Figure 21-34 shows electrons 1 and 2 on an x axis
and charged ions 3 and 4 of identical
charge q and at identical
angles θ. Electron 2 is free to
move; the other three particles
are fixed in place at horizontal
distances R from electron 2 and
are intended to hold electron 2 in
place. For physically possible values
of q [itex]\leq[/itex] 5e, what are the (a)
smallest, (b) second smallest, and
(c) third smallest values of θ for
which electron 2 is held in place?
Fx,2,net= F21 - cosθ(F24+F23)
2y = The distance from q3 and q4
I created a FBD for q2
The Attempt at a Solution
Okay, so I derived the above equation from the sum of the forces in the x direction. I'm trying to solve for cosθ, and the equation I ended up with is:
cosθ = (-e/2q3)1/3
I know that θ≥0 because q3 and q4 can't occupy the same space.
I also know that in order for F2,net to equal zero, F21 must equal cosθ(F24+F23).
Therefore: kq1q2/R2 = cosθ[(kq2q4)+(kq2q3)/(R2+y2)]
..and that's where I get lost. I end up with the cosθ equation from above. I feel like I should be taking a derivative. Perhaps δθ/δq3. Could someone please point me in the right direction. I tried working on it for quite some time but now my ADHD meds are wearing off and I'm about to take a nosedive directly into keyboard land. Thank you for any help.