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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2012

  • 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 which is enclosed in the surface is given by \[\sigma =\frac{4}{3}\pi {{r}^{3}}\rho \] Now according to Gaussian law                 \[\varepsilon \phi E\,ds,{{\varepsilon }_{0}}E\,4\pi {{r}^{2}}=\frac{4}{3}\pi {{r}^{3}}\rho \]                 \[E=\frac{\rho r}{3{{\varepsilon }_{0}}}\]


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