In a region, the potential is respresented by `V(x, y, z) = 6x - 8xy - 8y + 6yz`, where `V` is in volts and `x, y, z` are in meters. The electric force experienced by a charge of `2` coulomb situated at point `(1, 1, 1)` is

Options

A. `6 sqrt(5) N`
B. `30 N`
C. `24 N`
D. `4 sqrt(35) N`

Answer

D

Explanation

Given, `V = 6x - 8 xy - 8 y + 6 yz`
`(E_(x))_(1,1,1) = -(del V)/(dx) = -(6-8 y) = -(6-8xx1) = 2`
`(E_(y))_(1,1,1) = -(del V)/(dy) = - (-8x -8 + 6z)`
`= -(-8xx1-8+6xx1) = 10`
`(E_(z))_(1,1,1) = -(del V)/(dz) = -(6y) = -6xx1=-6`
`E = sqrt(E_(x)^(2) +E_(y)^(2) + E_(z)^(2)) = sqrt(2^(2) +10^(2) +(-6)^(2))`
`= sqrt(140) = 2 sqrt(35) N//C`
`F = qE = 2xx2 sqrt(35) = 4 sqrt(35) N`