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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 1

  • question_answer
    Electric potential in a 3-dimensional space is given by \[V=\left( \frac{1}{x}+\frac{1}{y}+\frac{2}{z} \right)\] volt where x, y and z are in metre. A particle has charge \[q={{10}^{-12}}\text{ }C\]and mass \[m={{10}^{-9}}\text{ }g\] and is constrained to move in xy-plane. Find the initial acceleration of the particle if it is released at (1, 1, 1) m.

    A) \[(2\hat{i}+\hat{j})m/{{s}^{2}}\]    

    B) \[(\hat{i}+\hat{j})m/{{s}^{2}}\]

    C) \[(\hat{i}+2\hat{j})m/{{s}^{2}}\]    

    D) \[\left( \frac{{\hat{i}}}{2}+\hat{j} \right)m/{{s}^{2}}\]

    Correct Answer: B

    Solution :

    [b] \[V=\frac{1}{x}+\frac{1}{y}+\frac{2}{z}\] \[\vec{E}=-\frac{\partial V}{\partial x}\hat{i}-\frac{\partial V}{\partial y}\hat{j}-\frac{\partial V}{\partial z}\hat{k}=\frac{1}{{{x}^{2}}}\hat{i}+\frac{1}{{{y}^{2}}}\hat{j}+\frac{2}{{{x}^{2}}}\hat{k}\] At \[(1,1,1)\,m\] \[\vec{E}=\hat{i}+\hat{j}+\hat{k}\] Resultant force on the particle in XY plane is             \[\vec{F}=q(\hat{i}+\hat{j})\]             \[\overrightarrow{a}=\frac{q}{m}(\hat{i}+\hat{j})=\frac{{{10}^{-12}}C}{{{10}^{-12}}kg}(\hat{i}+\hat{j})=(\hat{i}+\hat{j})m/{{s}^{2}}\]


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