Potential in the $x - y$ plane is given as $V = 5 (x^{2} + x y)$ volts. Find the electric field at the point $(1, - 2)$ .

(- 8^j) V / m

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(- 5^j) V / m

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(- 6^j) V / m

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(- 7^j) V / m

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Solution

The correct option is D $(- 5^j) V / m$ .
$V = 5 (x^{2} + x y)$
$E = \frac{- \partial V}{\partial r}$
$\to E = - [\frac{\partial V}{\partial x}^i + \frac{\partial V}{\partial y}^j]$
$\to E = - 5 [(2 x + y)^i + x^j]$
$\to E = - 5^j$ v/m $[(x, y) = (1, - 2)]$

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