Question

The potential field depends on the x - and y - coordinates as V = x^2 - y^2. The corresponding electric field lines in x y plane are as.

Answer 1

$\underline{\boxed{ \huge\purple{ \rm{Answer}}}} \\ \\ \underline{ \boxed{ \bold{ \rm{ \pink{E = - \frac{ \delta{V}}{ \delta{r}}}}}}}$

$\implies \rm \: V = {x}^{2} - {y}^{2} \\ \\ \implies \rm \: E_{x} = - \frac{ \delta{V}}{ \delta{x}} = - \frac{ \delta( {x}^{2} - {y}^{2}) }{ \delta{x}} = - 2x \\ \\ \implies \rm \: E_{y} = - \frac{ \delta{V}}{ \delta{y}} = - \frac{ \delta{( {x}^{2} - {y}^{2} ) }}{ \delta{y}} = 2y \\ \\ \therefore \: \underline{ \boxed{ \bold{ \orange{ \rm{E = 2(y - x)}}}}}$

Answer 2

Solution in attachment

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