Two equal small spheres each weighing 1g , hang by two equal silk threads from the same point. The spheres are charged when in contact and come to rest with their centres 2cm apart and 20cm vertically below the point of support. Find the charge on each sphere. 

Figure shows forces acting on charged sphere. Weight mg is acting downward.  Repulsive electrostatic force is shown as F_e .

 

Tension force T acting along string is resolved as ( T cosθ ) and ( T sinθ ) . 

(Tcosθ) component balances weight mg.   (T sinθ) component balances Electrostatic force F_e . 

 

T cosθ = mg ...................... (1)

T sinθ  = F_e ........................(2)

 

If we eliminate tension T in above equations, we get ,  F_e = m g tanθ .......................(3)

 

Eqn.(3) is written as

 

K × ( q² / d² ) = ( m g tanθ ) ........................... (4)

 

where K = 1/( 4 π ε_o ) = 9 × 10⁹ N m² C^-2 Coulomb's constant  and d = 2 cm  is the distance between charged spheres.

 

m is mass of sphere , g is acceleration due to gravity and θ is the angle made by the string with vertical

 

From eqn.(4) , we get