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

`V = 6x - 8xy - 8y + 6yz`
`E_(x) = - (delV)/(delx) = - (6 - 8y) = 2`
`E_(y) = (delV)/(dely) = - (-8x - 8+ 6z) = 10`
`E_(z) = - (delV)/(delz) = - 6y = - 6`
At `(1, 1, 1), vecE = 2 hati + 10 hatj - 6 hatk`
`(vecE) = sqrt(2^(2) + 10^(2) + 6^(2)) = sqrt(140) = 2sqrt(35) N//C`
`F = - qvecE = 2 xx 2 sqrt(35) = 4 sqrt(35) N`