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. `-(6hat(i) + 9hat(j) + hat(k))`
B. `-(3hat(i) + 5hat(j) + 3hat(k))`
C. `-(6 hat(i) + 5hat(j) + 2hat(k))`
D. `-(2hat(i) + 3hat(j) + hat(k))`

Answer

C

Explanation

`vec(E )= (del V)/(dx) hat(i) - (del V)/(del y) hat(j) - (delV)/(del z) hat(k)`
`vec(E )= -(6y) hat(i)- (6x-1+2z ) hat(j)- (2y)hat(k)`
at point (1,1,0)
`vec(E )= -6hat(i) - 5hat(j)- 2hat(k)= -(6hat(i) + 5hat(j) + 2hat(k))`