## define electric potential: know it with nature

Let’s define electric potential but before move forward let’s understand concept of potential energy:

Am sure you have also known about potential energy which is part of mechanical energy so when we move any object let’s suppose v m/s then at that particular time object contains some potential and kinetic energy , if v (velocity) increases then kinetic energy increases and potential energy decreases am right ? yes.

So now you are ready to understand about potential, in this example we take an object and raise it up to some height like H so as you can see in the figure we are doing some work to raise it up to H height so now this object has some potential energy against gravity.

**So work done by us = stored potential energy**

{Because W = F.ds}

**F = -mg**

(- sign denote force in the opposite direction with respect to applied force by us)

**ds = H (that height )**

So

**W = -mgH** (so this is the work done to raised object up to H height)

**By concept work done by us = stored potential energy**

**Î”U = W = -mgH**

**Or Î”U = -W**

**Here:**

**Î”U :**potential energy stored by object at height H

**-W :**conservative work done to raise the object up to H height .

**So potential energy words come from conservative forces.**

Now i think you know very well about potential energy now you are ready to understand about electric potential energy. Let’s define electric potential .

Electric potential energy is a concept that tells about how much energy is stored to create a system. Let's explore more in an easy way. For better understanding

**let's take an example:**

suppose we have a only one charge particle Q1 and have another charge charge Q2 which is the placed at the infinity so charge Q1 not experience any forces due to Q2 the reason is Q2 is very away from the Q1 so right now let's take Q2 and move near to the Q1 charge particle then what will be happened ?

Right now Q1 experiences some force due to Q2 so while doing this thing we have done some work and that work is reserved into the form of potential energy between the charge particles.

**If we assume that distance between these two charged particles r so Force applied by Q1 charge particle on the Q2 :**

**f = kq1q2 / r² (Which is variable force)**

and right now we know

**work done = force * distance**

So let's put the values of the forces and distance but before further we know force applied by Q1 on Q2 or Q2 on Q1 are variable so if we want to calculate exact work done when we bring the Q2 charge particle near to the Q1 charge particle so we have to do integration of force due to force is a variable so let's do it.

**So work done to create system = ∫ kq1q2 / r² * d r**

Right now in the term of force only 1/r² is variable so let's do integration of 1/r².

As we assume potential energy at the Infinity state is zero due to this is a finite state so let's assume potential energy at the Infinite is zero (Ui =0).

Note : we are talking about electric potential energy okay, now I have a doubt that where this electric potential energy is stored in these particles, have any idea?

**let's I provide you some options and guess it:**

**1) into the Q1 charge particle**

**2) with Q2 charge particle**

**3) equal withQ1 charge particle and Q2 charge particle**

**4) between the space of these two charges**

So the correct answer is: potential energy stored between the charge particles means potential energy of the electric charge particle stored in a space of these two charged particles .

**Some important point related to electric potential energy**

Each configuration or particle wants to minimize its own energy and that energy (potential energy).

So From here the concept arises negative potential energy and positive potential energy so let's get informed about the negative potential energy and positive potential energy.

**If we talk about the positive potential energy it means the electric potential energy is positive which is stored by two positive or negative charge particles. Let's know about it .**

Let's assume a charge particle +Q1 and +Q2 and both are placed some distance r so the electric potential energy stored by these two charge particles lies in between these two particles and that will be positive due to both charged particles being the same sign or the same charge particles.

- So When we move one of them charge particle near to the another charge particle or away from another charged particle so there are two concepts that arise from here.
- If both charges are +ve and both move towards each other then in this case potential energy increases due to repulsion increases and kinetic energy decreases.
- If both charges are negative and move opposite of each other then in this case potential energy decreases due to repulsion decreases and kinetic energy increases.
- and now if we take both particles negative and move towards each other then in this case potential energy also increases due to repulsion increases and kinetic energy also decreases.
- and if we take both partial negative and move opposite of each other then potential energy decreases due to repulsion decreases and kinetic energy increases.
- So these points arise when same charge particles move in the same or opposite direction of it and by doing these things potential energy increases or decreases.

**Note :**

- potential energy increases when repulsion increases or kinetic energy decreases.
- and potential energy decreases when repulsion decreases or kinetic energy increases.

**And now if we talk about negative potential energy then it is just opposite of the positive potential energy and the same concept arrives here also but remember that some points are different just like.**

- When one of them charges particle positive and another the charge particle negative then these two charge particles make a system which stores negative potential energy.
- Negative potential energy stored in opposite charges.

**Note:**conservation of potential energy : click here to read