1. ELECTROMAGETISM AND INDUCTION
CHAPTER-5

2. Content
Relation between magnetism and electricity, production of induced e.m.f & current, Faraday’s laws of electromagnetic induction
Direction of induced e.m.f and current, Lenz’s law, Self inductance and Mutual inductance
Magnetic hysteresis, residual magnetism, Energy stored in magnetic field, Rise and decay of current in inductive circuits

3. Relation between magnetism and electricity
Whenever an electric current flows through a conductor, a magnetic field is immediately brought into existence in the space surrounding the conductor. It can be said that when electrons are in motion, they produce a magnetic field.

4. Relation between magnetism and electricity

5. Relation between magnetism and electricity
The converse is also true i.e. when a magnetic field embracing a conductor moves relative to the conductor, it produce  a flow of electrons in the conductor. 

6. Electromagnetic Induction
The phenomenon whereby an e.m.f.  and hence current  is induced in any conductor which is cut across or is cut by a magnetic flux is known as electromagnetic induction. 

7. Production of Induced e.m.f & Current

8. Production of Induced e.m.f & Current

12. Michael Faraday formulated two laws on the basis of above experiments.
These laws are called Faraday’s laws of electromagnetic induction.

13. Faraday’s Laws of Electromagnetic Induction
First Law :
         Whenever the magnetic flux linked with a circuit changes, an e.m.f. is always induced in it.  or
         Whenever a conductor cuts magnetic flux, an e.m.f. is induced in that conductor. 

14. Faraday’s Laws of Electromagnetic Induction
Second Law :
          The magnitude of the induced e.m.f. is equal to the rate of change of flux linkages.
              d Ø 
                    e =  - N   volt      
                                     dt
Usually a minus sign is given to the right-hand side expression to signify the fact that the induced e.m.f. sets up current in such a direction that magnetic effect produced by it opposes the very cause producing it

15. Direction of induced e.m.f and current
There exists a definite relation between the direction of the induced current, the direction of the flux and the direction of motion of the conductor.
The direction of the induced current may be found easily by applying either Fleming’s Right-hand rule
Flat-hand rule
Lenz’s law.

16. Direction of induced e.m.f and current
Fleming’s Right-hand rule is used where induced e.m.f is due to flux-cutting (i.e., dynamically induced e.m.f) and Lenz’s when it is used to change by flux-linkages (i.e., statically induced e.m.f)

17. Direction of induced e.m.f and current
Another way of finding the direction of the induced e.m.f is Right-Flat-hand rule. Here, the front side of the hand is held perpendicular to the incident flux with the thumb pointing in the direction of the motion of the conductor. The direction of the fingers give the direction of the induced e.m.f and current.

18. Fleming’s Right hand rule
States that the thumb, fore finger and middle finger of right hand are stretched perpendicular to each other at right then thumb represents the direction of the movement of conductor, fore-finger represents direction of the magnetic field, then the middle finger represents direction of the induced current.

19. Fleming’s Right hand rule

20. Lenz’s law
States that, when an emf is induced according to Faraday's law, the polarity (direction) of that induced emf is such that it opposes the cause that produce it.
Heinrich Friedrich Emil Lenz

21. Induced e.m.f
Whenever a conductor is placed in a varying magnetic field, emf is induced in the conductor and this emf is called induced emf.
Induced emf is of two types,
Dynamically induced emf Statically induced emf

22. Dynamically Induced e.m.f
When the conductor is in motion and the field is in stationary, so the emf is induced in the conductor, this type of emf is called dynamically induced emf.

23. Statically Induced e.m.f
When the conductor is in stationary and the field is changing (varying) then in this case emf is also induced in the conductor, which is called statically induced emf.
Statically induced emf is of two types,
Self induced emf
Mutually induced emf

24. Self Induced emf
This is the emf induced in a coil due to the change of its own flux linked with it.
If current through the coil is changed, then the flux linked with its own turns will also change, which will produce in it what is called self-induced e.m.f.

25. Self Induced emf

26. Mutually Induced emf
When an alternating voltage or current is applied to the coil 'a' alternating current will flow in the coil' a' and is a result of which a varying magnetic field will produced around the coil' a' . If we placed another coil 'b' in the field of coil 'a' then e.m.f is induced in coil `b' this EMF is called mutually induced e.m.f.

27. Mutually Induced emf
The e.m.f induced in one coil by the influence of the other coil is called Mutually induced e.m.f.

28. Mutually Induced emf

29. Self Inductance
Self Inductance is the property of a coil by virtue of which the coil opposes the growth and decay of the current in it.
It is quantitatively measured in terms of coefficient of self induction L.

30. Coefficient of Self Induction L

31. Mutual Inductance
Mutual Inductance is the phenomenon in which a change of current in one coil causes an induced e.m.f in another coil placed near to the first coil.
It is measured in terms of coefficient of mutual induction M.

32. Coefficient of Mutual Induction M

33. Magnetic Hysteresis
Hysteresis - The lagging of an effect behind its cause; especially the phenomenon in which the magnetic induction of a ferromagnetic material lags behind the changing magnetic field.

34. Residual Magnetism
The magnetism remaining in the magnetic material, even when the magnetising field is reduced to zero is called residual magnetism.

36. B-H
Curve

37. Retentivity: the measure of the magnetisation remaining in the material when the field is totally removed.
Residual Magnetism or Residual Flux: The magnetic flux density that remains in a material when the magnetic field is zero.
Coercive Force: The amount of reverse magnetic field which must be applied to a magnetic material to make the magnetization to zero.

38. Permeability: A property of a material that describes the ease with which a magnetic flux is established in the component.
Reluctance: Is the opposition that a ferromagnetic material shows to the establishment of a magnetic field. Reluctance is analogous to the resistance in an electrical circuit.

40. Energy stored in magnetic field

41. Energy stored in magnetic field

42. Rise & Decay of Current in an Inductive circuit

43. Rise of Current in an Inductive circuit
𝑉 𝑅 =Im

44. Decay of Current in an Inductive circuit

45. END