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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 26

  • question_answer
    The electric field in a certain region is given by \[\overrightarrow{\operatorname{E}}=\left( 5\hat{i}\,-3\hat{j} \right)\,k\,V/m\]. The potential difference \[{{V}_{B}}-{{V}_{A}}\] between points A and B, having coordinates (4,0, 3)m and (10,3, 0)m respectively, is equal to

    A) 21 kV               

    B) -21 kV

    C) 39 kV   

    D)        -39 kV

    Correct Answer: B

    Solution :

    Here, \[\vec{E} = 5\hat{i}\,- 3\hat{j}\,k\,V / m\] \[{{\operatorname{V}}_{B}}-{{V}_{A}}=-\int\limits_{{{r}_{A}}}^{{{r}_{B}}}{\,\vec{E}\,.\,\partial r}\] \[=\,\,-\int\limits_{(4,\,\,0,\,\,3)}^{(10,\,\,3,\,\,0)}{(5\hat{i}-3\hat{j})\cdot (\partial x\hat{i}+\partial y\hat{j}+\partial z\hat{k})}\] \[=\,\,\,-\int\limits_{4}^{10}{5\partial x-\int\limits_{0}^{3}{(-3)\partial y+0=-\,5[x]_{4}^{10}+3[y]_{0}^{3}}}\] \[=\,\,-5~(10-4)+3(3-0)=-30+9=-21kV\]


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