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

Answer

3

Explanation

`V = 6x - 8xy - 8 y + 6yz`
`E_(x) = -(del V)/(del x) = -[6 - 8y] = 8y - 6`
`E_(y) = -(del V)/(delta y) = -[-8x - 8 + 6z] = 8x + 8 - 6z`
`E_(z) = -(del V)/(del z) = -[6y] = -6y`
At `(1,1,1)`
`E_(x) = 2 , E_(y) = 10 , E_(z) = -6`
`vec(E ) = E_(x) hat(i) + E_(y) hat(i) + E_(z) hat(k) = 2 hat(i) + 16 hat(j) - 6 hat(k)`
`E = |vec(E )| = sqrt((2)^(2) + (10)^(2) + (-6)^(2)) = sqrt(140) = 2 sqrt(35)`
`F = qE = 2 xx 2sqrt(35) = 4sqrt(35) N`