NEET Sample Paper NEET Sample Test Paper-39

  • question_answer The electric potential at a point in free space due to a charge Q coulomb is \[Q\times {{10}^{11}}\]volts. The electric field at that point is

    A) \[4\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}\,V/m\]

    B) \[12\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}\,V/m\]

    C) \[4\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}\,V/m\]

    D) \[12\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}\,V/m\]  

    Correct Answer: A

    Solution :

     The electric potential due to charge Q is \[V=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{r}\] where r is the distance of observation point from the charge. At the same point, electric field is \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{Q}{r}\] Combining Eqs. (i) and (ii), we have \[E=\frac{4\pi {{\varepsilon }_{0}}{{V}^{2}}}{Q}=\frac{4\pi {{\varepsilon }_{0}}\times {{(Q\times {{10}^{11}})}^{2}}}{Q}\] \[=4\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}\,V/m\]

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