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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Critical Thinking

  • question_answer
    A non-conducting ring of radius \[0.5\,m\] carries a total charge of \[1.11\times {{10}^{-10}}C\] distributed non-uniformly on its circumference producing an electric field \[\vec{E}\] everywhere in space. The value of the line integral \[\int_{l=\infty }^{l=0}{\,-\overrightarrow{E}.\overrightarrow{dl}}\,(l=0\] being centre of the ring) in volt is                                                                       [IIT 1997 Cancelled]

    A)                    + 2

    B)            ? 1

    C)                    ? 2                                    

    D)            Zero

    Correct Answer: A

    Solution :

                       \[\int_{\,-\infty }^{\,0}{-\overrightarrow{E}\,\cdot \overrightarrow{dl}}\]= potential at centre of non-conducting ring \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\times \frac{q}{r}=\frac{9\times {{10}^{9}}\times 1.11\times {{10}^{-10}}}{0.5}=2\,volt\]                       


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