EMF IN A STATIONARY CIRCULAR COIL

The electromagnetic theory was developed by the gradual interrelation built between the electric and the magnetic fields from time to time by the scientists. In the same sequence, Michael Faraday was the very first to introduce the concept that the electric field can also be  generated by a varying magnetic field. Later in this article you will see that it was actually the magnetic flux not the magnetic field which was responsible for the induced electric field. In this way you are going to understand that there can be emf in the stationary items that are circular in shape or of any shape. In the same sequence you will see what can be the substitute of the faraday’s law if the loop is not complete.

FARADAY’S EXPERIMENT

Michael Faraday was the very first experimental physicist. His law was very fundamental and had nothing to do with critical mathematics.. Though it was not sufficient to see and justify the behaviour of a stationary horizontal uniform circular disc, it gave clues about Lenz’s law which later helped in seeing the phenomenon like eddy current.

Faraday took a conductor coiled in a cylindrical manner. And there was a magnet whose magnetic field flowed past a circular cylindrical. He observed that there was a current flowing past a circular cylinder along the coiled wires. The only condition in which the current ws there in the coil is when the coil keeps  on moving relative to the magnet. Before understanding what  things were happening at the time, we need to be familiar with concepts like ‘Magnetic flux’

Magnetic flux is the magnetic field lines that are passing through a given area. It gives the idea of how the magnetic field is changing through a given coil. Faraday’s law in simple words says that whenever there is a change in the magnetic flux through a given area, an emf is induced. The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux. It can be mathematically written as;

ε=-dɸ/dt; where ɸ is the magnetic flux defined as ɸ=∫B.dA

 This way we can understand that the emf can be induced through a stationary horizontal uniform circular disc. But this phenomena also involves a pinch of other concepts like Lenz’s law and eddy current.

LENZ’S LAW AND EDDY CURRENT

Lenz’s law has something to do with the one of the most fundamental nature of the bodies which is to oppose any kind of change the body is going through. And the theory of eddy current was developed as an analogy to emf induced in a circular coil and was supported by Lenz’s law. Eddy current was first  observed when a magnetic field was flowing past a circular cylinder.

Lenz’s law says that when there is an emf induced in a coil or stationary items that are circular in shape; they abhor the change in flux. And consequently the change in emf. Let us assume a circular coil subjected to some relative motion with respect to a stationary magnet. Now the corresponding induced current will be such that it will oppose the cause of this change. Say it is going towards the north pole of the magnet. Thus the flux through the coil is increasing. Now the flux is increasing thus the corresponding area for the emf will be opposite to that of the increasing area. And the current corresponding to that sense of area as per the right hand rule will induce a magnetic field. This magnetic field will have the north pole facing the north pole of the magnet. In this manner the induced magnetic field will oppose the flux due to the initial field. And also the force due to the magnetic field on the electrons flowing due to the induced current i.e. BIL force(idl*B) will be reducing the area of the coil too.

While the coil has the proper loop for the induced current to flow. The solid circular discs or the current when the magnetic field flows past a circular cylinder or disc do not have any proper loop. So when the magnetic field varies along the surface of such solid shapes, the current flows as an eddy current of water as concentric whorls. Such a current is known as eddy current. Eddy current set-up to oppose the corresponding change in the magnetic field. By developing a field in the opposite direction by virtue of the induced current. 

MOTIONAL EMF

Motional emf comes into play when the current is to be induced in something which is neither a loop nor a solid 2D shape. Let us assume that a rod is moving with a velocity u, perpendicular to a uniform magnetic field. Now the magnetic field will accelerate and set the electrons in motion as per the equation F= qu*B. By virtue of the motion of the electrons, an electric field is set up. At the equilibrium of the two forces polling the electrons we can write;

Ee=eu*B; where E is the electric field, B is the magnetic field and e is the charge of electron.

E=u*B

ε = Bul ; where l is the length of the rod

This emf is what we say motional emf

CONCLUSION

We have seen so far in the article a basic introduction to electromagnetic induction. Now the readers are advised to go through some major inventions and applications based on this electromagnetic induction. Some of the such examples are motor, ac generator and dc generator. It can be really additive to your knowledge if you will try to understand what a transformer is and how it works. As a hint I can tell you that a transformer is somehow an application of eddy current. Here you have got enough on your platter. Now you know that faraday law is explanatory when there is a complete loop. But in the case of a stationary horizontal uniform circular disc we need to come up with a new concept of eddy current. In the case of the 1D wires we can deal as per the concept of the motional emf.