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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Self Evaluation Test - Electric Chages and Fields

  • question_answer
    N identical point charges are kept summetrically on the periphery of the circle \[{{x}^{2}}+{{y}^{2}}={{R}^{2}}\]in xy plane. The resultant electric field at (0, 0, R) is \[{{E}_{1}}\] and at (0, 0, 2R) is \[{{E}_{2}}\]. The ratio of \[\frac{{{E}_{1}}}{{{E}_{2}}}\]is

    A) \[\frac{5\sqrt{5}}{4\sqrt{2}}\]

    B) \[\frac{5}{2}\]

    C) \[\frac{5}{4}\]

    D) \[\frac{5\sqrt{5}}{2\sqrt{2}}\]

    Correct Answer: A

    Solution :

    [a] \[{{E}_{1}}=\frac{nkQR}{{{\left( {{R}^{2}}+{{R}^{2}} \right)}^{3/2}}},{{E}_{1}}=\frac{nkQ\left( 2R \right)}{{{\left( {{R}^{2}}+{{\left( 2R \right)}^{2}} \right)}^{3/2}}}\] \[\therefore \frac{{{E}_{1}}}{{{E}_{2}}}=\frac{5\sqrt{5}}{4\sqrt{2}}\]


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