Answer:
The number of electrons surplussed on each surface is .
Explanation:
Given:
The masses of the sphere,
The length of the strings,
The angle made by each string with vertical,
According to the diagram, the equilibrium condition for the vertical components of the forces acting on each sphere can be written as
The equilibrium condition for the horizontal components of the forces acting on each sphere can be written as
Here, is the electrostatic force experienced by the metal spheres.
The value of the electrostatic force is given by
Here, is the charge on each sphere and is the distance between them.
Referring to the figure, from ,
Substituting the value of in equation (3), we have
From equation (1),
Substituting the values of and in equation (2), we have
If is the number if electron surplussed with the metal sphere, then
Here, is the electronic charge.
Substituting the value of and in equation (5), we have