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# An electric field $\;\overrightarrow{E}=(2 \hat{i}+3\hat{j})\;N/C$ exists in space . if the potential at the origin is zero , find the potential at $\;(2 ,2 )\;m$

$(a)\;-100 V\qquad(b)\;10 V\qquad(c)\;- 10V\qquad(d)\;100 V$

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Answer : (c) -10 V
Explanation : $\;V_{a}-V_{b}=-\;\int_{b}^{a}\;\overrightarrow{E} . \overrightarrow{dl}$
$V_{(2 , 2)}-0= -\;\int_{(0 ,0)}^{(2 , 2)}\;(2 \hat{i}+3\hat{j})(dx \hat{i}+dy \hat{j})$
$V_{(2 , 2)}= -\;\int_{(0 ,0)}^{(2 , 2)}\;(2 dx +2 dy )$
$=(2\times2+3\times2)$
$V_{2 ,2 }=-10 V\;.$
answered Jan 29, 2014 by