Electrostatic Forces and Coulombs Law Question

[KMjuniormint5]

Homework Statement

Two small, positively charged spheres have a combined charge of 5.4 x 10-5 C. If each sphere is repelled from the other by an electrostatic force of 1.04 N when the spheres are 2.2 m apart, what is the charge on sphere with the smaller charge?

Homework Equations

Coulombs equation = k(q1)(q2)/(r^2)=E
Force=(q)(E)

The Attempt at a Solution

Plugging in what I knew I got E=1.00301x10^-5, took that and plugged it in the force equation . . .1.04=q(1.00301x10^-5) and found q to be 1.03687x10^-5 since Q+q=5.4 x 10-5 and we know now q . . .I just found Q to be 4.36313x10^-5 . . .so doesn't that make 1.03687x10^-5 the answer?

 

[Kurdt]

The equation you have for E is actually force. I don't understand how you could calculate E anyway since you don't know what the charges are. You just have to use the fact that you know the sum of the charges and rewrite it to get an equation for one charge in terms of the other. Sub that into the force equation and solve.

 

[KMjuniormint5]

ok I have done that as well where x+y=5.4 x 10-5 solved for say y and and plugged in:

1.04=[(k*x*((5.4 x 10-5)-x))]/(2.2^2) and I ended up with the quad. eq:

0=(-5.5991x10^-10)+(5.4x10^-5)x-x^2 . . then I used the quad equation to solve for x to be -8.9901x10^-5 or -1.8099x10^-5 . . .am I on the right track?

 

[Kurdt]

Yes you're on the right lines, but try and rearrange the quadratic so that the q^2 term has no constants in front of it and apply the quadratic formula.