The potential of electrostatic field is given by , where x & y are coordinate. Which of the following is correct?

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Solution

Q.
The potential of electrostatic field is given by $ϕ = x y$ , where $x$ & $y$ are coordinate. Which of the following is correct

1 Electric field at all points on positive x-axis is in positive y-direction.

2 Electric field at all points of positive y-axis is in negative x-direction.

3 Electric field at (2, 2) is $\sqrt{2} N / m$ .

4 Electric field at $x, y$ makes an angle $θ = \tan^{- 1} (\frac{y}{x})$ with x-axis

Ans.
(2)

$E = - y \hat{i} - x \hat{j},$ $\tan θ = \frac{E_{y}}{E_{x}} = \frac{x}{y}$

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