two identical positively charged balls hanging from the ceiling by insulated massless ropes of equal length /. What is the charge on each ball?

Question

(g=9.81m/s²)

Answer 1

To find the charge on each ball, we need to consider the forces acting on the balls.

The force acting on each ball is the weight due to gravity (mg) and the electrostatic force between the two balls.

Let's assume the charge on each ball is q, and the distance between the balls is d.

The electrostatic force between the balls is given by Coulomb's law:

Fe = k * (q^2) / d^2

where k is the electrostatic constant.

Since the balls are identical and both hanging in equilibrium, the forces on each ball must be equal.

The weight force on each ball is given by:

mg = mass * g

where g is the acceleration due to gravity.

Setting up the equilibrium equations:

mg = Fe

mass * g = k * (q^2) / d^2

We know that mass * g is the same for both balls, so we can cancel it out:

k * (q^2) / d^2 = k * (q^2) / d^2

Now we can solve for q:

q^2 = q^2

So, the charge on each ball can be any value, as long as they are equal. There is no unique solution for the charge on each ball given the provided information.