In a certain region, the electric potential is given by the formula V(x ,y, z) = 6xy - y + 2yz Find the components of electric field and the vector electric field at point (1, 1, 0) in this field. Find the vector of electric at (1, 1, 0).

Options

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

Answer

A, B

Explanation

`vecE=-((delV)/(delx)hati+(delV)/(dely)hati+(delV)/(delz)hatk)`
`=-[(6y)hati+(6x-1+2z)hatj+(2y)hatk]`
(1,1,0) ( Near point)
`vecE= -[6hati +(6-1+0) hatj+2hatk]`
`vecE = - [6 hati+5hatj+2hatk]`