We know about the definition of electric potential but that’s not it, there are many more things in this particular field. Well, not just that but there are many more derivations linked to this like ‘electric potential at the centre of a ring’ (sounds little tough but I’ll make it easy for you guys to understand).
Electric potential at the centre of the ring is the same as the potential due to a point charge. Whereas the electric field is 0 at the centre of the ring because the electric field at the half side of the ring cancels out the other half.
Before understanding electric potential at the centre of a ring, you need to understand electric potential and electric potential due to a point charge.
Proof of electric potential at the centre of the ring is the same as point charge:
What is electric potential ?
So before understanding electric potential, let’s understand the meaning of potential. Potential is characteristic of a “Location” and potential energy is the characteristic of a charged particle.
Electric potential is the work done by an applied force on a unit charge bringing it from infinity to a specific point. The work done is called electric Potential.
Electric potential to infinity is zero.
Potential of a point:
Electric potential at point A
So, here in the above image VA represents the electrical potential at point A, this point A can be anywhere.
Suppose we bring a charge from infinity to a point so we need some force to do that work in bringing a charge from infinity to a particular place and this energy or work which is done is what we call as potential of a place.
P.s: The term potential is a location-based characteristic. Every place has different potential. Just like one end of a battery has high potential and another end has low so that’s why when we connect both the sides of a battery with wire, current flows in the direction of higher potential.
Now let’s define electric potential due to point charge:
Electric potential due to a point charge:
Q is a charge and we have to find the potential at point A at distance r.
|Electric potential due to a point charge diagram|
To move it to a small distance ‘dx’ the work done is:
To work done :
Electric potential at the centre of the ring:
|Electric Potential at the centre of the charged ring|
Imagine a circular ring with radius ‘r’ and ϴ is the angle between the reference line ‘A’ to point on the ring. dӨ is the small angle from a point on the surface. The length of line A = radius of ring (∵ line A is the reference line from the centre to surface)
To find the total potential to the ring at the centre we need to integrate the above equation.
P.s:- ‘k’ in the above equation represents constant and ‘r’ represents the radius.
This is the potential at the centre of the charged ring. We will notice that the equation of electric potential at the centre of the ring is the same as the electric potential due to a point charge.
To understand the reason behind is, you can imagine that circular ring is nothing but will behave like a charge if we compare it to heavy bodies such as moon or earth. So that’s why electric potential equation for point charge and at the centre of the ring is the same,
Ring behaves as point charge due to which equation of potential difference is same for both of them
To understand the concept clearly, you will need to understand that electric potential is the work done on bringing a unit charge from infinity to a point and the electric potential difference is the difference between the potential of two points.
Q.1 Why electric field inside a ring is zero but the potential is not ?
Electric field is a vector quantity so it has magnitude as well as direction and due to this, electric field due to half ring is cancelled out by another half due to the opposite direction but electric potential is a scalar quantity due to which it doesn’t get cancelled out.
Q.2 How is electric potential and potential difference not the same ?
Electric potential is work done on a unit charge when bringing from infinity to a point. Whereas potential difference is the difference in electrical potential between two points.
Q.3 What is potential ?
Potential is the characteristic of a location.
Q.4 What does ‘r’ refer to in the equation of electric potential due to point charge ?
‘r’ is the distance between point and charge.