Question

Prediction

1. Make a force diagram showing the 3 forces of the string, the Earth, and the Coulomb force acting on one of the two Aluminum balls. In equilibrium, the sum of forces is 0 N.

2. When the Al ball is charged, it will repel from the other Al ball and the string will make a small angle θ with respect to the vertical line. Use trigonometry to relate the small angle θ to the gravitational and electrical force ratio. Since the angle is so small, the vertical distance will be very close to the total length L of the string. Relate the Al ball separation distance and the length of the string with the small angle θ

3. Derive an equation of the separation distance r between the two Al balls as a function of the charge Q. Note it will also depend on the mass m of the Al ball, and the length L of the string.

PLEASE HELP WITH QUESTION 3!!

Answer 1

• Let m be mass of each aluminium ball
• let charge on each ball be Q
• Let r is the separation distance

( I have assumed charge Q= ​​​​​​q , while deriving question)

Step:

1) Draw free body diagram on any charged mass

2) Balanced force in vertical and horizontal direction.

3) now find relation B/w angle   with length of string using trigonometry.

4) Now use electrostatic force Fe= Kq^{​​​​​2}​​​​/r^{​​​​​2}

⁵⁾ Find relation b/w r and Q using above equation.

Above is a relation between r , m, length of string L and charge q.