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Coulombs Law with one unknown charge 
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#1
Jan2505, 01:48 AM

P: 835

y(m)
/\ 2  q3   1 q1   q2> x(m) 2 *graphic* is kind of distorted. So the coordinates of the charges are: q1 = (0,1) q2 = (2,0) q3 = (2,2) given: q1 = 2.5 x 10^5 C q2 = 2.0 x 10^5 C q3 = ? Problem: If the force on q1 points in the x direction (a) what is q3. (b) what is the magnitude of the force on q1. Notation Key: Why? Sorry, but the LaTeX seems to be turned off or something. So I hope this is ok. r_ab = distance from a to b R_ab = unit vector from a to b Coulombs law: F_ab=k q_a q_b  R C r_13 = sqrt(1+2^2) = sqrt(5)m r_23 = 2m R_23 = J = <0,1> R_13 = (2IJ)/sqrt(5) = <(2sqrt(5))/5,sqrt(5)/5> F_net_3 = F_23 + F_13 from superposition principle F_23 = (9 x 10^9 N m^2) (2.0 x 10^5 C) q3 C R_23   C^2 (2m)^2 F_13 = (9 x 10^9 N m^2) (2.5 x 10^5 C) q3 C R_23   C^2 (2m)^2 F_23 = <0, 1 * (1.8 x 10^5 q3)/5> N F_13 = <(2.25 x 10^5 q3)/5 (2)sqrt(5)/5 ,2.25 x 10^5 q3)/5 (sqrt(5))/5> F_23 = <0, 3.6 x 10^4 q3> N F_13 = <40249.2 q3, 20124.6 q3> N Now this is where I get stuck since I have to many unknowns. I just don't know what to do from here... ANY help would be amazing. Thanks. 


#2
Jan2505, 01:54 AM

P: 610

your r_13 and r_23 is completely wrong already, I didn't check the rest....
do you having difficulty finding distance? 


#3
Jan2505, 12:05 PM

P: 835

Sorry about that. Actually the mistake was in the coordinate system. q3 is supposed to be (2,2) not (0,2) like I had... so I guess I have trouble typing in proper numbers, not finding the distance :)
P.S. It looks god awefull without latex. Is it turned off or something? 


#4
Jan2505, 01:12 PM

P: 610

Coulombs Law with one unknown charge
draw the graph, use symmetry argue q3 is equal to q2(hopefully you can see that), it will save you a lot of time
then find the x component of the force (should be easy for you) 


#5
Jan2505, 01:34 PM

P: 835

I don't really see why q3 is equal to q2. But, I'll just go under the assumption that it is and work though the process.
Thank you for the help :) 


#6
Jan2505, 01:57 PM

HW Helper
P: 4,124

Write an equation for the sum of the 2 ycomponents and set it equal to zero. Then you'll see that q3=q2. 


#7
Jan2605, 12:57 PM

P: 835

Thank you guys so much. I guess I was just making the problem harder then it was. I definitely see why the forces cancel if q3=q2. Ok cool... :) Just glad I got that done.
By the way, this board is awesome. 


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