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

  • question_answer
    A solid metallic sphere has a charge \[+\,3Q\]. Concentric with this sphere is a conducting spherical shell having charge \[-Q\]. The radius of the sphere is \[a\] and that of the spherical shell is \[b(b>a)\]. What is the electric field at a distance \[R(a<R<b)\] from the centre                                                                  [MP PMT 1995]

    A)                    \[\frac{Q}{2\pi {{\varepsilon }_{0}}R}\]

    B)                                      \[\frac{3Q}{2\pi {{\varepsilon }_{0}}R}\]

    C)                    \[\frac{3Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]             

    D)            \[\frac{4Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}\]

    Correct Answer: C

    Solution :

               Electric field at a distance R is only due to sphere because electric field due to shell inside it is always zero. Hence electric field =\[\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{3Q}{{{R}^{2}}}\]


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