AMU Medical AMU Solved Paper-1999

  • question_answer The electric field in a region is radially outward with magnitude\[E=Ar\]. The charge contained in a sphere of radius\[{{r}_{0}}\]centered at the origin is

    A)  \[\frac{1}{4\pi {{\varepsilon }_{0}}}Ar_{0}^{3}\]

    B)  \[4\pi {{\varepsilon }_{0}}\,Ar_{0}^{3}\]

    C)  \[\frac{4\pi {{\varepsilon }_{0}}A}{r_{0}^{3}}\]

    D)  \[\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{A}{r_{0}^{3}}\]

    Correct Answer: B

    Solution :

    : Intensity [E] at surface of sphere\[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{r_{0}^{2}}\] Since\[E=A{{r}_{0}}\] \[\therefore \] \[A{{r}_{0}}=\frac{Q}{4\pi {{\varepsilon }_{0}}r_{0}^{2}}\] or  \[Q=4\pi {{\varepsilon }_{0}}Ar_{0}^{3}\]

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