Electric Potential & Electric Potential Energy
In this article I will discuss briefly about electric potential energy, electric potential , derive formula for them and will also discuss the difference between the two terms.
Potential energy
Potential energy is the energy that is stored in an object and later the energy can be converted into another form of energy like kinetic energy. If an object falls from a height, it will gain kinetic energy when it hits the ground. Because the gravity will cause the object to speed up.
When an object with mass m falls from a height h, the work done by the gravity is = mgh. According to the work energy theorem, this work converts into the kinetic energy of the object. The gravitational potential energy at height h is, how much work can be done by gravity on the object. In this case, it is mgh. Because this is the work that gravity can do if the object is dropped from height h.
This energy is equal to the work done by external force F to raise the object at height h from ground against gravity.
The object has to be raised with constant velocity, otherwise the force F will be greater than the gravitational pulling force mg. U is used for potential energy.
U = mgh
Electric Potential Energy
Let, there is a stationary point charge q and another free moving charge q0. The distance between them is r, the stationary charge q will exert a repulsive force on q0 and hence, it will go up to infinity. Because at r = ∞, the coulomb’s force F = 0 . So, the electric force will do some work on the q0 charge and the work will be converted into kinetic energy, according to the work energy theorem.
Like gravitational potential energy, the work that can be done by the electric force is the potential energy of q0 charge at distance r. So, we have to calculate the work done by the electric force as q0 moves from r to ∞. As this is the work that electric force can do on q0. The force is not constant, and we must integrate ∫ F.dr from r to ∞.
The total work done by the electric force to move the charge from distance r to infinity is :
This is the potential energy of q0 charge. This energy is same as the work done by an external force to bring q0 from infinity to distance r with constant velocity. If we want to move q0 closer to q, we have to exert an external force opposite to the direction of electric force.
So, the work done by the external force to bring q0 from infinity to r is :
This is the same result that we saw before.
So, the electric potential energy of a charge at any point in an electric field is, the work required to bring that charge from an infinite distance.
Electric Potential
Electric potential is the electric potential energy per unit charge. The electric potential V is the potential energy of 1 coulomb charge.
potential energy of q0 is U . So, potential energy of 1 coulomb charge = U/q0
So, the electric potential V of a point charge q at a distance r is,
Potential Difference & Work Done By Electric Force
Let , a point charge q0 is moved from point a to point b by the electric repulsive force. The work done by the electric field Wa→b is :
Now the work on per unit charge = Wa→b/q0
So the work done by electric field to move a charge q0 from a to b is ,
If q0 = 1 coulomb, then W = V. So, the potential difference between the two point a and b is, the work done by the electric field if 1 coulomb charge is moved from a to b.
