Calculating Charge of Two Spheres in Equilibrium

[Pseudopro]

Homework Statement

Two plastic spheres each of mass 100.0 mg are suspended from very fine insulating strings of length 85 cm. When equal charges are placed on the spheres, the spheres repel and are in equilibrium when 10 cm apart.
(a) What is the charge on each sphere?

Homework Equations

F=kq²/r²

The Attempt at a Solution

I assumed that the strings were attached to the same place at the top. This eventually gave tan theta = kq²/mgr².
I did sin^-15/85 to get theta
I then plugged in all the values and got around 2.5x10^-7
The book answer is 8x10^-9.

Thanks for your time

 

[rl.bhat]

Show your substitution and calculation.

 

[ileacus]

I am hesitant to mention this, because when I follow this method, I arrive at a different answer than the given book answer. That said, I would analyze it like so:

Each sphere is repelled by an electric force that is sufficient to balance the gravitational force when the sphere is deflected 5 cm.

Draw a diagram - the spheres are connected to the ceiling by 85 cm strings and are displaced a total of 10cm (5cm each from vertical). What is the height difference from their displaced position and their straight down position? How much energy does that require?

 

[rl.bhat]

Take the projection of L on the vertical line.
Difference in height h = L - Lcosθ.