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The electric potential V at any point $(x, y, z)$ in space is given by equation $V = 4 x^{2}$ volt where x, y and z are all in metre. The electric field at the point $(1 m, 0, 2 m)$ in V/m is:

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8 along negative x-axis

8 along positive x-axis

16 along negative x-axis

16 along positive x-axis

answer is A.

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Detailed Solution

$\vec{E} = - [\hat{i} \frac{\partial V}{\partial x} + \hat{j} \frac{\partial V}{\partial y} + \hat{k} \frac{\partial V}{\partial z}]$

Given $V = 4 x^{2}$

$\vec{E} = - \hat{i} (8 x) [Magnitude of \vec{E} is - 8 V / m]$

Hence, electric field is 8V/m along negative x-axis

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