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**BENE 1113 PRINCIPLES OF ELECTRICAL AND ELECTRONICS**

CHAPTER 2: MAGNETIC AND ELECTROMAGNETIC

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**TOPICS COVERED: MAGNETIC UNITS POLES OF MAGNET MAGNETIC FIELD**

ELECTROMAGNETISM ELECTROMAGNETIC INDUCTION RIGHT HAND RULE FLEMING LEFT HAND RULE FARADAY’S LAW LENZ’S LAW

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INTRODUCTION The first experience with magnetism occurred when pieces of stone were found to have the ability to attract iron or similar materials. These stones were called magnets. Magnetic forces are refer to the force that acts between magnets and magnetic materials: -There are two types of magnetic poles, conventionally called North and South. -Like poles repel, and opposite poles attract.

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INTRODUCTION Magnetic fields are described by drawing flux lines that represent the magnetic field. Each of magnetic flux line travels from the north pole to the south pole thro space. The line returns to the north pole thro the magnet itself. Where lines are close together, the flux density is higher. Where lines are further apart, the flux density is lower.

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INTRODUCTION Magnetic flux lines are invisible, but the effects can be visualized with iron filings sprinkled in a magnetic field.

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LAWS OF MAGNETISM 1. Like poles repel each other

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LAWS OF MAGNETISM 2. Unlike poles attract each other

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LAWS OF MAGNETISM 3. The attractive/repelling force increases as the distance between the magnet decreases. To demonstrate this law, one bar magnet is placed on the table. By slowly sliding one pole of a second bar magnet toward the opposite pole of the first bar that resting on the table. When the two magnets become closer enough, the magnet on the table will be drawn to the second magnet. When the attractive force gains enough strength to overcome the force of friction that holding the first magnet to the table, the first magnet slides toward the second.

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**Magnetic attraction and repulsion**

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**Lines of force tend to take the path of least magnetic**

resistance. This fact introduces two features: - The lines tend to take the shortest possible path between the north and south poles when this path is through materials that cannot be magnetized. - When a material that can be magnetized is placed within the magnetic field, the path of some of the lines of force is distorted in order to pass through this material.

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**NON MAGNETIC MATERIALS**

Materials that have no obvious magnetic properties. Magnetic fields of the individual atoms are randomly aligned and thus tend to cancel out. Non magnetic material such as paper, glass, wood and plastic.

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PERMANENT MAGNET Magnets made of steel alloys hold their magnetism for a long period of time. That is called permanent magnet. Magnetic fields of the individual atom are aligned in one preferred direction, giving rise to a net magnetic field.

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MAGNETIC MATERIALS Materials respond differently to the force of a magnetic field. A magnet strongly attract Ferromagnetic materials A magnet weakly attract Paramagnetic materials A magnet weakly repel Diamagnetic materials The orientation of the spin of the electrons in an atom, the orientation of the atoms in a molecule or all ability of domains of atoms or molecules to line up are the factors that how a material responds to a magnetic field. the responds to magnetic field, that substance become magnetized (to become a magnet)

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**MAGNETIC MATERIAL MAGNETIC MATERIALS**

Ferromagnetic Material – A material easy to magnetize. (i.e., Iron Steel, Cobalt, Perm-alloy, and Alnico) Paramagnetic Material- A material that can be slightly magnetized. Diamagnetic Material – A material that is difficult to magnetize.

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**FERROMAGNETIC MATERIALS**

There are domains in which the magnetic fields of the individual atoms align, but the orientation of the magnetic fields of the domains is random. This offer no net magnetic field.

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A useful property of ferromagnets is that when an external magnetic field is applied to them, the magnetic fields of the individual domains tend to line up in the direction of this external field, due to the nature of the magnetic forces. This cause the external magnetic field to be enhanced. Ferromagnet material such as iron, nickel and cobalt.

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**MAGNETIC MATERIALS Paramagnetic materials**

Weakly attracted to magnetic field. Aluminum and copper These materials can be a magnet, but their attractive force can only be measured with sensitive instruments. The force of a ferromagnetic magnet is about a million times that of a force made with a paramagnetic force. Sometimes, this materials are typically considered as non magnetic materials.

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**MAGNETIC MATERIALS Diamagnetic material**

Means that when they are located at the strong magnetic field, they induce a weak magnetic force in the opposite direction. In other words, they weakly repel a strong magnet. Bismuth and carbon graphite are the strongest diamagnetic, followed by mercury, silver, water, diamonds, wood and living tissues.

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**Magnetic Flux The unit of magnetic flux is weber (Wb)**

One weber equals 1x108 lines of magnetic flux. The weber is a very large unit thus microweber (μWb) is used. 1 μWb equals 100 lines of magnetic flux.

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**MAGNETIC UNITS 1. Flux Density: Is the amount of flux per unit area**

Symbolized by B Unit: tesla (T) or Wb/ m2 1 Wb/m2 = tesla where is the flux (group of 1x108 lines of force) A is the cross-sectional area in m2 The many invisible lines of magnetic force surrounding a magnet are called the magnetic flux. The strength of a magnetic field can be determined by the flux density. 20

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Example 1 Compare the flux and the flux density in the two magnetic cores shown in Figure below. The diagram represents the cross section of a magnetized material. Assume that each dot represents 100 lines or 1 μWb.

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Example 2 What happens to the flux density if the same flux shown in the first figure is in a core of 5.0cm x 5.0cm? If the flux density in a certain magnetic material is 0.23T and the area of the material is 0.38in2, what is the flux through the material? Calculate B if A = 0.05 in2 and Φ = 1000μWb

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ELECTROMAGNETISM Electromagnetism is related to the magnetic field generated around a conductor when current is passed through it. When electricity passed through a wire, a magnetic field is created around the wire in a specific direction. The magnetic field disappears when the current flow stop

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**Visible affects of an electromagnetic field.**

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**ELECTROMAGNETISM Right Hand Rule**

To find the direction of the magnetic field. The field strength is not uniform throughout the magnetic field; the further away from the conductor, the weaker the field intensity. The magnetic field strength and flux density can be increased by increasing the no of turn or current or adding an iron core

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**Electromagnetic Properties**

1. Permeability (μ): The ability of a material to establish a magnetic field The higher the permeability, the more easily a magnetic field can be established. The permeability of a vacuum (μ0) is 4πX10-7 Wb/At·m (Webers/ampere-turn.meter). The relative permeability (μr) of a material is the ratio of its absolute permeability to the permeability of a vacuum. Unit is dimensionless

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**Electromagnetic Properties**

2. Reluctance ( ): The opposition to the establishment of a magnetic field in a material. The value of reluctance is directly proportional to the length (l) of the magnetic path and inversely proportional to the permeability (μ) and to the cross-sectional area (A) of the material, as expressed by the following equation: Unit is At/Wb

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Example 3 Calculate the reluctance of a torus (a doughnut shaped core) made of low carbon steel. The inner radius of the torus is 1.75cm and the outer radius of the torus is 2.25 cm. Assume the permeability of low carbon steel is 2 x 10-4 Wb/At.m.

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Example 4 Mild steel has a relative permeability of Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 1.0cm x 1.2 cm.

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Example 5 A square magnetic core has a dimension of 8cm x 8cm x 3cm(its thickness) with 0.5cm air gap at one of its side. It has a relative permeability of 6000.The cross section is 2cm by 3cm.Calculate the reluctance of the core and the gap.

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**Electromagnetic Properties**

3. Magnetomotive Force (mmf): Current in a conductor produces a magnetic field. The cause of the magnetic field is called the magnetomotive force (mmf). The unit of mmf is ampere-turn (At). The formula for mmf is where Fm is the magnetomotive force, N is the number of turns of wire and I is the current in amperes.

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**Electromagnetic Properties**

Figure above illustrates that a number of turns of wire carrying a current around a magnetic material creates a force that sets up flux lines through the magnetic path. The amount of flux depends on the magnitude of the mmf and on the reluctance of the material as expressed by: This equation is known as Ohm’s Law for magnetic circuits since Φ is analogous to current, the mmf (Fm) is analogous to voltage, and reluctance (R) is analogous to resistance

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**OHM’S LAW APPLIED TO MAGNETIC CIRCUITS**

Ohm’s Law, when applied to electrical circuits, gave the formula: I=V/R (2.1) where: I = current flow in amperes V = electromotive force/voltage R = current flow opposition/resistance A similar version can be applied to magnetic circuits, that is: (2.2) where: = magnetic flow of lines of force (webers) Fm = magnetomitive force (ampere-turns) R = magnetic reluctance (NI/ Wb)

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MAGNETIC UNITS From Eq. 2.2, it can be seen that increasing either the current or turns of a solenoid will increase the flux. A decreases in R would also increases the flux. Ohm’s Law for magnetic circuits may be given in three variations to suit particular problems: For Electrical Equivalent;

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**MAGNETIC UNIT 1. Magnetizing Force (Magnetic Field Intensity), H**

The m.m.f. required to magnetize a unit length of a magnetic path. The unit is expressed in ampere-turns per metre (At / m) and the symbol is H. where H = magnetizing force or magnetic field intensity NI = Ampere turns l = length between poles of the coil

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**RELATIONSHIP BETWEEN B & H**

When the magnetomotive force, Fm increases, the magnetizing force, H increases. At the same time, the flux increases since The flux density also increases as In other word, B is also proportional to H B H B / H = Constant =

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**RELATIONSHIP BETWEEN B & H**

The ratio B/H in a material is always constant and is equal to the absolute permeability, of the material. (= o r) Obviously, B = orH (in medium) B = oH (in air) RECALL: μ = relative ability of substance to conduct magnetic lines of force as compared with air.

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Example 5 How much flux is established in the magnetic path of Figure below if the reluctance of the material is 2.8 x 105 At/Wb? Figure 10-12

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**Example 6 There is 85mA of current through a coil with 500 turns.**

What is mmf? What is the reluctance of the circuit in the flux is 500 μWb?

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EXERCISE An electromagnet has 600 turns and the total reluctance of the magnetic core is 800 units. Calculate the flux produced when 10 A flows through the coil. A contractor coil has 7200 turns, which are wound on iron core, rectangular in section, and having cross-sectional dimension of 20mm x 30 mm. If the flux density in the magnetic circuit is 1.2 Tesla, find the reluctance of the magnetic core. The current drawn is 0.1 A.

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**POLES OF A MAGNET The points about the poles of a magnet:**

(i) The poles of a magnet cannot be separated. If a bar magnet is broken into two parts, each part will be a complete magnet with poles at its ends. No matter how many times a magnet is broken, each piece will contain n-pole at one end and s-pole at the other. (ii) The two poles of a magnet are equal in strength - The force between two magnetic poles is directly proportional to the product of their poles strengths and inversely proportional to the square of distance between them

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**ELECTROMAGNETIC INDUCTION**

When there is a relative motion between a conductor and a magnetic field, a voltage is produced across the conductor. This principal is known as electromagnetic induction and the resulting voltage is induced voltage.

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**ELECTROMAGNETIC INDUCTION**

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**ELECTROMAGNETIC INDUCTION**

When a current carrying conductor is placed at right angles to a magnetic field, it experiences a mechanical force F, given by; where: B = flux density in wb/m2 I = current through conductor in ampere = length of conductor metres The direction of this force can be found by Fleming’s Left-hand rule.

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**ELECTROMAGNETIC INDUCTION**

Faraday’s Law The amount of voltage induced in a coil is directly proportional to the rate of change of the magnetic field with respect to the coil. (a) (b)

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The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N). (a) (b)

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**ELECTROMAGNETIC INDUCTION**

Faraday’s Law Faraday’s Law state that: The voltage induced across a coil of wire equals the number of turns in the coil times the rate of change of the magnetic flux. In mathematic,

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**ELECTROMAGNETIC INDUCTION**

Lenz’s Law Lenz’s Law is used to find the direction of induced e.m.f and hence current in a conductor or coil. Lenz’s Law is stated as follows: The direction of the induced current is such as to oppose the change causing it.

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**ELECTROMAGNETIC INDUCTION**

The diagram shows the north pole of a bar magnet approaching a solenoid. According to Lenz's law, the current which is generated in the coil must opposes the approaching magnetic field. This is achieved if the direction of the induced current creates a north pole at the end of the solenoid closest to the approaching magnet, as the induced north pole tends to repel the approaching north pole. LENZ’S LAW:

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**ELECTROMAGNETIC INDUCTION**

The diagram shows the north pole of a bar magnet withdrawing from a solenoid. According to Lenz's law, the current which is generated in the coil must oppose the departing magnetic field. This is achieved if the direction of the induced current creates a south pole at the end of the solenoid closest to the departing magnet, as the induced south pole tends to attract the departing north pole. Lenz’s Law

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ELECTRIC CIRCUIT ANALYSIS - I

ELECTRIC CIRCUIT ANALYSIS - I

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