# Potential Energy Vs Potential Difference: Detailed Facts

In this article, we will see the difference between the potential energy and potential difference.

The potential energy is the energy stored in the system whereas the potential difference is the difference between the potential at two points.

## Some Facts on Potential and Potential Energy

• The energy acquired by the system due to the varying potential between the two positions on the system is potential energy.
• The object at a certain height above the ground, having its own potential energy decreases with the distance as it approaches the ground.
• The gravitational potential energy of the Earth tends to pull the objects towards the center of the gravity of Earth, decreasing the potential energy of the object converting it into kinetic energy while approaching towards the ground.
• In an atom, a region with the least potential exists near the nucleus, and electrons in an atom tend to be near the nucleus attaining the low potential energy.
• Once the electron built enough potential energy it becomes unstable and jumps into a higher energy level, releasing its energy falls back to the lower energy level of the atom.
• Potential energy is available in 5 main different categories; gravitational, electrical, nuclear, elastic and chemical.
• Electric charges move from the higher potential level to the lower potential level after transmitting their energy to a higher energy state on exciting.
• In the case of capacitors, the potential difference is generated due to the separation of the opposite charge carrier plates, due to the separation of the plates the potential energy is stored inside the capacitor to do the work.
• Potential energy on the close loop conductor is always zero.
• In elastic materials, the potential energy can be stored by either stretching or compressing.

Let us evaluate the potential energy and potential difference relationship of some fundamental forces in nature:-

## Gravitational Potential Energy and Potential Difference

The potential energy is the energy required to displace the unit mass from one point to another. The potential energy associated with the object due to gravity is given by the relation

U=mgh

Since, the weight of the object due to the gravity on the earth becomes the product of the mass of the object and its acceleration due to gravity which is constant, the only variable is the height. Hence, the potential energy of the object mainly varies depending upon the rise and fall of the object from above the ground. As the object opposes the gravitational pull of the Earth increasing the distance of separation between the ground and the object, it starts gaining its own potential.

The gravitational potential difference is the work done in moving the unit mass and is given by

ΔU=Work/m

We have seen above that the only variable quantity is the height of the object from above the ground

ΔU=mg/Δh

Where Δh is the change in height

ΔU is the potential difference

Since the gravitational force between the two objects having mass M and m separated by the distance ‘r’ is given by

F=G*(Mm)/r2

The work done on the objects due to gravity

Work=∫F.dr

Work =-GMm/r2

Since the potential difference is the work done per unit mass

Read more on gravitational potential energy.

## Electric Potential Energy and Potential Difference

Electric potential energy is the energy required to bring the charged particle from infinity to the point of consideration. This is equal to the work done on the particle in bringing the unit charge.

Consider two point charges of charge q1 and q2 separated by a distance ‘r’ between them.

The force acting between the two charges q1 and q2 is equal to

The work is done in bringing the charge q1 at point ‘s’ to a distance r2. Work is the force required to displace the charge q1 to a distance r2.

Work =Force*displacement

Therefore the work done on the particle to displace it from r1 to r2 is

Work done is equal to the potential energy of the charge.

The difference between the potential energy between the two points is the potential difference resulting due to the action of work.

Electric potential is a potential energy per unit charge; given by the relation

V=U/q
Where V is a potential
U is potential energy
q is a charge

Implies U=qV

Therefore, from above relation, electric potential will be equal to

## Elastic Potential Energy and Potential Difference

When the elastic material is stretched or compressed, it gains potential energy. The amount of potential energy acquired depends upon the change in the length of the material. The static potential energy of the elastic component is given by

U=(1/2)kx2

Where k is an elastic constant and x is a displacement due to stretching or compression.

The potential difference is the difference between the potential energy stored in the object by the change in the position of the object or the load applied to stretch or compress the object.

Therefore, the potential difference is measured as

ΔU=(1/2)kΔx2

Where Δx=x2-x1

## SI Units

The SI unit of potential energy is Joules. SI unit for gravitational potential energy is N.m/kg. Whereas, the SI units of potential difference is Volts also written as Joule per Coulomb J/C. One volt is equal to 1 J of energy per to displace a unit charge of 1C.

Read more on What Affect Potential Energy: Detailed Facts.

## Q1. Calculate the work done by the charge of 2C to displace from point A to point B having a potential difference of 10 Volts.

Given:

Charge Q=2C

Potential difference V=10V

V=W\Q

=>W=QV

=2C*10V=20 J

## Q2. The potential energy of the ball at height 2m is 4J. If the ball is thrown in the air. Calculate the potential difference of the ball attaining a height of 10m above the ground.

The potential energy of the ball at a height is 1J.

Therefore, the mass of the ball is 204 grams.

On reaching the height of 10m, the potential energy of the ball becomes

U=mgh=0.204*9.8*10=20J

Hence, the potential difference is

Δ=U2-U1=10-4=6

## What is nuclear potential energy?

The nucleus comprises protons and neutrons, thus adding a positive charge to the nucleus and hence electrons tend to remain towards the nucleus.

It is potential energy that keeps the neutrons and protons bonded in the nucleus. During nuclear fusion, the nucleus gains energy while on nuclear fission nucleus gives out energy along with the products.

## What is chemical potential energy?

Chemical potential energy is the energy acquired by molecular bonds.

During the exothermic reactions, the bonds break, and energy is released, while in endothermic reactions the energy is acquired from the surroundings to make new bonds.