Two 0.09 pith balls are suspended from the same point by threads 40 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

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

You need to say what the units of the mass are. All you said was 0.09

The above formula will allow you to compute the Coulomb force F. From that and the separation of the pith balls, you can get the charge

To find the magnitude of the charge on each ball, we can use Coulomb's Law, which states that the force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:

F = (k * |q1 * q2|) / r^2

Where:
- F is the electrostatic force between the balls.
- k is the electrostatic constant (9 * 10^9 Nm^2/C^2).
- q1 and q2 are the charges on the balls.
- r is the distance between the balls.

In this case, the balls are given equal charges, so we can assume q1 = q2 = q. The force between the balls is given by the equation:

F = (k * |q * q|) / r^2

Given that the balls come to rest 19 cm apart (r = 19 cm = 0.19 m), we can rearrange the equation to solve for q:

q = sqrt((F * r^2) / k)

Now, we need to find the value of F to substitute into the equation. The problem states that when the balls are given equal charges, they come to rest. This means that the electrostatic force between them is equal to the force due to the tension in the strings. Since the balls come to rest, the net force acting on each ball in the horizontal direction (perpendicular to the strings) must be zero.

The horizontal component of the tension in each string can be calculated using trigonometry:
T * sin(θ) = F

Where:
- T is the tension in the strings.
- θ is the angle the strings make with the vertical.

Since the strings are vertical, θ = 90 degrees, so sin(θ) = 1. Therefore, T = F.

Now, let's calculate the tension in the strings using Newton's second law. Since the balls are at rest, the net force acting on each ball in the vertical direction must be zero:

T + T = mg

Where:
- m is the mass of each ball (negligible in this case).
- g is the acceleration due to gravity (9.8 m/s^2).

Simplifying the equation, we have:
2T = mg
T = (1/2)mg

Now, substituting T = F into the equation, we get:
F = (1/2)mg

Finally, we can substitute the value of F into the equation for q:
q = sqrt(((1/2)mg * r^2) / k)

Since the problem statement does not provide the mass of the balls, we cannot determine the value of q using the given information alone.