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  4. In a certain region of space, variation of potential with distance from origin as we move along x-axis is given by V=8 x2+2, where x is the x-coordinate of a point in space. The magnitude of electric field at a point (-4,0) is

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Q. In a certain region of space, variation of potential with distance from origin as we move along $x$-axis is given by $V=8 x^{2}+2$, where $x$ is the $x$-coordinate of a point in space. The magnitude of electric field at a point $(-4,0)$ is

Electrostatic Potential and Capacitance

Solution:

$V=8 x^{2}+2$
$E_{x}=\frac{-d V}{d x}=-16 x$
$x=-4$
$E_{x}=64\, V / m$