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Electric Potential at a Point in Space Due to a Point Charge Q

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Question

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

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Solution

$V = 4 x^{2}$
$E = - \frac{d V}{d x} = - 8 x$
$\Rightarrow E (1, 0, 2) = - 8 (1) = - 8 V / m$

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