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Manipal Medical Manipal Medical Solved Paper-2014

  • question_answer
    If an insulated non-conducting sphere of radius ?R has charge density\[\rho \]. The electric field at a distance r from the centre of sphere (r > R) will be

    A)  \[\frac{\rho R}{3{{\varepsilon }_{0}}}\]                                    

    B) \[\frac{\rho r}{{{\varepsilon }_{0}}}\]

    C) \[\frac{\rho r}{3{{\varepsilon }_{0}}}\]                                      

    D) \[\frac{3\rho R}{{{\varepsilon }_{0}}}\]

    Correct Answer: C

    Solution :

    Charge, \[\sigma =\frac{4}{3}\pi {{r}^{3}}\rho \] According to Gaussian law \[\varepsilon \oint{E\,ds=\sigma }\]  \[{{\varepsilon }_{0}}E4\pi {{r}^{2}}=\frac{4}{3}\pi {{r}^{3}}\rho \]  \[E=\frac{\rho r}{3{{\varepsilon }_{0}}}\]


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