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JEE Main & Advanced Sample Paper JEE Main Sample Paper-35

  • question_answer
    Three spherical conductors \[{{S}_{1}},{{S}_{2}}\] and \[{{S}_{4}}\] of radii a, b and d respectively \[(a<b<d)\] are arranged concentrically. \[{{S}_{1}}\] and \[{{S}_{2}}\] are connected and \[{{S}_{4}}\] is grounded. Find the equivalent capacitance of the system

    A)  \[\frac{4\pi {{\varepsilon }_{0}}abd}{(b-a)(d-b)}\]          

    B)  \[\frac{4\pi {{\varepsilon }_{0}}ab}{(b-a)}\]

    C)  \[\frac{4\pi {{\varepsilon }_{0}}ab}{(d-b)}\]                       

    D)  \[\frac{4\pi {{\varepsilon }_{0}}ad}{(d-a)}\]

    Correct Answer: C

    Solution :

    \[{{E}_{r}}=\frac{q}{4\pi {{\varepsilon }_{0}}{{r}^{2}}}\]             \[-\int_{b}^{d}{dV=\frac{q}{4\pi {{\varepsilon }_{0}}\,{{r}^{2}}}\,\int_{b}^{d}{\frac{dr}{{{r}^{2}}}}}\]             Or \[{{V}_{b}}-{{V}_{a}}=\frac{q}{4\pi {{\varepsilon }_{0}}}\,\frac{(d-b)}{bd}\]           Or \[C=\frac{4\pi {{\varepsilon }_{0}}bd}{(d-b)}\]


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