Find equilibruium position for charged partical problem

[FocusedWolf]

Find equilibrium position for charged particle problem

3 charged particles on y axis. A third particle is somewhere such that the resultant force on it is zero.

What is distance from 0rigin of x y-axis to Q 3.

http://focusedwolf.googlepages.com/1.bmp

Node: for particle 3, that's the absolute value of 3 microcolumbs (not 131, those are absolute value things :P)... I'm assuming it's positive for this.

So I drew up a free body diagram for Forces on 3 net.

http://focusedwolf.googlepages.com/2.bmp

So,

http://focusedwolf.googlepages.com/3.bmp

Ok so how do I figure out which is the correct value of y?

[their are 3 image above...if you can't see them, then it'll look like i didn't do any work]

 

[Doc Al]

What range of values for y makes sense?

 

[FocusedWolf]

i'd say above Q1...so distance from y-axis =

2m + 5.84992=7.84992 or
2m + 2.29823=4.29823

hmm...unless... it's that distance (5.84992 or 2.29823) below q1 and under q2... that makes more sense.

so

2m - 5.84992=-3.84992 or
2m - 2.29823=-0.29823

below q1

 

[Doc Al]

Before you even start "turning the crank" on a problem such as this, first ask yourself: What region must the 3rd charge be in? There are three choices:
(1) Above Q1
(2) Between Q1 and Q2
(3) Below Q2
Only one region allows for the possibility of equilibrium. Which? (Think it through. Imagine that the third charge is a negative charge.) Once you figure out which region Q3 must be in, then you'll know which answer is correct.

 

[FocusedWolf]

I figured it out...only took a few days

Q3 is the negative charge between q1 and q2.

http://focusedwolf.googlepages.com/work.png

I know the anser is right cause the it gets submitted online and was confirmed to be correct. Just don't know if my way of picking the right X is right.

 

[Doc Al]

You should be able to figure out which of the three potential regions is the only one that makes sense without doing any calculations. Realize that Q1 and Q2 are both positive. For Q3 above Q1 (or below Q2) the forces on Q3 would add instead of cancel. So the answer must be between Q1 and Q2.