The electric potential at a point (x, y, z) is given by `V=-xy+z-z^3yx` . The electric field `vecE` at the point (1,0,1) is (all quantities are in SI units)

Options

A. `(2hati-hatk)V//m`
B. `(2hatj + hatk)V//m`
C. `(2hatj-hatk)V//m`
D. `2hatj +2hatk)V//m`

Answer

C

Explanation

Use `vecE = -(dV)/(dr)`
Given `V=-xy+z-z^3yx`
`E_x=(-deltaV)/(deltax) = y+z^3y |_(1,0,1)=0`
`E_y=(-deltaV)/(deltay) = x+z^3x|_(1,0,1) = 2`
`E_z = (-deltaV)/(deltaz) = - 1+3z^3yx|_(1,0,1)= -1`
`vecE = E_xhati + E_y hatj + E_z hatk`
`=(2hatj - hatk) V//m`