Oscillation of point charge due to electric field

[sushichan]

Homework Statement

[/B]
14. Two positive point charges of magnitude Q and 9Q are a distance d apart, as shown in Figure 2.22 (image attached).

a) Calculate the electric field strength at point P, a distance d/4 from Q.​

A third positive point charge is placed at P and is then displaced a bit to the right.

b) Explain why the charge will perform oscillations when released.
c) Are the oscillations simple harmonic?
d) How does your answer to b) change if the third charge is negative?
​

15. Consider again the previous problem. Suppose that the third positive charge placed at P has a magnitude q and mass m. It is displaced to the right of P by a small amount x.

a) Find an expression for the net force on the charge q.
b) In mathematics it can be proved that if x is small then (1+x)^-2≈1-2x. Use this approximation on the expression for the net force you found in a) to show that it is is approximately equal to F≈(-256kQq)x/(3d³) where x is the displacement from point P.
c) Hence determine the nature of the oscillations that will take place when the charge q is released.​

Homework Equations

E=kQ/r² (electric field)

The Attempt at a Solution

14.
a) I solved it, ans: 0
b) I was thinking that the force would try to place the charge into the equilibrium position (where electric field is 0). But I don't understand why it would oscillate.
c)
d)

15.

 

[haruspex]

Try some equations. If the third charge is a small distance x from the equilibrium position, towards the charge Q say, what is the net force on it?