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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 30

  • question_answer
    Two identical metallic small spheres of radius R are placed at very large separation and they are connected by a coil of inductance L having negligible resistance as shown in the figure. One of the sphere is given charge Q and then switch S is closed. The maximum current through the coil will be

    A) \[\frac{Q}{\sqrt{\pi {{\varepsilon }_{0}}RL}}\]   

    B)        \[\frac{Q}{\sqrt{8\pi {{\varepsilon }_{0}}RL}}\]

    C) \[\frac{Q}{2\sqrt{\pi {{\varepsilon }_{0}}RL}}\]  

    D)        \[\frac{Q}{\sqrt{2\pi {{\varepsilon }_{0}}RL}}\]

    Correct Answer: B

    Solution :

    [b] At  \[i={{i}_{\max }},{{Q}_{1}}-{{Q}_{2}}=\frac{Q}{2}\] \[\therefore \,\,\,\,\,\frac{1}{2}Li_{\max }^{2}=\frac{{{Q}^{2}}}{2C}-2\times \frac{{{(Q/2)}^{2}}}{2C}\] \[\frac{1}{2}Li_{\max }^{2}=\frac{{{Q}^{2}}}{4c}\]


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