## Saturday, July 30, 2016

### Electric Potential Expression and Explanation

Electric potential is a parameter which causes the flow of the charges from one place to other. It is like pressure difference because of which there is flow of fluids from one place to other. It is even similar to temperature difference because of which there is flow of heat energy from once place to other.

Electric potential is defined as the amount of work done in bringing a unit positive charge from infinite distance up to a particular point of electric field. Let us consider a charge. Around the charge there will be a field up to where its influence can be felt. To bring a similar charge around it, we shall do some work against the electric field of the system. Once this work is done, the charged particle to will come to a particular place of that field. This work done is called potential.

There shall be potential difference between two points and it will felicitate the flow of current and charges between that two points. More the potential difference, more the flow of current and vice versa.

Mathematical Expression

Let us consider a positive charge around which there is a electric field. Let us consider a test charge at infinite and we would like to bring that charge towards this charge to a particular separation. At  that point, there will be certain electric intensity and we can find it out using the definition of intensity. It is the force experienced by a unit positive charge when it is placed in a electric field.

To displace the unit positive charge by a small distance, we need to do some small work and it can be identified as the product of force and displacement. Further in the place of force, we can write as the product of electric intensity and unit positive charge.

Any way this is only small amount of work and similar small amounts of work has to be done in getting the unit positive charge by the similar small distances. To get the total work done in the whole process, we shall integrate the work done equation.

It is done as shown in the diagram below.

Further integration process and application of the limits from infinite distance to a particular point is as shown in the below diagram.

Electric potential is measured with a standard unit called volt. One volt is the amount of work done in bringing unit positive charge from infinite distance to a particular point.

We can also find the relation between electric potential and electric intensity. Simply rewriting the basic definition of potential, we can find the relation as shown below.

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