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 apart.

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

Duplicate post. Already answered.

To find the magnitude of the charge on each ball, we can use Coulomb's law and the principle of electrostatic equilibrium.

Coulomb's law states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them:

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

Where F is the electrostatic force, q1 and q2 are the charges of the objects, r is the distance between them, and k is the electrostatic constant.

In this case, both pith balls have the same charge (let's call it q), and the distance between them is 19 cm. We can also assume that the electrostatic force is balanced by the tension in the threads.

Using the principle of electrostatic equilibrium, we can set up the following equation:

Tension1 * sin(θ) = Tension2 * sin(θ)

Where Tension1 and Tension2 are the tensions in the threads, and θ is the angle between the thread and the vertical direction.

Since the threads are of equal length and the pith balls are at rest, we can assume that the angle θ is the same for both threads.

Next, we need to find the tensions in the threads. Since the mass of the thread is neglected, tension is equal to the weight of the pith ball. The weight of an object is given by:

Weight = mass * gravity

Since the mass is negligible, we can assume that the weight is also negligible, so the tension in each thread can be considered equal to zero.

Now, we can rewrite the equation using the electrostatic force and the tension in the thread:

k * (q^2) / r^2 = Tension1 * sin(θ)

Since Tension1 is zero, the equation simplifies to:

k * (q^2) / r^2 = 0

We can ignore this equation since it doesn't give us any useful information. However, we can conclude that the magnitude of the charge on each pith ball is zero.

Therefore, the magnitude of the charge on each ball is zero.