Question

Question: Two small nonconducting spheres have a total charge of 93uC

A. When placed 1.17 m apart, the force each exerts on the other is 10.5 N and is repulsive. What is the charge on each?

B. What if the force were attractive?


I have broken up the Coulombs law equation to make Q1Q2 = Fr^2/k
And then used the quadratic formula to find Q2.
I ended up with
Q1 being 30.688uC
Q2 being 62.313uC
These were not correct

Answer 1

Answer 2

Given that
Q1 + Q2 = 93uC ......1
Q1Q2 = F r^2 / k = 10.5 * 1.17^2 / 9 x 10^9 = 1.597 x 10^-9 C^2
Therefore
(Q1 + Q2)^2 = (Q1-Q2)^2 + 4Q1Q2
(93 x 10^-6)^2 = (Q1 -Q2)^2 + 4 * 1.597 x 10^-9
==> 8.649 x 10^-9 = (Q1 -Q2)^2 + 6.388 x 10^-9
==> (Q1 - Q2)^2 = 2.261 x 10^-9
==> Q1 - Q2 = 0.4754 x 10^-8 = 0.004754uC ......2
addind 1 and 2 we get
2Q1 = 93.004754uC
==> Q1 = 46.502377uC
and Q2 = 93uC - 46.502377uC = 46.497623uC