Determine the electric field strength vector if the potential of this field depends on x, coordinates as
(a) `V = a (x^2 — y^2)` (b) `V = axy`
where, a is a constant.

Explanation

(a) Given, `varphi = a(x^(2) - y^(2))`
So, `vec(E) = -vec(grad) varphi = -2a (x vec(i) - y vec(j))`
The sought shape of field lines is as shown in fig of answersheet assuming `a gt 0` :
(b) Since `varphi = axy`
So, `vec(E) = -vec(grad) varphi = -ay vec(j) - ax vec(j)`
Plot as shown in fig(b) of answersheet.