Find Solution for Electrostatic Force Neutralization

[popo902]

Electrostatic Forcce :(

Homework Statement

In Fig. 21-26, particle 1 of charge q1 = +1.4 µC and particle 2 of charge q2 = -4.2 µC, are held at separation L = 12 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a) x and (b) y coordinates of particle 3?

Homework Equations

F = (Q1 * Q2)K/ r^2

The Attempt at a Solution

At first i thought i could go about this problem setting the particle to the left of the two
i figured that the charge on Q2 > Q1 so its pull would be compensated by Q1's push
(i made my particle three positive)
then i set F31 = F32 so that their forces would balance out to 0
that would make my y placemnt 0 as well
but now...im stuck
i did som canceling until i finally go to this:

(r^2) Q2
------------ = ---------
(0.12 +r)^2 Q1

or
(r^2) / (0.12 +r)^2 = Q2/ Q1

and i don't know wehre to go from there
so...
is there a way out or was i supposed to envision particle three somewhere else??

 

[gerben]

If you put your particle on left or right side of q1 and q2 so that it is closest to the one that pulls, you can set up two equations:

Fpull = q3*1.4/d^2
Fpush = q3*4.2/(d+12)^2

when the push and pull forces are equal...

 

[popo902]

Thats wuht i did
and i simplified it to get this


(r^2) / (0.12 +r)^2 = Q2/ Q1

i dint plug in the chrge values for Q1 and 2 yet
but i hope u see the jist
i pretty much started with waht u gave me, (except ur d was my r of course)
but from the equation above i can't figure out how to solve for r
so i was wondering if there was any other way to solve it?? :S

 

[gerben]

just equate them and solve the equation... here is a start:

q3*1.4/r^2 = q3*4.2/(r+12)^2 (--divide both sides by q3)
1.4/r^2 = 4.2/(r+12)^2 (--evaluate right side)
1.4/r^2 = 4.2/(r^2+24r+144) (--multiply both side by (r^2)(r^2+24r+144) )
1.4(r^2+24r+144) = 4.2r^2
etc...

 

[rwisz]

I would suggest looking at the problem in a different way. Instead of trying to solve for the x and y coordinates of particle 3, let's think about the conditions for the net electrostatic force to be zero.

We know that the electrostatic force between two particles is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance between them (L). In this problem, we have two particles with known charges (q1 and q2) and a third particle with an unknown charge (q3).

To find the conditions for the net electrostatic force to be zero, we can set up the following equation:

F13 + F23 = 0

Where F13 is the force between particles 1 and 3, and F23 is the force between particles 2 and 3. We can then substitute in the equations for these forces, using the given values for q1, q2, and L:

F13 = (q1 * q3)K/ r13^2
F23 = (q2 * q3)K/ r23^2

Where r13 and r23 are the distances between particles 1 and 3, and particles 2 and 3, respectively.

Now, we can solve for the conditions for the net electrostatic force to be zero:

(q1 * q3)K/ r13^2 + (q2 * q3)K/ r23^2 = 0

This equation can be simplified to:

(q1/r13^2) + (q2/r23^2) = 0

Since we know the values for q1, q2, and L, we can solve for the distances r13 and r23. Once we have these distances, we can then use trigonometry to find the x and y coordinates of particle 3.

In summary, instead of trying to solve for the coordinates of particle 3 directly, we can use the conditions for the net electrostatic force to be zero to find the distances between particle 3 and particles 1 and 2. From there, we can use trigonometry to find the coordinates of particle 3. This approach may be more straightforward and less algebraic.