# Define Potential Energy: Electric & Gravitational Energy

Usually some terms like potential and potential energy are confusing, because there is very negligible difference in such terms, but that is necessary to understand. In this article, we will discuss the difference b/w the terms like potential energy, electric potential, gravitational potential, potential difference electric potential gradient and gravitational potential gradient. Moreover the relation b/w these terms will also be discussed.

Energy is basically divided into two types: kinetic and potential. Kinetic energy means energy due to motion while, Potential energy is a type of energy, which is stored in an object due to the position of that object. Its unit is Joule, which is actually the unit of work done. Since P.E is stored as work done, so both have same units.

The objects which are at certain height, have greater potential energy, as compared to the objects, which are near to ground level. Secondly, massive object will have more potential energy. The reason behind these 2 factors is that potential energy is directly related to mass and height of object.

Potential energy can be classified as:

- Gravitational potential energy
- Elastic potential energy

Gravitational potential energy means the energy which an object possesses due to position, in gravitational field. It is stored in object as the amount of work done in moving that object from one point to another. Since,

W = F . d

And F = ma, where “a” is the acceleration, but in this case, since weight is equal to upward force, so a = g, secondly, object is at certain height, so d = h, we get,

W = m g h

Or U = m g h

To compress a spring, we do work on spring, which is stored in spring as its potential energy. Now when you leave the spring, it expands due to the stored potential energy. Such kind of potential energy is known as elastic potential energy.

**Electric potential**

Electric potential means the ability of a charged body to do work. When a body is charged i.e. electrons are supplied to it or removed from it, in both cases work is done, which is stored in form of potential. Simply, a charged body can do work by exerting force of attraction or repulsion on other charged objects.

Electric potential is defined as the amount of work done in moving a unit positive charge from one reference point to some other point, against the electric field, without producing acceleration. Usually earth is taken as reference point.

Here, the diagram shows the force acting on a positive charge, which is present b/w two plates A and B. the force that the field exerts on charge is F = qE, similar opposite but equal amount of force is exerted by other plate, to move charge from A to B, which is given by F = -qE. So overall, the work done in moving unit charge through a distance “d” is given by W = -q E d

Electric potential is indicated by “V” and is given by

V = k . q / r

Where k is coulomb constant with the value of 9×10^{9 }Nm^{2}/C^{2}. The unit of electric potential is volt or joule per coulomb.

**Gravitational potential**

Gravitational potential is defined as the work done per unit mass, which is required to move an object from one point to another. Its definition is similar to electric potential, only the charge has been replaced with mass. Its formula is as

V = U / m

Where, U is gravitational potential, U is work done or gravitational potential energy and m is the mass. Its unit is joule per kg.

**Relation b/w electric potential and potential energy**

Basically, potential energy is the property of a system. When two charges are in vicinity to each other, then they are said to possess potential energy. If these charges are separated by distance “r”, then for such a system potential energy is given by

U = ( k q_{1} q_{2 }) / r

On the other side, electric potential is the property of points, in space, which is given by

V = k q /r

Comparing both above equations, we get

U = V q

Or

V = U / q

So electric potential means the potential energy per unit charge or the work done per unit charge.

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**Potential difference**

Electrical potential difference is defined as the amount of work done to carry a unit charge from 1 point to another, in an electric field. i.e. the difference of electric potential of two charged objects.

In electric circuits, the difference in the energy, carried by charge carriers b/w two points in a circuit is called potential difference. It is also termed as voltage and is denoted by “V” and is given by

V = I R

I is the current passing through circuit and R is the resistance. It is measured in volts.

**Difference b/w electric potential and potential difference**

The amount of work done in bringing a test charge from infinity (or from any point which is outside the influence space of 1^{st} charge) to the inside influence space of source charge, is known as the electric potential.

In the case of potential difference, the test charge is already in the influence space of source charge, so that it already has some electric potential. Now if we take 2 points within this influence space, then potential at both points will be different. The difference of these 2 potential values is known as potential difference.

**Electric potential gradient**

As it is clear from name, that it is a term of electrostatics, so definitely, it is related to electric field. Electric potential gradient is defined as

E = – dV / dr

The rate of change of electric potential with respect to position, in the direction of electric field, is known as potential gradient. In above relation, it is clear that electric field intensity is equal to negative of rate of change of potential. Unit of potential gradient is volt per meter.

At some point, if V is constant then E = 0. The negative sign indicates that the potential will decrease as the distance increases.

**Gravitational potential gradient**

As electric field strength is defined as, force per unit charge (F = q E), similarly, gravitational field strength is given as force per unit mass at that point.

So the gravitational potential is defined as the amount of work done in bringing a unit mass from infinity to that point.

V = – Gm/r

Again the negative sign indicates that potential decreases if r increases, r is the distance of object from center.

The change in gravitational potential means the change in energy per unit mass, when object is moved from one point to another.

ΔV_{G} = ΔE/m

The gravitational potential gradient means the rate of change of gravitational potential with respect to distance in the gravitational field, which is also equal to gravitational field intensity (g = E_{G}) at that point.

g = E_{G} = -ΔV_{G }/ Δr

This relation is analogous to that of electric potential gradient, with same units.