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The electrical potential existing in space is $\;V\;(x , y, z) = A\;(xy+yz+zx)\;$ . Find the expression for the electric field

$(a)\;A\;((y+z) \hat{i}+(x+z) \hat{j} +(x+y) \hat{k})\qquad(b)\;A\;(x \hat{i}+y \hat{j} +z \hat{k})\qquad(c)\;-A\;((y+z) \hat{i}+(x+z) \hat{j} +(x+y) \hat{k})\qquad(d)\;-A(x \hat{i}+y \hat{j} +z \hat{k})$

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Answer : (c) $\;-A\;((y+z) \hat{i}+(x+z) \hat{j} +(x+y) \hat{k})$
Explanation :
$\overrightarrow{E}=-(\large\frac{\partial V}{\partial x}\;\hat{x}+\large\frac{\partial V}{\partial y}\;\hat{j}+\large\frac{\partial V}{\partial z}\;\hat{k})$
$\overrightarrow{E}=-(A\;(y+z) \hat{i}+A\;(x+z) \hat{j} +A\;(x+y) \hat{k})$
$\overrightarrow{E}=-A\;((y+z) \hat{i}+(x+z) \hat{j} +(x+y) \hat{k})\;.$
answered Feb 5, 2014 by yamini.v

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