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

16

along positive x-axis.

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8

along negative x-axis.

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16

along negative x-axis.

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8

along positive x-axis.

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Solution

The correct option is B $8$ along negative x-axis.
The electric field along x-axis is given by,

$\to E = - \frac{d V}{d x}^i$

$= - \frac{d (4 x^{2})}{d x}$

$= - 8 x^i volt/meter$
${\to E}_{(1, 0, 2)} = - 8^i V/m$

Hence, $(D)$ is the correct answer.

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