Finding the distance between 2 charges in electric equilibrium.

[Ram012593]

Homework Statement

Charge A and charge B are 2.2m apart.Charge A is 1.0C, and charge B is 2.0c. Charge C, which is 2.0C, is located between them and is in electrostatic equilibrium. How far from charge A is charge C.

Homework Equations

E = KcQ1Q2/r^2-------Electric force Formula where E = electric force, Kc = 8.99*10^9, r = radius
E=Kq/r^2--------------Electric field formula where q = charge of particle, E = electric field, K = 8.99 * 10^9
EQ = F----------------E = electric field, Q = charge of particle, F = force

The Attempt at a Solution

Not really sure how to start this one so if anyone would help me it would be great thanks much in advanced!

 

[tiny-tim]

Hi Ram012593!

If the distance AC is r, then the distance BC is 2.2 - r.

Show us what you get. ​

 

[Ram012593]

Ok I've tried setting the formulas for the forces equal to each other since its electric equilibrium so the forces must be the same and tried to solve for ra the radius of the first two and I am not sure if i did it incorrectly or i made an algebra mistake it could easily be both as I'm not very good at algebra at the moment if anyone would correct me this would be great thanks much:D. Here is a link to a snapshot i took of what i did so far. If i am doing it correctly which is not likely can someone tell me how I could continue. http://postimg.org/image/q4md6ins1/

 

[tiny-tim]

Hi Ram012593!

… I'm not very good at algebra at the moment …

Yes, your method is fine, but your algebra has let you down …

your 1/r² = 2/(2.2 - r)² is correct ,

but you left out the 4.4r term when you expanded that square!

(btw, why use two letters, ra, or maybe r_a, when one letter will do? )