Two 0.09g pith balls are suspended from the same point by threads 40cm long. (Pith is a light insulating material once used to make helmets worn in tropical climates.) When the balls are given equal charges, they come to rest 19 cm apart

What is the magnitude of the charge on each ball? (Neglect the mass of the thread.)
q = C

I got this from drwls but I am still unable to figure it out.

I got the angle A as 12.27 and then
tan12.27 = F/Mg = F/.09g x9.8m/sec^2
.2174 x .09g x 9.8m/sec^2 = F = .1917468
I used F so F=E = kq/r^2
.1917468 = 9.0 x 10^9 x q/.19^2
.1917468 x 19^2/9.0 x 10^9 = 7.69117722 x 10^13 C = q
This the wrong answer. Please help.
This is the help from drwls.

physics - drwls, Sunday, January 24, 2010 at 2:50am
Compute the angle of the strings from vertical. It is sin^-1 (8.5/40)
Call this angle A

If the string tension is T

T sin A = F (the Coulomb force)
T cos A = M g

tan A = F/Mg

To find the magnitude of the charge on each ball, you need to solve for the Coulomb force using the tension in the strings and the angle between the strings and the vertical direction.

Here's a step-by-step approach to solving the problem:

1. Start by finding the angle A between the strings and the vertical direction. Use the given information that the balls come to rest 19 cm apart and the lengths of the threads are 40 cm. The vertical distance between the balls is 8.5 cm (since the length of each thread in the vertical direction is 40 cm - 19 cm = 21 cm). The angle A can be found using the sine function: A = sin^(-1)(8.5 cm / 40 cm).

2. Next, find the tension in the strings (T) and the weight (M g) of each ball. The tension in each string is equal to the weight of each ball (since the system is in equilibrium). So, T = M g, where M is the mass of each ball and g is the acceleration due to gravity.

3. Use the tangent function to find the Coulomb force (F) acting on each ball: tan(A) = F / (M g).

4. Rearrange the equation to solve for F: F = tan(A) * (M g).

5. Once you have the value of F, you can use the equation F = k * (q / r^2) to solve for the magnitude of the charge on each ball (q). The value of k is the Coulomb constant (k ≈ 9.0 x 10^9 N m^2 / C^2), and r is the distance between the balls (r = 0.19 m).

6. Rearrange the equation to solve for q: q = F * r^2 / k.

7. Plug in the values you have calculated into the equation to find the magnitude of the charge on each ball (q).

It's important to note that in your initial calculation, you used the incorrect angle value. Calculating the correct angle and following the steps above should give you the correct answer.