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12th Class Physics Electrostatics & Capacitance Question Bank MCQ - Electrostatic Potential and Capacitance

  • question_answer
    Three charges \[1\mu C\], \[2\mu C,\,3\mu C\]are kept at vertices of an equilateral triangle of side 1 m. If they are brought nearer, so they now form an equilateral triangle of side 0.5 m, then the work done is:

    A) 11J                              

    B) 1.1J

    C) 0.01 J              

    D) 0.1 J

    Correct Answer: C

    Solution :

    (c) 0.01 J Initial PE of the three charges, \[{{U}_{i}}k\frac{{{q}_{1}}{{q}_{2}}+{{q}_{2}}{{q}_{3}}+{{q}_{1}}{{q}_{3}}}{r}\] \[=9\times {{10}^{9}}\left[ \frac{1\times 2\times {{10}^{-12}}+2\times 3\times {{10}^{-12}}+1\times 3\times {{10}^{-12}}}{1} \right]\]\[=99\times {{10}^{-3}}\,J\] Final PE of the system \[{{U}_{f}}=9\times {{10}^{9}}\left[ \frac{1\times 2\times {{10}^{-12}}+2\times 3\times {{10}^{-12}}+1\times 3\times {{10}^{-12}}}{1} \right]\]\[=\frac{99\times {{10}^{-3}}}{0.5}=198\times {{10}^{-3}}J\] \[W={{U}_{f}}-{{U}_{i}}=\left( 198-99 \right)\times {{10}^{-3}}J\] \[=99\times {{10}^{-3}}J=0.099=0.01\,J\]


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