Work required to move a charge through an electric field (3D)

[GAtechie291]

Homework Statement

"This problem regards the work required to move a 6nC charge through an electric field given by

E =

Initial point is at (2,-2,3)

Total length the charge is being moved = 2µm

Unit path length vector: a_l = -6/7 * a_x + 3/7 * a_y + 2/7 * a_z

Homework Equations

W = -Q * integral(E dL, from init position --> final position)

The Attempt at a Solution

I'm having trouble setting up this integral because I'm not sure how to determine the final position given the initial position and the distance traveled. Or is that not necessary?

 

[Spinnor]

I think the charge is moving in a straight line in the direction given by the above,

"Unit path length vector: a_l = -6/7 * a_x + 3/7 * a_y + 2/7 * a_z"

You know the distance traveled and the starting point.

Good luck!