Electric potential is given by
`V = 6x - 8xy^(2) - 8y + 6yz - 4z^(2)`
Then electric force acting on `2C` point charge placed on origin will be

Options

A. `2 N`
B. `6 N`
C. `8 N`
D. `20 N`

Answer

4

Explanation

`V = 6x - 8xy^(2) + 6 yz - 4x^(2)`
`E_(x) = -(del V)/(del x) = - [ 6 - 8y^(2) - 8x]`
`E_(y) = - (del V)/(del y) = -[ -16 xy - 8 + 6z]`
`E_(z) = -(del V)/(del z) = -[6y]`
At `(0,0,0) ,E_(x) -6 , E_(y) = 8 , E_(2) = 0`
`vec(E ) = -6 hat(i) + 8 hat(j)`
`vec(F) = q vec(E ) = 2(-6 hat(i) + 8 hat(j)) = -12 hat(i) + 16 hat(j)`
`|vec(F)| = sqrt((-12)^(2) + (16)^(2)) = 20 N`