Question

Find the potential V of an electrostatic field E = a(yi + xj)

Answer 1

We know, relation between potential and electric field is given by
$\bold{V = - \int{E.dr}}$
Here, E = a(yi + xj) and dr = (dx i + dy j)
∴ $\bold{V = - \int{a(yi + xj).(dx i + dyj)}}$
V = -a∫(ydx + xdy)
= -a∫d(xy) = -axy

Hence, potential , V = - axy