RAJASTHAN ­ PET Rajasthan PET Solved Paper-2002

  • question_answer
    Shown in the given diagram, the electric potential energy of the system will be \[\left( k=\frac{1}{4\pi {{\varepsilon }_{0}}} \right)\]

    A)  \[\frac{k{{q}^{2}}}{a}[\sqrt{2}-4]\]

    B)  \[\frac{k{{q}^{2}}}{a}\]

    C)  \[0\]

    D)  \[\frac{kq}{a}[\sqrt{2}-4]\]

    Correct Answer: A

    Solution :

     \[U=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ -\frac{{{q}_{2}}}{a}-\frac{{{q}^{2}}}{a}-\frac{{{q}^{2}}}{a}-\frac{{{q}^{2}}}{a}+-\frac{{{q}^{2}}}{a\sqrt{2}}+\frac{{{q}^{2}}}{a\sqrt{2}} \right]\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{\sqrt{2}{{q}^{2}}-4{{q}^{2}}}{a} \right]=\frac{k{{q}^{2}}}{a}(\sqrt{2}-4)\]


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