Small identical balls with equal charges of magnitude 'q' each are fixed at the vertices of a regular 2019-gon (a polygon of 2019 sides) with side 'a' = 4µm. At a certain instant, one of the balls is released and a sufficiently long time interval later, the ball adjacent to the first released ball is freed. The kinetic energies of the released balls are found to differ by K = 9 ×10 9 J at a sufficiently large distance from the polygon. Determine the charge q in mC.
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Sol. When 1 st ball is released, its potential energy due to the rest of the system will be converted into kinetic energy:
K.E. 1 = 
[Here (P.E.) 1,i = Potential energy between 1 st ball and i th ball]
K.E 1 = (P.E) 1, 2 + 
............
Now, when 2 nd ball is released, it also takes its self potential energy from system :
So, kinetic energy of 2 nd ball: K.E. 2 = 
Now (K. E ) 1 – (K. E) 2 = (P. E) 1, 2 + 
– 
(K. E) 1 – (K. E) 2 = (P. E) 1, 2
Given: (K. E) 1 – (K. E) 2 = K and (P. E) 1, 2
= 
; K = 
⇒ q = 
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