Electric potential energy

Electric potential energy is a potential energy that is measured in joules. It results from conservative Coulomb forces. It is associated with the configuration of a particular set of point charges within a defined system. Any object may possess electric potential energy through two key elements: its own electric charge and its relative position to another electrically charged object. It can also be alternatively defined as the total work done by an external agent to bring the charge or the system of charges from infinity to the present configuration without undergoing any acceleration.

Definition of Electric Potential Energy

An object possesses electric potential energy through virtue of two elements: the charge that the object itself possesses and the object’s relative position with regard to other electrically charged objects. The magnitude of electric potential is dependent on the total work done to move the object from one point to another against the electric field. When an object moves against the electric field, it will gain some energy that then gets defined as the electric potential energy of that object. To obtain the electric potential energy for any charge, the potential energy gets divided by the quantity of the charge. It is more convenient in electricity to use the electric potential energy per unit charge, which is called the electric potential or voltage.

Zero Potential

The zero point is arbitrary in the nature of the potential. It can be set off as the origin of a coordinate system. It is not insignificant; once set, then all values of potential are measured with respect to the zero. Alternatively, it is the change in potential that also has physical significance. The zero of electric potential is set usually for convenience. But, usually, some physical or geometric logic is present to the zero point’s choice. Logically, the zero point should be set at infinity for an infinite line charge. That is because the local values of potential would go to infinity. The ground potential is taken as zero for practical electrical circuits.

Electric Potential Difference

Electric potential difference is defined as the difference in electric potential between the final and initial location when work is done upon a charge to change its potential energy. The standard metric unit for it is the Volt or V. It was named after Alessandro Volta. One Volt is equal to one Joule per Coulomb. Given that the electric potential difference between two locations is one Volt, then one Coulomb of charge gains one joule of potential energy as it moves between those locations. Electric potential difference is also sometimes referred to as the voltage because it is expressed in units of Volts.

Mathematically, it can be stated as

     E=W/Q

Here, E is the electrical potential difference between two points

W is the work done to move charge from one point to another

And Q denotes the quantity of charge in Coulombs.

Electric Potential Due to Multiple Charges

The electric potential at a point in space that is produced by any number of point charges is calculated from the point charge expression. This is done using simple addition as voltage is a scalar quantity. The potential from a continuous charge distribution is obtained through the summing of contributions from each point in the source charge. Calculating the potential is simpler than the vector sum that is required for calculating the electric field. The electric potential due to multiple charges is obtained by calculating the potential energy for every pair of charges separately and then adding their results algebraically.

Electric Potential due to a Point Charge

By definition, electric potential is electric potential energy per unit charge. Mathematical expression is V=PE/q. The electric potential tells one how much potential energy a single point charge at any given location possesses. The electric potential at one point is equivalent to the electric potential energy of any charged particle at that location divided by the charge of the particle. Since the charge of the test particle is divided, the electric potential becomes a “property” related to the electric field itself. Basically, since PE is dependent on q, the q in the above equation cancels out so V does not depend on q. The potential difference between two points is often termed as voltage. 

Electrostatic Potential Energy of a System of Two Point Charges

The definition of electrostatic potential energy of a system of point charges is the work required to assemble the system of charges after bringing them closer together.

Formula: 

UE=kq1q2r

UE= electric potential energy

k= Coulomb constant

q1,q2 = charges

r = distance of separation

Electrostatic Field

An electrostatic field is associated with static electric charges. It is an electric field that does not change with time. An electrostatic field is present when systems of charged matter are stationary or in cases of unchanging electric currents. Coulomb’s law thus fully describes the field in such cases. Electrostatic fields differ from electric fields. Electric fields are produced by stationary charge. If an electric field is produced by a moving charge and oscillating electric field in electromagnetic waves, it cannot be termed as an electrostatic field. Let us assume two points are there in an electric field, q and Q. To move q closer to Q, one needs to push on q hard enough that it overcomes the repulsive electric force. So we apply just enough force to overcome the repulsive force generated by Q.

Conclusion:

Electric potential energy is measured in joules. It is a potential energy and results from conservative Coulomb forces. It can also be defined as the work done by external agents to bring the charge or system of charges from infinity to the present configuration. The magnitude of electric potential depends upon the amount of work done to move the object from one point to another against the electric field. It is also termed as voltage. Mathematically, electric potential difference is stated as E=W/Q. The electric potential due to multiple charges is obtained by calculation of the potential energy for every pair of charges separately and then adding their results. This article talks about the concepts of electric potential energy and the electric potential difference.