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NEET Sample Paper NEET Sample Test Paper-64

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

    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 \[E={{\overrightarrow{E}}_{1}}+{{\overrightarrow{E}}_{2}}\] \[=\,\,\,\sqrt{E_{1}^{2}+E_{2}^{2}+2{{E}_{1}}{{E}_{2}}\,\cos \,60{}^\circ }\,\,=\,\,\frac{\sqrt{3}\eta q}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}\] 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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