Two identical small insulating balls are suspended by separate 0.23-m threads that are attached to a common point on the ceiling. Each ball has a mass of 8.70 10-4 kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, spread apart with an angle of 34° between the threads.

Determine the charge on each ball.

Determine the tension in the threads.

To determine the charge on each ball, we can use the principle of electrostatics that like charges repel each other. In this case, as the balls spread apart, it indicates that they have the same positive charge.

To find the charge on each ball, we can use the following steps:

1. Draw a diagram: Sketch the setup with the balls hanging from the ceiling, attached to individual threads, and separated by the angle of 34°.

2. Identify the forces acting on the balls: The two forces acting on each ball are gravity (mg) pulling the ball downward and the electrostatic repulsion force (F) pushing the balls apart.

3. Analyze the forces: The net force acting on each ball is the vector sum of the gravitational force and the electrostatic force. Since the balls are in equilibrium (i.e., not accelerating), the net force on each ball is zero.

4. Resolve the forces: Resolve the gravitational force into its components. The vertical component cancels out the tension in the threads, while the horizontal component balances the electrostatic repulsion force.

5. Write equations: Equate the horizontal component of the gravitational force to the electrostatic force.

6. Solve for the charge: Use the equation F = k * q^2 / r^2, where F is the electrostatic force, k is the electrostatic constant, q is the charge on each ball, and r is the distance between the balls.

7. Calculate the charge: Substitute the known values into the equation and solve for q.

To determine the tension in the threads, we can use the concept of static equilibrium. In static equilibrium, the sum of the forces acting on an object is zero. In this case, the tension in the threads balances the vertical component of the gravitational force.

To find the tension in the threads, we can use the following steps:

1. Draw a free-body diagram: Sketch the forces acting on one of the balls, including the tension in the thread, the electrostatic repulsion force, and the gravitational force.

2. Analyze the forces: The net force acting on the ball in the vertical direction is zero since it is in equilibrium. The vertical component of the gravitational force is balanced by the tension in the thread.

3. Write equations: Equate the vertical component of the gravitational force to the tension in the thread.

4. Solve for the tension: Use the equation m * g * cosθ = T, where m is the mass of the ball, g is the acceleration due to gravity, θ is the angle between the threads, and T is the tension in the thread.

5. Calculate the tension: Substitute the known values into the equation and solve for T.

By following these steps, you should be able to determine the charge on each ball and the tension in the threads.