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Electric potential is given by $\;V=2x^2\;$ Find the electric field at $\;(1 ,0 ,2)\;$ in Volt/metre.

$(a)\;4 \hat{i}\qquad(b)\;-4 \hat{i}\qquad(c)\;8 \hat{i}\qquad(d)\;-8 \hat{i}$

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Answer : (b) $\;-4 \hat{i}$
Explanation : $\overrightarrow{E} = -\large\frac{\partial V}{\partial x} \hat{i} -\large\frac{\partial V}{\partial y} \hat{j} - \large\frac{\partial V}{\partial z} \hat{k} $
$\overrightarrow{E} = -4x \hat{i}$
$\overrightarrow{E}|_{1 , 0 , 2} = -4 \hat{i}\;.$
answered Jan 31, 2014 by yamini.v

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