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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Self Evaluation Test - Electric Chages and Fields

  • question_answer
    A point charge \[50\mu C\] is located in the x-y plane at a point whose position vector is \[\vec{r}=\left( 2\hat{i}+3\hat{j} \right)m.\]Then electric field at the point whose position vector is \[\vec{r}=\left( 8\hat{i}-5\hat{j} \right)m.\](in vector form) will be

    A) \[90\left( -3\hat{i}+4\hat{j} \right)V/m\]\[\]           

    B) \[900\left( 3\hat{i}-4\hat{j} \right)V/m\]

    C) \[90\left( 3\hat{i}-4\hat{j} \right)V/m\]     

    D) (d)\[900\left( -3\hat{i}+4\hat{j} \right)V/m\]

    Correct Answer: B

    Solution :

    [b] \[\vec{E}=\frac{kQ}{{{r}^{3}}}\vec{r}=\frac{9\times {{10}^{9}}\times 50\times {{10}^{-6}}}{|\vec{r}-{{{\vec{r}}}_{0}}{{|}^{3}}}\times \left( \vec{r}-{{{\vec{r}}}_{0}} \right)\] Where \[\vec{r}-{{\vec{r}}_{0}}=(8\hat{i}-5\hat{j})-(2\hat{i}+3\hat{j})=6\hat{i}-8\hat{j}\] \[\vec{E}=900\,(3\hat{i}-4\hat{j})\,V/m\]


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