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Redistribution of Charges and Loss of Energy

When two charged conductors joined together through a conducting wire, the charge begins to flow from one conductor to another from higher potential to lower potential. This flow of charge stops when they attain the same potential.
 
Due to the flow of charge, loss of energy also takes place in the form of heat through the connecting wire.
 
Suppose there are two spherical conductors of radii r1 and r2, having charges Q1 and Q2, potentials V1 and V2, energies U1 and U2, and capacitances C1 and C2, respectively (Fig. 2).
 
64911.png
Fig. 2
 
If these two spheres are connected through a conducting wire, then the alteration of charge, potential, and energy takes place.

New charge

According to the conservation of charge, 66644.png (say),
 
64938.png
Fig. 3
 
Also 63581.png
63588.png and similarly 63594.png

Common potential

63600.png
63606.png63612.png

Energy loss

The loss of energy due to redistribution of charge is given by
63619.png




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