Exploring Electric Force & Charge of Pith Ball

[mich_v87]

A positive charge Q is located at the origin.A small pith ball of mass m and positive charge q is attached to a light string and hangs from a point on the y-axis above the origin.The length of the string is.The teo posotove charges repel,and at equilibrium the pith ball is stationnary with the string making an angle θ to the y-axis, and with the pith ball being a distance L from Q,as shown in the sketch below.
1-Express the tension in the string T in terms of the electric force F on the pith ball and possibly other quantities
2-Express the charge q on the pith ball in terms of m,θ,L,Q and possibly other constants.

 

[Pyrrhus]

Well what have you done?

 

[quicknote]

1. The tension in the string, T, can be expressed in terms of the electric force, F, on the pith ball using the following equation:

T = Fcosθ

Where θ is the angle between the string and the y-axis. This equation takes into account the vertical component of the electric force acting on the pith ball.

2. The charge q on the pith ball can be expressed in terms of m, θ, L, Q, and other constants using the following equation:

q = √(2mgLsinθ)/(Q)

This equation takes into account the gravitational force acting on the pith ball, as well as the distance L and angle θ between the pith ball and the origin, and the magnitude of the charge Q at the origin. Other constants, such as the mass of the pith ball and the acceleration due to gravity, may also be included in this equation.