Notes

## Electromagnetic Induction

- A quick revision of all the important concepts
1
Electromagnetic Induction

The phenomenon in which electric current is generated by varying magnetic fields is appropriately called electromagnetic induction. Induction means to induce something or to generate something. Therefore, electromagnetic induction means induction of electric current due to magnetic field.

Experiment 1: Faraday took a coil and attached a galvanometer to it. As there is no battery attached therefore there is no source of current. He brought the magnet near the coil. When the magnet is moved towards the coil galvanometer showed deflection. Galvanometer even showed the deflection in the opposite direction when the magnet is taken away from the coil. When magnet was not moved there was no deflection in the galvanometer.
This show current is related to magnet: Relative motion between magnet and coil induced electric current in the coil.
Experiment 2: Faraday took a coil but instead of taking magnet he took another coil which was connected to the battery. When the coil attached with battery was brought near another coil, the galvanometer showed the deflection. The same phenomenon repeated even when there was no magnet.
This shows current flowing in one coil was able to induce current in another coil.
Experiment 3: In this case he took a coil, one more coil attached with a battery. When the circuit was open there was no current flowing through the coil. But as soon as the circuit was switched on there was deflection in the galvanometer. When the circuit was on continuously for longer period of time there was no current. When the circuit is switched off there was a deflection in the galvanometer in the opposite direction. And if the circuit is switched off for long time there was no deflection in the galvanometer. He observed that the galvanometer showed momentarily deflection only when the system was undergoing a change.
Relative motion is not an absolute requirement for inducing current: There was induced current only when there is change in the system.
Magnetic Flux: The total number of magnetic lines of force passing normally through an area placed in a magnetic field is equal to the magnetic flux linked with that area.
The represents the angle between A and B
1. According to the first law an emf is induced in the circuit whenever the amount of magnetic flux linked with a circuit change.
2. According to the second law the magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit. i.e., . For turns . Negative sign indicates that induced emf (e) opposes the change of flux.

Lenz's Law (Conservation of energy principle)
According to Lenz's law, the polarity of the induced emf is such that it tends to produce induced current in such a direction that it opposes the change in magnetic flux that produced it. Lenz's law obeys conservation of energy.
Motional emf: When an electrical conductor is introduced into a magnetic field, due to its dynamic interaction with the magnetic field, emf is induced in it. This emf is known as induced motional emf.
If conducting rod moves on two parallel conducting rails as shown in following figure then phenomenon of induced emf can also be understand by the concept of generated area (The area swept of conductor in magnetic field, during its motion).
As shown in figure in time distance travelled by conductor =
Area generated . Flux linked with this area . Hence induced emf
• Induced emf due to rotation: Emf induced in a conducting rod of length rotating with angular speed about its one end, in a uniform perpendicular magnetic field is .
• EMF Induced in a rotating disc: Emf between the centre and the edge of disc of radius rotating in a magnetic field B is
Energy Consideration: For uniform motion of rod ON, the rate of doing mechanical work by external agent or mech. Power delivered by external source is given as

Eddy Current: Eddy currents are induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. Application of eddy currents are as follows:
Electromagnetic damping
Electric-brakes
Induction furnace

Induction: It is the magnetic field which is proportional to the rate of change of the magnetic field. This definition of induction holds for a conductor. Induction is also known as inductance. L is used to represent the inductance and Henry is the SI unit of inductance. Unit =

Following are the factors that affect the inductance:
The number of turns of the wire used in the inductor.
The material used in the core.
The shape of the core.

Two types of inductance are there:
Self-Induction: where is the self-inductance in Henries, is the number of turns, is the magnetic flux, is the current in amperes

Mutual Induction: where is the permeability of free space, is the relative permeability of the soft iron core, is the number of turns in coil, is the cross-sectional area in , is the length of the coil in .
 Self induction Mutual induction Self inductance is the characteristic of the coil itself. Mutual inductance is the characterstic of a pair of coils. The induced current opposes the decay of the current in the coil when the main current in the coil decreases. The induced current developed in the neighbouring coil opposes the decay of the current in the coil when the main current in the coil decreases. The induced current opposes the growth of the current in the coil when the main current in the coil increases. The induced current developed in the neighbouring coil opposes the growth of the current in the coil when the main current in the coil increases
Combination of Inductance
Series Connection
Parallel Connection
AC Generator: It is an electric generator that converts mechanical energy into electrical energy in form of alternative emf or alternating current. AC generator works on the principle of "Electromagnetic Induction".

Parts of an AC Generator
An Ac generator consists of two poles i.e. is the north pole and south pole of a magnet so that we can have a uniform magnetic field. There is also a coil which is rectangular in shape that is the armature. These coils are connected to the slip rings and attached to them are carbon brushes. The slip rings are made of metal and are insulated from each other. The brushes are carbon brushes and one end of each brush connects to the ring and other connects to the circuit. The rectangular coils rotate about an axis which is perpendicular to the magnetic field. There is also a shaft which rotates rapidly.

Working of an AC Generator
When the armature rotates between the poles of the magnet upon an axis perpendicular to the magnetic field, the flux which links with the armature changes continuously. Due to this, an emf is induced in the armature. This produces an electric current through the galvanometer and the slip rings and brushes. The galvanometer swings between the positive and negative values. This indicates that there is an alternating current flowing through the galvanometer.