Magnetic and Electromagnetic DR. MOHD IRFAN HATIM MOHAMED DZAHIR

What you should know at the end of this chapter Magnetic field Magnetic Flux Flux Density Permeability Different magnetic materials Reluctance Ohms Law for Magnetic Circuits Magnetizing Force Hysteresis Ampere’s Circuital Law Airgap Faradays Law Lenz’s Law

Application of magnetic effects

Speaker The shape of pulsating waveform of the input current is determined by the sound to be reproduced by the speaker. The higher the pitch of the sound pattern, the higher the oscillating frequency between the peaks and valleys resulting higher frequency of the vibration of the cone.

Coaxial High-Fidelity Loudspeaker (b) Basic operation (a) Overall view (a) Cross-sectional view

Hall Effect Sensor (b) Effect on electron flow (a) Orientation of controlling Hall effect sensor is a semiconductor device that generates an output voltage when exposed to the magnetic field. The difference in potential is due to separation of charge established by the Lorentz force. The direction of force can be determined by left-hand rule.

Bicycle Speed Indicator Use as sensor for alarm systems

Magnetic Field Magnetic field Magnetic flux lines (Φ) exists in the region surrounding a permanent magnet can be represented by magnetic flux lines Magnetic flux lines (Φ) Representation of magnetic field. do not have origins or terminating points exist in continuous loops radiate from the north pole to the south pole returning to the north pole through the metallic bar

Magnetic Field The strength of a magnetic field in a particular region is directly related to the density of flux lines in that region Magnetic field strength at point a is twice that at point b since twice as many magnetic flux lines are associated with the perpendicular plane at point a than at point b.

If like poles are brought together, the magnets repel Magnetic Field Continuous magnetic flux line will strive to occupy as small an area as possible. This results in magnetic flux lines of minimum length between the unlike poles If unlike poles of two permanent magnets are brought together, the magnets attract If like poles are brought together, the magnets repel

Magnetic Field If a nonmagnetic material, such as glass or copper, is placed in the flux paths surrounding a permanent magnet, an almost unnoticeable change occurs in the flux distribution if a magnetic material, such as soft iron, is placed in the flux path, the flux lines pass through the soft iron rather than the surrounding air because flux lines pass with greater ease through magnetic materials than through air.

Magnetic Field If a nonmagnetic material, such as glass or copper, is placed in the flux paths surrounding a permanent magnet, an almost unnoticeable change occurs in the flux distribution if a magnetic material, such as soft iron, is placed in the flux path, the flux lines pass through the soft iron rather than the surrounding air because flux lines pass with greater ease through magnetic materials than through air.

Magnetic Field The previously stated principle is used in shielding sensitive electrical elements and instruments that can be affected by stray magnetic fields

Magnetic Field A magnetic field is present around every wire that carries an electric current Right-hand rule can be used to determine the direction of magnetic flux line

Magnetic Field If the conductor is wound in a single-turn coil the resulting flux flows in a common direction through the center of the coil. A coil of more than one turn produces a magnetic field that exists in a continuous path through and around the coil

Magnetic Field The field strength of the coil can be effectively increased by placing certain materials, such as iron, steel, or cobalt, within the coil to increase the flux density within the coil The whole concept  electromagnetic

Magnetic Field 2 type of magnets Electromagnet Permanent magnet A material such as steel or iron that will remain magnetized for long periods of time without the aid of external means. Electromagnet Electromagnet Magnetic effects introduce by the flow of charge or current. Flux distribution is quite similar to permanent magnet Have north and south pole Concentration of flux line is less than that of permanent magnet Field strength may be increase by placing a core made of magnetic materials (iron, steel, cobalt) Parameters affecting field strength Currents Number of turn Material of the core Without core With core

Magnetic Field Right Hand Rule Case 1 Case 2 Thumb : Direction of current flow Other fingers : Direction of magnetic flux Case 2 Thumb : Direction of magnetic flux Other fingers : Direction of current flow

Magnetic Flux Representation of magnetic field. Group of force lines going from the north pole to the south pole In the SI system of units, magnetic flux is measured in webers (Wb) and is represented using the symbol phi (𝚽). 1 Weber = 108 lines Similar to current in electric circuit

Flux Density The number of flux lines per unit area Use symbol ‘B’ Measured in Tesla (T) Magnitude of flux density If 1 weber of magnetic flux passes through an area of 1 square meter, the flux density is 1 tesla.

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

Example 1 For figure a Flux is simply the number of lines Finding flux density

Example 1 For figure b Finding flux density Note : the core with the largest flux does not necessarily have the highest flux density.

Example 2 If the flux density in a certain magnetic material is 0.23 T and the area of the material is 0.38 in2 , what is the flux through the material? Convert the area to m2 1 m = 39.37 inch

Magnetomotive force External force or 'Pressure' required to set up the magnetic flux lines within the magnetic material. The cause of a magnetic field Similar to the applied voltage in electric circuit Measured in ampere-turns (At) The magnetomotive force (mmf),  is proportional to the product of the number of turns around the core (in which the flux is to be established) and the current through the turns of wire

Permeability Definition the measure of the ability of a material to support the formation of a magnetic field within itself degree of magnetization that a material obtains in response to an applied magnetic field. Measure of the ease in which magnetic flux lines can be established in the material Ability of magnetic material to conduct flux

Permeability Permeability of air (free space) Relative permeability The ratio of the permeability of a material to that of free space

Nonmagnetic materials Permeability Material Description Example µr Nonmagnetic materials Permeability same as that of free space copper, aluminium, glass, air and wood µr = 1 Diamagnetic Permeability slightly less than that of free space. Bismuth, pyrolitic carbon µr < 1 Paramagnetic Permeability slightly more than that of free space. magnesium, molybdenum, lithium, and tantalum 1 < µr < 100 Ferromagnetic materials have a very high level permeability Iron, nickel, steel and alloys of these materials µr  100

Reluctance The reluctance of a material to the setting up of magnetic flux lines in the material Unit : Ampere-turns / Weber Compare this to the resistance in electric circuit

Ohm’s Law for Magnetic Circuit Recall Effect = Flux Cause = Magnetomotive force Opposition = Reluctance For Magnetic Circuit

Example 3 Calculate the reluctance of a torus (a doughnut-shaped core) made of low-carbon steel. The inner radius of the torus is 1.75 cm and the outer radius of the torus is 2.25 cm. Assume the permeability of low- carbon steel is 2X10-4 Wb/ At m Solution: The length is equal to the circumference of the torus measured at the average radius a b c

Example 4 Mild steel has a relative permeability of 800. Calculate the reluctance of a mild steel core that has a length of 10 cm and has a cross section of 1.0 cm X 1.2 cm. Solution:

Magnetizing Force Magnetomotive force per unit length Also called magnetic field intensity Symbol : H Independent of the type of core material determined solely by the number of turns, the current, and the length of the core.

B-H Relationship Flux density (B) and magnetizing force are related by the equation However, we know that So

Hysterisis Hysteresis is a characteristic of a magnetic material whereby a change in magnetization lags the application of the magnetic field intensity. The magnetic field intensity (H) can be readily increased or decreased by varying the current through the coil of wire, and it can be reversed by reversing the voltage polarity across the coil. In other word, hysteresis is the lagging effect between the flux density, B of a material and the magnetizing force, H applied.

Hysterisis Series magnetic circuit used to define the hysteresis curve.

Hysterisis The entire curve (shaded) is called the hysteresis curve.

Hysterisis The flux density B lagged behind the magnetizing force H during the entire plotting of the curve. When H was zero at c, B was not zero but had only begun to decline. Long after H had passed through zero and had equaled to –Hd did the flux density B finally become equal to zero

Hysteresis If the entire cycle is repeated, the curve obtained for the same core will be determined by the maximum H applied

Normal magnetization curve for three ferromagnetic materials.

Magnetic Equivalent Circuit Magnetic circuit Electric circuit

Ampere’s Circuital Law The algebraic sum of the rises and drops of the mmf around a closed loop of a magnetic circuit is equal to zero. Or The sum of the rises in mmf equals the sum of the drops in mmf around a closed loop. Similar to KVL in electric circuit

Ampere’s Circuital Law Steel Cobalt Iron

Flux  The sum of the fluxes entering a junction is equal to the sum of the fluxes leaving a junction Similar to KCL in electric circuit

Series Magnetic Circuit 2 types of problem:  is given, and the impressed mmf, NI must be computed – design of motors, generators and transformers NI is given, and the flux  of the magnetic circuit must be found – design of magnetic amplifiers B-H curve is used to find H if B is given to find B if H is given

Example 5: Series Magnetic Circuit

Example 5: Series Magnetic Circuit Part a: Finding I

Example 5 Use B-H curve to find H Part a: Finding I For cast steel When B=0.2  H=170 At/m 170

Example 5 Part a: Finding I Use Ampere’s circuital law

Example 5 Part b: Finding µ and µr

Example 6

Example 6 Length of each material Area

Example 6 Finding H for sheet steel

Example 6 Finding H for cast iron

Example 6 Use Ampere’s circuital law

Example 7: NI is given, find flux 

Air Gaps Fringing Only ideal case will be covered in this course The spreading of the flux lines outside the common area of the core for the air gap. Only ideal case will be covered in this course

Air Gaps For ideal case Mmf drop across the air gap Permeability of air is assumed to be equal to permeability of free space so magnetizing force of air gap can be determined by:

Example 8 : Air Gap

Example 8 : Air Gap

Example 8 : Air Gap

Example 9 : Air Gap

Example 9 : Air Gap

Example 9 : Air Gap

Application of magnetic effects

Faraday’s law of electromagnetic induction Michael Faraday discovered the principle of electromagnetic induction in 1831. Basically he found that moving a magnet through a coil of wire induced a voltage across the coil, Two observation: 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 (d /dt). The amount of voltage induced in a coil is directly proportional to the number of turns of wire in the coil (N).

Faraday’s law of electromagnetic induction First observation S N Magnet is moved at certain rate and certain voltage is produced Magnet is moved at faster rate and creating a greater induced voltage.

Faraday’s law of electromagnetic induction Second observation Magnet is moved through a coil and certain voltage is produced Magnet is moved at same speed through coil that has greater number of turn and greater voltage is induced

Faraday’s law of electromagnetic induction Faraday’s Law is stated as follows: 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. Faraday's law is expressed in equation form as

Example 10 : Faraday’s Law Apply Faraday's law to find the induced voltage across a coil with 500 turns that is located in a magnetic field that is changing at a rate of 8000 µWb/s.

Lenz’s Law Defines the polarity or direction of the induced voltage. “an induced effect is always such as to oppose the cause that produced it.” “When the current through a coil changes, an induced voltage is created as a result of the changing electromagnetic field and the polarity of the induced voltage is such that it always opposes the change in current.”

Lenz’s Law The magnetic flux linking the coil of N turns with a current I has the distribution shown in Fig. 11.30. If the current through the coil increases in magnitude, the flux linking the coil also increases. We just learned through Faraday’s law, however, that a coil in the vicinity of a changing magnetic flux will have a voltage induced across it. The result is that a voltage is induced across the coil in Fig. 11.30 due to the change in current through the coil. It is very important to note in Fig. 11.30 that the polarity of the induced voltage across the coil is such that it opposes the increasing level of current in the coil.