Electromagnetism

1. Electromagnetism Elements Of Electrical Engineering

2. Introduction • Magnetic circuits • Electromagnetic induction • Magnetic hysteresis

3. Introduction • Magnet : • Any object that attracts iron and which when freely suspended points towards the poles of the earth is called magnet. • Any magnet will exist only as dipole. • When a magnet freely suspended the end which point towards the north pole of earth is called its north pole and which points towards earth’s south pole is called magnet’s south pole.

4. Conti… • Magnetism: • The power by which a magnet attracts certain substances is called magnetism. • Magnetic material: • The substance or materials that are attracted by magnet is called magnetic material.

5. Magnetic quantities • Magnetic field: • Whenever a magnet is placed near another magnet, it experiences a force. • The region around the magnet in which another magnet or magnetic material experience a force is called its magnetic field. • It is shown by hypothetical magnetic lines called magnetic flux lines.

6. Conti… • Magnetic flux : • The total number of magnetic lines of force passing through a surface in magnetic field is called the magnetic flux. • Unite of magnetic flux is Weber (Wb). • 1 Weber = 108 magnetic lines = 108 Maxwell • These lines of flux are purely imaginary.

7. Conti… • Characteristics of flux lines : • They have no physical existence. • They form closed path • They never intersect each other. • Lines of magnetic flux (parallel lines ) closer to each other and having same direction repel each other. • Lines of magnetic flux (parallel lines ) closer to each other and having opposite direction attract each other. • They exert lateral pressure. • They emerge from the N-pole and enter into S-pole and are then continuous through the body of the magnet.

8. Conti… • Magnetic flux density : • It is defined as the magnetic flux per unit area of a surface at right angle to the magnetic field. • It is denoted by symbol B. • Unit : Wb/m2 • The recommended name for the unit in S.I. system is Tesla (T). • 1 Wb/m2 = 1 Tesla (T) Mathematically ,

9. Conti… • Magneto motive force : • It is define as force required to produce magnetic flux. • The m.m.f. is given by the product of the current through the coil and the number of turns of the coil. • mmf(Fm) = NI • Where, N = number of turns on a coil I = current through the coil (A) • Unit :Ampere turn(AT)

10. Conti… • Magnetic field intensity (H) : • It is defines as the m.m.f per unit length of the magnetic circuit. It is also known as magnetic field strength. • Mathematically, • Where, • I = current(A) • N= no. of turns • l =length of magnetic circuit • Unit ampere-turn / meter (AT/m) or ampere / meter (A/m)

11. Conti… • Permeability: • When the magnetomotive force is applied to ferromagnetic material, the flux produced is very large compared with that in air , vacuum or non- magnetic material. • Thus magnetic material establish more magnetic flux than others under similar conditions. • Permeability is the ability of a material to establish the magnetic flux. It is measure of ease with which the material can be magnetized. • SI unit : Henry / meter (H/m) • Symbol : µ (permeability of any material)

12. Conti… • The permeability of free space is written as µ0 . It is also called as magnetic space constant. • µ0 = 4 * 10-7 H /m • When the permeability of any material is compared with that of air (µ0), it shows the permeability of the material is how many times that of air and it is called its relative permeability (µr ).

13. Conti… • Reluctance : • The property of a material that opposes the production of magnetic flux through it is called reluctance. • Where, S =reluctance of the magnetic circuit F = magnetomotive force (mmf)  = magnetic flux • Unit : ampere turn /Wb (AT/Wb) or ampere/Wb (A/Wb)

14. Conti… • Now • Where , l = length of magnetic circuit A = area of cross section of magnetic path

15. Conti… • Reluctivity : • Reluctivity or specific reluctance is defined as the reluctance offered by a magnetic circuit of a unit length and unit cross section. • When l = 1 and A =1 then , • Unit : meter/Henry

16. Conti… • Permeance : • It is define as the reciprocal of the reluctance. • Thus it is matter of ease with which the flux can be setup in the magnetic circuit. • Unit : Weber / ampere (Wb/A) or Henry(H)

17. Coulomb’s law of magnetic force • Like poles repel and unlike poles attract. • If we consider two isolated poles to be placed near each other they will experience a force. This force between the two magnetic poles is directly proportional to the product of their pole strength and inversely proportional to the square of the distance between their centers.

18. Conti… • Two poles having magnetic strengths of m1 and m2 respectively are placed at a distance of ‘d’ meters in any medium. • Thus the force between the poles ,

19. Conti… • Where K is constant and its value depends on the surrounding medium. • In SI units , force F is measured in Newton , the pole strength in Weber and distance in meter ; • Hence K is given by , • Where, • µ0 = absolute permeability of air or vacuum = 4 * 10-7 H /m • µr = relative permeability of the surrounding medium

20. Electromagnetic induction • The phenomenon by which an emf is induced in a circuit (hence current flows when the circuit is closed), when magnetic flux linking with it changes is called electromagnetic induction. • The deflection of galvanometer indicates the production can be sudden approach or with drawl of the magnet from the coil or vica versa. • It is found that the actual cause of this emf is the change of flux linking with the coil. This emf exists so long as the change in the flux exists. • Stationary flux, however strong will never induce any emf in stationary conductor

21. Faraday’s laws of electromagnetic induction • First law : Whenever the flux linking with the coil or a circuit changes there is an emf induced in the coil or circuit. • Second law : The magnitude of the emf that is induced is proportional to the rate of change of flux linkage.

22. Conti… • Consider a coil having N number of turns. And initially the linking flux is 1 Wb. In time t it would increase to 2 Wb. • Thus , • Initially flux linkages = N 1 • Final flux linkages = N 2 • So , change in the flux linkages = N 2 - N 1 the induced emf ‘e’ is equal to the rate of change of flux linkages.

23. Lenz’s law • According to faraday’s law , • Faraday’s law does not give any idea about the direction of the induced emf. This information is given by Lenz’s law. • It states that the direction of the induced emf (or current) is such that it opposes the very cause of its production. • The cause of production of the induced emf ( or current) is the charge in the flux linking. • Thus the induced emf acts in such a direction so as to oppose the change in the flux linking. • So a minus sign is given to the induced emf.

24. Fleming’s right hand rule • Fleming’s right hand rule is used to get direction of induced e.m.f. when conductor is moving in a magnetic field. • According to this rule outstretch three fingers of right hand namely the thumb , fore finger and the middle finger , perpendicular to each other. • Arrange the right hand so that first finger point in the direction of flux lines (from N to S) and thumb in the direction of motion of conductor with respect to the flux then the middle finger will point in the direction of the induced e.m.f. (or current).

25. Conti…

26. Fleming’s left hand rule • The direction of force experienced by the current carrying conductor place in magnetic field can be determined by a rule called “Fleming's left hand rule”. • The rule states that , ‘outstretch the three fingers of the left hand namely the first finger , middle finger and thumb such that they are mutually perpendicular to each other. • Now point the first finger in the direction of magnetic filed and the middle finger in the direction of current then the thumb gives the direction of the force experienced by the conductor.’

27. Conti…

28. Dot convention and cross convention

29. Corkscrew law • Imagine a right handed screw to be along the conductor carrying current with its axis parallel to the conductor and tip pointing in the direction of the current flow. • Then the direction of the magnetic field is given by the direction in which the screw must be turned so as to advance in the direction of the current. • This is shown in fig.

30. Conti…

31. Similarities Electric circuit Magnetic circuit • The closed path for electric current is called electric circuit. • Flow of electron through conductor is called current. • Unit : Ampere • The driving force required for current is called E.M.F. • Unit : Volts • The closed path for magnetic flux is called magnetic circuit. • Lines of force through a medium from N pole to S pole forms flux. • Unit : Weber • M.M.F is driving force for flux in magnetic circuit. • Unit : Ampere -turn

32. Conti… Electric circuit Magnetic circuit • Resistance opposes the flow of current. • Unit : Ohms • Resistance depends on conductor material. • Resistivity : (ρ) • Conductance = 1/ resistance • Conductivity = 1/ resistivity • Reluctance opposes the flux production. • Unit : AT/Wb • Reluctance depends on permeability of medium. • Reluctivity : 1 / µ0µr • Permeance= 1/reluctance • Permeability= 1/ reluctivity

33. Conti… Electric circuit Magnetic circuit • Current density δ = I / a • Unit : Amp/m2 • Electric field intensity E=V/d • Unit : Volts/m • KCL and KVL are applicable to electric circuit. • Flux density B = Φ / A • Unit : Wb / m2 • Magnetic field intensity E=NI/l • Unit : AT/m • Kirchhoff's flux and m.m.f. laws are applicable to magnetic circuit.

34. Dissimilarities Electric circuit Magnetic circuit • The electric current actually flows in circuit. • Energy is required to produce current and to maintain it. • Current does not pass through air. • Resistance is almost constant , it varies vary slight. • There are many insulations for electric circuit. • Magnetic flux does not actually flow in circuit. • Energy is required to produce flux but not for its maintenance. • Flux can pass through air. • Reluctance depends on permeability, it vary to a great extent. • There are no insulation for magnetic circuit.

35. CONTI…

36. Magnetic circuit • An iron ring of length ‘l’ meter and cross-section area ‘A’ m2 . A coil having N number of turns is wound over the iron ring. • When this coil carries a current, magnetic field is produced inside the ring. • This is called its magnetic circuit.

37. Analysis of simple magnetic circuit

38. Relation between B and H Thus if magnetic force H produces a flux density of B0 in a material placed in air then , If the same magnetic force H is now applied to the same material placed in a medium then the flux density produced in the material, Thus the relative permeability of a material is the ratio of the flux density Produced in that material to the flux density produced in air by the same magnetising force.

39. Composite magnetic circuit • Series magnetic circuit :

40. Conti… • Parallel magnetic circuit :

41. Example 1 • A coil having 600 turns is wound uniformly over an iron ring whose mean diameter is 41cm. The relative permeability of iron ring is 1200. if a current of 3.2 a flows through the coil , find the flux density.

42. Example 2 • An iron ring having a cross sectional area of 5cm*4cm and a mean length of 18 cm has a coil of 270 turns uniformly wound over it. A current of 1.27 A flows through the coil which produces a flux of 1.13 mWb in the ring. Find the • Reluctance of the circuit • The absolute and relative permeability of iron

43. Example 3 • A circular iron ring has a cross sectional area of 15 cm2 and a mean length of 6π cm in iron , has an air gap of 0.6 π mm made by a saw cut. The relative permeability of iron is 1300. the ring is wound with a coil of 2400 turns and carries 4mA current. Find the air gap flux neglecting leakage and fringing.

44. Example 4 • A circular ring of mild steel has a diameter of 20cm and a 2mm side air gap. The cross sectional area is 3.2cm2 . Estimate the mmf required to establish 0.6mwb flux. Assume relative permeability of mild steel = 900.

45. Example 5 • An iron ring of 40cm mean diameter and 7cm2 cross sectional area has an air gap of 2mm. It is wound with 750 turns of wire and carries a current of 3A. The iron takes 60% of the total mmf. Neglect magnetic leakage. Find the total mmf , magnetic flux, reluctance and flux density.

46. Leakage flux • The magnetic flux which does not follow the intended path in a magnetic circuit is called leakage flux. • In most of magnetic circuit, a large part of the flux is through the magnetic material and the remaining flux through air. Fig shows a narrow air gap in an iron ring on which a coil is wound.

47. Conti… • The total flux produced by the coil does not pass through the air gap. However some part of it leaks through the air paths at X surrounding the iron. • These flux lines as at X which do not pass through the desired path but take different paths and thus do not become useful are called the leakage flux lines. • The flux lines passing through the air gap tends to buldge outwards as shown by the lines ‘yy’. This increases the effective area of the air gap thus reducing flux density. • This effect of the flux not totally confining to the air gap but spreading near it is called fringing.

48. Conti… • The flux in the gap can be utilized for many purposes. So it is called the useful flux. • The co – efficient λ is defined as , • λ is called Hopkinson’s leakage co – efficient. Its value is always greater than 1.

49. Magnetisation curve • The magnetisation curve is a plot of flux density (B) verses the magnetising force (H). • From this curve we can fiend the magnetising force required to produce a certain flux density in a particular magnetic material. • For , • Non- magnetic material • Magnetic material

50. For non-magnetic material • For non- magnetic material such as air , wood , rubber etc. • Since µr = 1 the relation between B and H is given by B = µ0 H • Since µ0=constant =4*10-7 H/m. • A larger mmf will be required to produce a given flux in these non- magnetic material.