Why a common potential is attained? Lets say we have a 50 v conductor .Now is we touch the conductor,by another conductor , both the conductors will attains a common potential.Why is this so?
How do they acquire such a common potential??
 A: Since, as long as there is a potential difference there is an electric field in the direction of higher to lower potential.
$$
\textbf E = -\nabla V \qquad \qquad \textbf F = q \textbf E
$$
The charges keep flowing from higher potential region to a lower potential region due to the force of this electric field. The accumulation of charge in the lower potential region gradually increases the potential in that region until there is no potential difference between these two regions. In the absence of such a potential difference, there is no force and hence they cease to flow.
As an analogy, you can take an example of two identical barrels of water connected by a pipe in the bottom with one of them being full and the other empty. The water will continue to flow from the full barrel to empty one until the water in both barrels have reached the same height.

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A: Because the potential is a word that describes how much charges want to move somewhere else. They will always want to move to the lowest possible potential. 


*

*If you have high potential in one conductor, then it means that there is a lot of equal excess charge in it. These charges repell each other, so of they were allowed they would move away. 

*If you have lower potential in another wire, there is less equally-signed charge here, so they repell each other less. 


When those two conductors touch, then the charges in the high potential wire will move to a place where they are repelled less, which is in the other wire. They will move until there are equally many in both conductors, so that the repulsion in both are the same. 
Which in other words means that the potential is the same. 
As such, the potential in the lower-potential conductor rises a bit, while it in the other decreases a bit - until they are equal. 
