Question

What is the common potential? Show That whenever two conductors share charges by bringing them into electrical contact there is a loss of energy

Answer 1

During the sharing of charges between the different bodies no net loss of charge takes place. During this process some energy is disappeared in the form of heat. But some amount of energy is scattered in sharing between these charges.Now if we want to calculate the total loss of energy during the process then we have to take two capacitors having capacity C1, C2.These also have their distinct potentials say V1 and V2. As we have discussed above that the charge always flows from the capacitor having higher potential to the capacitor having less potential.

So, their common potential is given by the equation below:

V=(C1V1+C2V2) / C1+C2

Total energy of the system will be given by:

Loss in energy on doing the sharing of the charges

Loss in energy on doing the sharing of the charges

From the above equations we have find that E1 – E2 > 0

Or E1> E2

Or E2 < E1

The above results shows that some loss of energy takes place when the bodies are in communication with each other. This energy wastage or scattering is in the form of heat and sparking in the wire connecting the two conductors with each other.

Answer 2

Let 1 & 2 be 2 charged conductors & let them touch each other.

Now their potentials will change but will become equal & this potential is called common potential.

Initially Q = Q1 + Q2 = C1V1 + C2V2

Finally Q = (C1 + C2)V

Q1 = Q2 From the law of conservation of charges

C1V1 + C2V2 = (C1+C2)V

V = (C1V1+C2V2)/C1+C2

Final V1 = final V2 but they may be or may not be unequal to (initial V1 + initial V2)/2 because potential depends on charge and capacitance.

Experimentally initial energy may not be equal to the final energy due to the fact that energy can neither be created nor be destroyed but can be transformed (Law of conservation of energy)

In this case electrostatic or potential energy is mostly & mainly dissipated as heat.

:-)