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Chapter 6 Magnetic Circuits v D. C. Kulshreshtha Next

Thought of the DAY There are no secrets to success. It is the result of preparation, hard work, and learning from failure. --Colin Powell. . Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 3

Topics to be Discussed n n n Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance (R). Analogy between Electric and Magnetic Circuits. Composite Magnetic Circuit. Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 4

Introduction n Unlike electric field lines, the lines of magnetic flux form closed loops. n A magnetic circuit is a closed path followed by lines of magnetic flux. n A copper wire, because of its high conductivity, confines the electric current within itself. n Similarly, a ferromagnetic material (such as iron or steel), due to its high permeability, confines magnetic flux within itself. Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 5

Magnetomotive Force (MMF) n n n The electric current is due to the existence of an electromotive force (emf). By analogy, we may say that in a magnetic circuit, the magnetic flux is due to the existence of a magnetomotive force (mmf). mmf is caused by a current flowing through one or more turns. The value of the mmf is proportional to the current and the number of turns. It is expressed in ampere turns (At). But for the purpose of dimensional analysis, it is expressed in amperes. Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 6

Magnetic Field Strength (H) n n n The mmf per metre length of the magnetic circuit is termed as the magnetic field strength, magnetic field intensity, or magnetizing force. It units are ampere-turns per metre (At/m). Its value is independent of the medium. Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 7

Magnetic Permeability (μ) n n n If the core of the toroid is vacuum or air, the magnetic flux density B in the core bears a definite ratio to the magnetic field strength H. This ratio is called permeability of free space. Thus, for vacuum or air, Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 8

n The flux produced by the given mmf is greatly increased, if iron replaces the air in the core. n As a result, the flux density B also increases many times. n In general, we can write B = μH. n μ is called the permeability of the material. n Normally, we write μ = μr μ 0. n μr is called relative permeability (just a number). Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 9

Reluctance (R) and Permeance (G) n n The current in an electric circuit is limited by the presence of resistance of the electric circuit. Similarly, the flux Φ in a magnetic circuit is limited by the presence of the reluctance of the magnetic circuit, The reciprocal of reluctance is known as permeance (G). Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 10

Magnetic Circuit Theory n For a toroid, mmf, F = NI ampere-turns. n Because of this mmf, a magnetic field of strength H is set up throughout the length l. Therefore, F = Hl n n n If, B is the flux density, total flux is given as Φ=B A Dividing, we get Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next Click 11

Comparing this with We get Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 12

Analogy between Electric and Magnetic Circuits Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 13

Example 1 Calculate the magnetomotive force (mmf) required to produce a flux of 0. 015 Wb across an air gap of 2. 5 mm long, having an effective area of 200 cm 2. Solution : n Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 14

Composite Magnetic Circuit Case 1 : Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 15

Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 16

Case 2 : (with air gap) Total reluctance, Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 17

n Since the relative permeability μr (= μ 1/ μ 0) of steel is very large (of the order of thousand), the major contribution in the total reluctance R is by the air-gap, though its length l 2 may be quite small (say, a few millimetres). Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 18

Kirchhoff’s Laws n Kirchhoff’s Flux Law (KFL) : The total magnetic flux towards a junction is equal to the total magnetic flux away from that junction. n Kirchhoff’s Magnetomotive Force Law (KML): In a closed magnetic circuit, the algebraic sum of the product of the magnetic field strength and the length of each part of the circuit is equal to the resultant magnetomotive force. Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 19

Steps to solve a problem on magnetic circuit Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 20

Review n n n Magnetomotive Force (MMF). Magnetic Field Strength (H). Magnetic Permeability. Reluctance (R). Analogy between Electric and Magnetic Circuits. Composite Magnetic Circuit. Saturday, October 24, 2020 Ch. 6 Magnetic Circuits Next 21