Electrical potential 'v' in space as a function of co-ordinates is given by, v=1x+1y+1z. Then the electric field intensity at (1, 1, 1) is given by

E=−dvdxi^+dvdyj^+dvdzk^⇒E=−1x2i^+1y2j^+1z2k^⇒E=−[i^+j^+k^]

Electrical potential 'v' in space as a function of co-ordinates is given by, v=1x+1y+1z. Then the electric field intensity at (1, 1, 1) is given by

E=−dvdxi^+dvdyj^+dvdzk^⇒E=−1x2i^+1y2j^+1z2k^⇒E=−[i^+j^+k^]

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Electrical potential 'v' in space as a function of co-ordinates is given by, $v = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ . Then the electric field intensity at (1, 1, 1) is given by

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zero

$- (\hat{i} + \hat{j} + \hat{k})$

$\hat{i} + \hat{j} + \hat{k}$

$\frac{1}{\sqrt{3}} (\hat{i} + \hat{j} + \hat{k})$

answer is A.

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Detailed Solution

$\begin{array}{l} E = - [\frac{dv}{dx} \hat{i} + \frac{dv}{dy} \hat{j} + \frac{dv}{dz} \hat{k}> \\ \Rightarrow E = - [\frac{1}{x^{2}} \hat{i} + \frac{1}{y^{2}} \hat{j} + \frac{1}{z^{2}} \hat{k}] \Rightarrow E = - [\hat{i} + \hat{j} + \hat{k}] \end{array}$