Question

Two small nonconducting spheres have a total positive charge of 108.4uC. When placed 1.08m apart, the force each exerts on the other is 12.8N and is repulsive. What is the (larger) charge on the spheres? What is the smaller charge on the other sphere?

Answer 1

Let the charges on the two spheres be q1 and q2, respectively.

We know that net charge is 108uC
i.e. q1 + q2 = 108uC

Also, a charged sphere can be considered to be point charge placed at its center for any point outside the sphere.
Therefore, force = k q1 q2 / r^2 (Coulomb's Law)
k = coulomb's constant = 9*10^9 H/m, r = distance of separation between the two point charges
Since the force is attractive, one sphere is positively charged and the other is negatively charged.

12.8 = 9*10^9 * q1q2 / (1.08)^2
q1q2 = 1.659 * 10^-9 C
q1q2 = 1.659 uC
q1 = 0.001659/ q2 uC

Putting this in the previous equation
0.001659 / q2 + q2 = 0.108

q2=108 uC

or q2=0.00001536 uC
On solving the resulting quadratic you will get values for q2 put them back in the equation to get q1, just make sure that q1 and q2 are opposite in sign because the force is repulsive.

q1= 0.001659/108 =0.00001536uC

or q2= 0.001659/0.00001536 =108 uC

108 uC larger charge

0.00001536uC small charge