# E&M Electric Fields (Harmonic Motion?)

1. Oct 1, 2007

### physicsnewblol

E&M Electric Fields (Harmonic Motion????)

This problem comes out of "Physics (for scientists and engineers w/ modern physics) Volume 2 7th Edition" by Serway/Jewett

Review Problem Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between the two fixed charges.

A. Show that if x is small compared with d, the motion of -Q is simple harmonic along the perpendicular bisector. Determine the period of that motion.

Regarding harmonic motion, I don't even know where to begin. This problem most likely has something to do with Coulomb's law but I don't see how that helps.

Edit: I can find the net forces by adding each of the respective components together, but I have no clue what to do then.

Anyone have ideas?
-Physicsnewblol

Last edited: Oct 1, 2007
2. Oct 1, 2007

### Hootenanny

Staff Emeritus
This sounds like a good plan. I would write out the net force acting on the third particle as a function of position (x).

3. Oct 1, 2007

### robphy

Alternatively, one could try to compute the electric potential energy of the system... as a function of position (x).

4. Oct 6, 2007

### physicsnewblol

found a little blurb in my book: "If the equation of the force is in the form of the f = -kx (I forget the name, it has to do with springs) then the motion is simple harmonic"

5. Oct 7, 2007

### robphy

Yes, that hooks in directly with Hootenanny's hint.
If you know how to determine the period of a spring, then you could finish the problem... by analogy.
(By the way, my suggestion uses energy instead of force, which might be easier to work with. But, at this stage, it might be better to follow the suggestion in your blurb.)

6. Oct 7, 2007

### Hootenanny

Staff Emeritus
:rofl: