Two identical small insulating balls are suspended by separate 0.27 m threads that are attached to a common point on the ceiling. Each ball has a mass of 6.20 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 20° between the threads.

(a) What is the charge on each ball?
q = ----------C

(b) What is the tension in the threads?
F = ---.0062---N

cant figure out part (a) show all workings pliz

To calculate the charge on each ball, we need to use the concept of electrostatic forces between charged objects.

When the balls are given identical positive charges, they become positively charged and repel each other. This repulsion causes the balls to spread apart, forming an angle of 20° between the threads.

Let's analyze the forces acting on one of the balls:

- The weight force acting on the ball points vertically downward and is given by the equation:

F_weight = m * g

where m is the mass of the ball and g is the acceleration due to gravity (9.8 m/s²).

- The electrostatic force between the two charged balls acts horizontally and causes the ball to move away from the other. The magnitude of this force can be calculated using Coulomb's Law:

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

where k is the electrostatic constant (8.99 × 10^9 N·m²/C²), q is the charge on each ball, and r is the distance between the center of the balls.

- The tension force in the thread acts upward to balance the vertical component of the electrostatic force. This tension force keeps the ball in equilibrium vertically.

Now, let's find the charge on each ball (part a):

Since the balls are identical and the angles between the threads are the same, we can assume that the total electrostatic force on each ball due to the other ball is the same. Therefore, each ball experiences half of the total electrostatic force.

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

The vertical components of the electrostatic force and the tension force must be equal to maintain equilibrium:

F_electrostatic * sin(20°) = F_tension

Substituting the expressions for these forces, we get:

(k * (q^2) / r^2) * sin(20°) = m * g

Now we can solve for q:

q^2 = (m * g * r^2) / (k * sin(20°))

q = sqrt((m * g * r^2) / (k * sin(20°)))

Plugging in the given values:
m = 6.20 * 10^-4 kg (mass of each ball)
g = 9.8 m/s^2 (acceleration due to gravity)
r = 0.27 m (length of the thread)
k = 8.99 * 10^9 N·m²/C² (electrostatic constant)
sin(20°) ≈ 0.3420

q = sqrt((6.20 * 10^-4 * 9.8 * 0.27^2) / (8.99 * 10^9 * 0.3420))

Calculating this value will give you the charge on each ball.