Lecture 4by Moeen Ghiyas

Chapter 11 – Magnetic Circuits

03/05/23 1

TODAY’S LECTURE CONTENTS

Review Ohm’s Law For Magnetic Circuits

Magnetizing Force

Hysteresis

Ampere’s Circuital Law – (Applying KVL)

The Flux Φ – (Applying KCL)

Series Magnetic Circuits

Ohm’s Law For Magnetic Circuits

Ohm’s law for magnetic circuit

Where the magnetomotive force F is proportional to the product

of the number of turns N around the core (in which the flux is to

be established) and the current I through the turns of wire

Obviously, an increase in the number of turns N or the current I

through the wire will result in an increased “pressure” on the

system to establish flux lines through the core.

Magnetizing Force The magneto-motive force per unit length is called the

magnetizing force (H). In equation form,

But from Ohm’s law for magnetic circuits, we know

Substituting above, we have

03/05/23 4

Magnetizing Force The applied magnetizing force has a pronounced effect

on the resulting permeability of a magnetic material.

03/05/23 5

Magnetizing Force Also the flux density and the magnetizing force are

related by the following equation:

This equation indicates that for a particular magnetizing

force, the greater the permeability, the greater will be the

induced flux density.

03/05/23 6

03/05/23 7

Hysteresis

03/05/23 8

Hysteresis

03/05/23 9

Hysteresis

03/05/23 10

Hysteresis

03/05/23 11

Hysteresis

03/05/23 12

Hysteresis

Domain Theory of Magnetism

The atom, due to its spinning electrons, has magnetic field

associated.

In nonmagnetic materials, the net magnetic field is zero since the

magnetic fields due to the atoms oppose each other.

In magnetic materials such as iron and steel, however, the

magnetic fields of groups of atoms in the order of 1012 are

aligned, forming very small bar magnets.

03/05/23 13

Hysteresis

Domain Theory of Magnetism

This group of magnetically aligned atoms is called a domain.

Each domain is a separate entity; that is, each domain is

independent of the surrounding domains.

For an un-magnetized sample of magnetic material, these

domains appear in a random manner, such as shown in fig.

The net magnetic field in any one direction is zero.

03/05/23 14

Hysteresis

03/05/23 15

Ampere’s Circuital Law – KVL

03/05/23 16

Ampere’s Circuital Law – (KVL)

03/05/23 17

The Flux Φ – (KCL)

Magnetic circuit problems are basically of two types:

In one type, Φ is given, and the impressed mmf NI must be

computed (problem encountered in the design of motors,

generators, and transformers).

In the other type, NI is given, and the flux Φ of magnetic circuit

must be found (problem encountered primarily in the design of

magnetic amplifiers and is more difficult since the approach is

“hit or miss.”

For magnetic circuits, the level of B or H is determined from

using the B-H curve.

03/05/23 18

Series Magnetic Circuits

Ex ample – For the series magnetic circuit of fig:a) Find the value of I required to develop a magnetic flux of Φ = 4

x 10-4 Wb.b) Determine μ and μr for the material under these conditions.

03/05/23 19

Series Magnetic Circuits

a) Find the value of I required to develop a magnetic flux Φ = 4 x 10-4 Wb Solution

03/05/23 20

Series Magnetic Circuits

a) Find the value of I required to develop a magnetic flux Φ = 4 x 104 Wb Solution

Using B – H curves of fig, we can determine magnetizing force H: . H = 170 At / m

03/05/23 21

Series Magnetic Circuits

b) Determine μ and μr for the material under these conditions.

03/05/23 22

Series Magnetic Circuits

Summary / Conclusion Review

Ohm’s Law For Magnetic Circuits

Magnetizing Force

Hysteresis

Ampere’s Circuital Law – (Applying KVL)

The Flux Φ – (Applying KCL)

Series Magnetic Circuits

03/05/23 24