How Much Work Is Needed to Move a Charge in an Electric Field?

[seang]

A positive point charge q1 = 2.30uC is located at the origin (x=0, y=0). The charge is held fixed. Another point charge q2 = 5.60uC starts at the point (0.180 m,0). What is the magnitude of the work required to move q2 to
(0,0.370 m) (in J)?

How do I do this?

I know W =Fd, but I don't think I can use the equation F = (k1q2)/r^2, because the distance is constantly changing.

Can anyone at least give me a hint or some insight?

 

[scholzie]

Remember, the electric force is conservative. That means that the path traveled does NOT affect the total work done. It's simply a matter of where the point starts, and where it ends. Find the potential energy at each place, and W = -\Delta PE.

Note that work is only done when r changes, by the way. Otherwise, the charge is traveling on an equipotential surface, and you get to move it around for free.

Also, W = F DOT d, which is an important distinction.

 

[Galileo]

Indeed, W=Fd holds only if F is constant. If F changes over the distance, you have to cut the distance into many small pieces and take F to be constant over each piece and sum up the contributions. In other words: integrate.