A Brief Note on Electric Potential Energy Definition

The amount of work needed for moving a unit of charge from one reference point to another specific point against an electric field is known as electric potential. Electric charges have electric fields around them, and a charge has to do work to change its position in the field. Central forces are said to be conservative. This means that when a particle is moving under the effect of central forces, the work done on the particle depends upon the particle’s initial and final positions.

Electric Potential Energy

Suppose we have a large plate that is negatively charged, and a tiny positively charged particle is stuck to the plate via the electric force. An electric field is present around the plate, pulling all the positively charged particles towards it and repelling all the negatively charged particles. A person tries to pull off the positively charged particle against the attraction of an electric field. It is hard as the electric field is pulling the particle towards it. The person’s energy to move the particle far from the plate would be stored in the particle as electric potential energy.

Suppose the plate is positively charged instead of negatively charged. In that case, the plate will push away the positively charged particles because both are positively charged. Now, we need to put energy to move the particle nearer to the plate. We would be putting more energy to move the particle closer to the plate, and as a result, the particle would have more electric potential energy.

Electric Potential energy formula

When we place a charge in an electric field, it holds potential energy which can be measured by the work done by moving the charge from an infinite point to a point against the electric field. If a distance d separates two charges q1 and q2 then the electric potential energy is given by

                     U = [1/(4πεo)] × [q1q2/d]

The system’s potential energy will increase if two like charges are taken towards each other. However, the system’s potential energy would decrease if two unlike charges were attracted towards each other.

Derivation of Electric Potential

If we take a charge q1 into consideration. We can assume that it is placed at ‘r’ distance from each other. Then we can define the total electric potential of the charge as the total work done via an external force to bring the charge from infinity to a given point.

It could be written as 

–ba(ra→rb)F.dr = -(Ua – Ub)

It can be seen that the point which is present at infinity is rb and r is ra.

We can substitute the values and write it as 

–∞r(r→∞)F.dr = -(Ur – U∞)

It is known that Uinfity is equivalent to zero.

Hence,-∞R(r→∞)F.dr = -(UR )

We can use the Coulomb’s law, to write:

    F  ∝    q1q2r2

    F  =  ke  q1q2r2

Hence, UR = -kqqo/r.

Important Points of Electric Potential

Some important Points of electric potential are:

1.    If there is a point halfway between two equal and opposite charges, then the electric potential would be zero but the electric field will not be zero.
2.    It is said that electric potential would be one volt if the work done to move one-coulomb charge against an electric field is one joule.
3.    There will be an increase in the electric potential of the system when a negative charge will be moved from point A to point B.
4.    Infinity is used as a reference level to express electric potential at a point. It shows that the force on a test charge would be zero at the reference level.
5.    It is assumed that the Earth’s surface has zero potential because Earth is so massive that if we add or remove a charge from it, there will not be any alteration in its electrical state.

Conclusion

The required energy to move a particle from one point to another in an electric field is known as electric potential energy. Electric charges contain an electric field around them that has a force of attraction; hence, it is tough for charged particle to move against it. The work done by the particle depends upon the particle’s initial and final position. The electric potential energy of a particle depends on its electric charge and its relative position with respect to other electrically charged objects.