The electirc potential at a point `(x, y, z)` is given by
`V = -x^(2)y - xz^(3) + 4`
The electric field `vecE` at that point is

Options

A. `vec(E ) = hat (i) (2xy + z^(3)) + hat(j) x^(2) + hat(k) 3 xz^(2)`
B. `vec(E ) = hat(i) 2 xy + hat(j) (x^(2) + y^(2)) + hat(k) (3xy - y^(2))`
C. `vec(E ) = hat(i) z^(3) + hat(j) x y z + hat(k) z^(2)`
D. `vec(E ) = hat(i)(2xy - z^(2)) + hat(j) xy^(2) + hat(k) 3z^(2) x`

Answer

1

Explanation

`V = -x^(2)y - x z^(3) +4`
`E_(x) = -(del V)/(del x) = 2xy + z^(3)`
`E_(y) = -(del V)/(del y) = x^(2)`
`E_(z) - (del V)/(del z) = 3xz^(2)`
`vec(E ) = E_(x) hat(i) + E_(y) hat(j) + E_(z) hat(k)`
`= (2xy + z^(3)) hat(i) + x^(2) hat(j) + 3 xz^(2) hat(k)`