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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    Water from a tap at a very large distance maintained at a potential of V is allowed to fall by drops of radius r through a small hole into a hollow conducting sphere of radius R standing on an insulating stand until it fills the entire sphere. Then the potential of the hollow conductor is

    A)  \[\frac{{{x}^{2}}}{2R}\]                                

    B)  \[\frac{r}{R}V\]

    C)  \[\frac{{{r}^{2}}}{{{R}^{2}}}\]                                    

    D)  \[\frac{{{R}^{2}}}{{{r}^{2}}}V\]

    Correct Answer: D

    Solution :

                    \[R={{n}^{1/3}}r\] \[q=4p{{\varepsilon }_{0}}rV\] \[Q=n.4p{{\varepsilon }_{0}}rV\] \[\therefore \]  \[V'=\frac{n.\,4\pi {{\varepsilon }_{0}}rV}{4\pi {{\varepsilon }_{0}}{{n}^{1/3}}r}={{n}^{2/3}}V=\frac{{{R}^{2}}}{{{r}^{2}}}V\]


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