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. `vecE = hati (2xy + z^3) +hatj x^2 + hatk 3 xxz^2`
B. `vecE = hati 2xy + hatj (x^2 +y^2) +hatk (3xz-y^2)`
C. `vecE = hati z^3 +hatj xyz + hatk z^2`
D. `vecE = hati (2xy -z^3) +hatjxy^2 +hatk 3z^2 z`

Answer

A

Explanation

`V=-x^2y-xz^3+4`
`E=-((delV)/(delx)hati+(delV)/(dely)hatj+(delV)/(delz)hatk)`
`=-[(-2xy-z^3)i+(-x^2)hatj+(-3xz^2)hatk]`
`=(2xy+z^3)hati+x^2hatj+3xz^2hatk`