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If electric field $\overrightarrow{E} = 2\hat i +3 \hat j $ , Potential difference between two point $V_A- V_B$, where $r_A=\hat i+ 2 \hat j $ and $r_B=2 \hat i +\hat j + 3 \hat k $ will be

$(A)\;-1V \\ (B)\;1V \\ (C)\; 2V \\ (D)\;3V $

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$V_A-V_B= - \int \limits_B^A (E_x \hat i + E_y \hat j + E_z \hat k ). (dX \hat i +dy \hat j + dz \hat k)$
$\qquad= - \bigg[\int \limits_B ^A E_x dx+\int \limits_B ^A E_y dy+\int \limits_B ^A E_z dz\bigg]$
$V_A-V_B =- \bigg[\int \limits_1^2 2 dx +\int \limits _1^2 3 dy \bigg]$
$V_A-V_B= -1V$
Hence A is the correct answer.
answered Jan 15, 2014 by meena.p

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