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NEET Sample Paper NEET Sample Test Paper-69

  • question_answer
    C Two charges each equal to \[nq({{\eta }^{-1}}<\sqrt{3})\] are placed at the corners of an equilateral triangle of side a. The electric field at the third corner is \[{{E}_{3}}\] where \[({{E}_{0}}=q/4\pi {{\varepsilon }_{0}}{{a}^{2}})\]

    A) \[{{E}_{3}}={{E}_{0}}\]                    

    B) \[{{E}_{3}}<{{E}_{0}}\]

    C) \[{{E}_{3}}>{{E}_{0}}\]                    

    D) \[{{E}_{3}}\ge {{E}_{0}}\]

    Correct Answer: C

    Solution :

    \[{{E}_{1}}=\frac{\eta q}{4\pi {{\varepsilon }_{0}}{{a}^{2}}},\,\,{{E}_{2}}=\frac{\eta q}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}\] Therefore \[E={{\vec{E}}_{1}}+{{\vec{E}}_{2}}\] \[=\,\,\,\sqrt{E_{1}^{2}+E_{2}^{2}+2{{E}_{1}}{{E}_{2}}\cos \,\,60{}^\circ }\,\,=\,\,\frac{\sqrt{3}\,\eta q}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}\,\,\] Since \[{{\eta }^{-1}}<\sqrt{3},\,1\,<\,\sqrt{3}\eta ,\,\,\sqrt{3}\eta >1\] \[\Rightarrow \,\,\,\,\frac{\sqrt{3}\eta q}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}>\frac{q}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}\] \[\Rightarrow \,\,\,\,\,\,\,{{E}_{3}}>{{E}_{0}}\,\left( {{E}_{0}}=\frac{q}{4\pi {{\varepsilon }_{0}}{{a}^{2}}} \right)\]


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