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=hati2xy+hatj(x^(2)+y^(2))+hatk(3xz-y^(2))`
B. `vecE=hatiz^(3)+hatjxyz+hatkz^(2)`
C. `vece=hati(2xy-z^(3))+hatjxy^(2)+hatk3z^(2)x`
D. `vecE=hati(2x+z^(3))+hatjx^(2)+hatk3xz^(2)`

Answer

D

Explanation

The electric field at a point is equal to negative of potential gradient at that point.
`vecE=-(delV)/(delr)=[-(delV)/(delx)hati-(delV)/(dely)hati-(delV)/(delz)hatk]`
`=[(2xy-z^(3))hati+hatjx^(2)+hatk3xz^(2)]`