An electrostatic potential is given by $ϕ = 2 x \sqrt{Y}$ volts in the rectangular co-ordinate system. The magnitude of the electric field at x=1 m, y = 1 m is V/m
2.24

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Solution

The correct option is A 2.24
Electrostatic potential, $ϕ = 2 x \sqrt{y}$
$∴ \to E = - g r a d (ϕ) = - ▽ ϕ$
$∴ \to E = - [{^a}_{x} \frac{\partial}{\partial x} (2 x \sqrt{y}) + {^a}_{y} \frac{\partial}{\partial y} (2 x \sqrt{y})]$
$\to E = - {^a}_{x} 2 \sqrt{y} - {^a}_{y} \frac{x}{\sqrt{y}}$
Now, at x = 1 m and y = 1 m
$\to E = - 2 {^a}_{x} - {^a}_{y}$
Magnitude of $\to E$
$| \to E | = \sqrt{2^{2} + 1^{2}}$
$= \sqrt{5} = 2.24$ V/m

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