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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Capacitance

  • question_answer
    A solid conducting sphere of radius \[{{R}_{\text{1}}}\] is surrounded by another concentric hollow conducting sphere of radius \[{{R}_{\text{2}}}\]. The capacitance of this assembly is proportional to [MP PET 2001; UPSEAT 2001]

    A)            \[\frac{{{R}_{2}}-{{R}_{1}}}{{{R}_{1}}{{R}_{2}}}\]

    B)                                      \[\frac{{{R}_{2}}+{{R}_{1}}}{{{R}_{1}}{{R}_{2}}}\]

    C)            \[\frac{{{R}_{1}}{{R}_{2}}}{{{R}_{1}}+{{R}_{2}}}\]     

    D)            \[\frac{{{R}_{1}}{{R}_{2}}}{{{R}_{2}}-{{R}_{1}}}\]

    Correct Answer: D

    Solution :

                       Capacitance of the given assembly \[C=4\pi {{\varepsilon }_{0}}\,\left( \frac{{{R}_{1}}{{R}_{2}}}{{{R}_{2}}-{{R}_{1}}} \right)\] Þ \[C\propto \frac{{{R}_{1}}{{R}_{2}}}{({{R}_{2}}-{{R}_{1}})}\]


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