If potential (in volts) in a region is expressed as `V (x, y, z) = 6xy - y + 2yz`, the electric field (in `N//C)` at point `(1, 1, 0)` is

Options

A. `-(6 hati + 9hatj + hatk)`
B. `-(3hati + 5hatj + 3hatk)`
C. `-(6 hati + 5 hatj + 2hatk)`
D. `-(2hati + 3hatj + hatk)`

Answer

C

Explanation

`V (x, y, z) = 6xy - y + 2yz`
`E_(X) = - (delV)/(delx) =- 6y = - 6`
`E_(y) = - (delV)/(dely) = - 6x + 1+ 2z = - 5`
`E_(z) = - (delV)/(delz) = - 2y = - 2`
`vecE = E_(x) hati + E_(y) hatj + E_(z) hatk`
`vecE = - (6 hati + 5 hatj + 2 hatk)`