# What is the difference between electrostatic potential energy and electric potential?

I can remember this question repeatedly in my class. Repeated explanations can lead to some confidence for the students. What is the reason…

Potential and potential energy (Electrostatic or any other form of mechanical energy) are fundamentally different things! However, they can merge under certain circumstances. Because you’ve asked me about “electrostatic” I’ll adhere to it.

Electrostatic Potential Energy (Denoted by the letters W and U)Let me take a friend who shares the same name, namely potential difference.Potential variation (is every time between 2 points namely the a and the b) between the two points is equal to the amount of work per unit charge that is required to move the particle from b.
i.e. V(b) – V(a) = W/Q

If you decide to bring the charge Q into out of “far from” and put it in point r, the task you’ll need to complete is the following:
W = Q[V(r) V(r) – V(infinity)[W = Q[V(r) – V(infinity)]

Also, If you have a point of reference at infinity,

W=Q*V(r)

In the previous scenario it is the potential energy (work required to build this system) per unit.

If we attempt to stay clear of the derivation process and representation of analytical data for the moment the amount of work that is required to build a system of point charges also represents what you’ll receive back from the system in the event that you decide to tear it down or take apart the system. This is essentially the energy stored within the configuration that we can refer to it potential energy. This is applicable to electrostatics and mechanics however, as we’re focusing on electrostatics, we will looking at assembling or dismantling the charge systems.

Electrostatic Potential (Denoted in the form V)
The first thing to note is that it is a scalar value similar to W(or U). In order to understand V, it is necessary to understand what can be V. It is the Electric Field (E), an unidirectional vector. You must be aware that it isn’t anything like a normal vector. Therefore, if we writing as follows:

it will not be an electrostatic field; no set of charges, regardless of their sizes and position, could ever produce such a field along x-direction. So there exists a vector problem that needs another way of solving and in the event we go further and define a scalar that can be solved to find the vector. Paradoxical? Yeah! What can you do!

Theorems exist which states that If you’ve got the case of a vector field that’s curl is zero, then you have define the vector in terms of a scalar’s gradient. We are aware that the curvature of Electric Field is zero, which means that it is the case that E’s line integral in every closed loop will be zero. With the line integral independent of the path We can define the following function:

where O is some standard reference point. V now which depends only on the position vector r, is called as electrostatic potential.

In short, energy is about the structure of the system. Potential refers to the position of the charge as well as the associated electric field generated by the charge.

Hope I’ve explained it with the bare minimum of math so that it is comprehensive.