The potential `phi(x,y)` of an electrostatic field
`E=a(y hat(i)+c hat(j))` is [ a is a constant and `hat(i) and hat(j)` are unit vectors along X and Y axes ]

Options

A. `-2axy +` c (c is a constant)
B. `-axy +` c (c is a constant)
C. `a^(2)xy +` c (c is a constant)
D. `a(xy)^(2)+` c (c is a constant)

Answer

B

Explanation

(No option is mathing)
Usingn, `phi=-intE.dr`
we get `phi = - int a (y hat(i)+xhat(j)) (dx. hat(i)+dy.hat(j))`
`=-a(int(ydx + xdy)=-aintd(xy)`
= - a xy + C
`therefore` Potential,`phi(x , y) = - axy + C`