Two identical pith balls, each carrying a charge q, are suspended from a common point by two strings of equal length ℓ. Find the mass of each ball if the angle between the strings is 20 in equilibrium.

Question

Philoid · Accepted Answer

Given:

Charges on ball = q

Angle between the balls = 2θ

Length of the strings = l

Let the magnitude of Tension be T. Let the electric force between the pitch balls be F_e. Let the mass of each pitch ball be m. The free body diagram is as follows:

Now, let the distance between the two charges be r.

By trigonometry,

By Coulomb’s law, the electric force id given by:

Where ϵ₀ is the permittivity of free space

q₁ and q₂ are the magnitude of charges

r is the distance of separation between the charges

Here, q₁ =q₂ = q.

Now, let us find the magnitude of the electric force, F_e :

Substituting eq (1), we get

As the system is in equilibrium, all the forces in each direction must sum up to zero.

Substituting (2) in (3), we get

Substituting (4), we get

Substituting (5) in (6), we get