 3rd September Evening Slot Physics - Electrostatics Question 150 English Explanation
σ=Q14πR2=Q24π16R2\sigma = {{{Q_1}} \over {4\pi {R^2}}} = {{{Q_2}} \over {4\pi 16{R^2}}}

⇒\Rightarrow 16Q1=Q216{Q_1} = {Q_2}

∴\therefore VR−V4R=KQ1R+KQ24R−KQ14R−KQ24R{V_R} - {V_{4R}} = {{K{Q_1}} \over R} + {{K{Q_2}} \over {4R}} - {{K{Q_1}} \over {4R}} - {{K{Q_2}} \over {4R}}

=3KQ14R=3Q116πε0R= {{3K{Q_1}} \over {4R}} = {{3{Q_1}} \over {16\pi {\varepsilon _0}R}} [As K = 14πε0{1 \over {4\pi {\varepsilon _0}}} ]

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