The electric potential at a point in space is given as V=1x+1y+1z. The electric field magnitude at point (1, 1, 1) will be

Ex=−∂V∂x=1x 2 Ey=−∂V∂y=1y 2 Ey=−∂V∂z=1z 2 E→z=+1x2i^+1y2j^+1z 2k^ at (1, 1, 1) E→=+i^+j^+k^ |E→|=3N/C

The electric potential at a point in space is given as V=1x+1y+1z. The electric field magnitude at point (1, 1, 1) will be

Ex=−∂V∂x=1x 2 Ey=−∂V∂y=1y 2 Ey=−∂V∂z=1z 2 E→z=+1x2i^+1y2j^+1z 2k^ at (1, 1, 1) E→=+i^+j^+k^ |E→|=3N/C

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The electric potential at a point in space is given as $V = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ . The electric field magnitude at point (1, 1, 1) will be

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3 N/C

$2 \sqrt{3} N / C$

$3 \sqrt{3} N / C$

$\sqrt{3} N / C$

answer is B.

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Detailed Solution

$E_{x} = - \frac{\partial V}{\partial x} = \frac{1}{x_{}^{2}} E_{y} = - \frac{\partial V}{\partial y} = \frac{1}{y_{}^{2}} E_{y} = - \frac{\partial V}{\partial z} = \frac{1}{z_{}^{2}} {\vec{E}}_{z} = + \frac{1}{x^{2}} \hat{i} + \frac{1}{y^{2}} \hat{j} + \frac{1}{z_{}^{2}} \hat{k} at (1, 1, 1) \vec{E} = + \hat{i} + \hat{j} + \hat{k} | \vec{E} | = \sqrt{3} N / C$