Module M2-1 Electrical Engineering

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1 Module M2-1 Electrical Engineering LECTURE 6 MAGNETIC FORCES MATERIALS INDUCTANCE SEPTEMBER 22, Magnetic forces Magnetic materials Magnetization Inductance Magnetic energy Topics 2 After this lecture, you will be able to understand natural phenomena and engineering applications related to the topics in previous slide calculate Lorenz force calculate force in a current-carrying wire in a uniform magnetic field state the relationship of B and H in magnetic materials calculate the inductance of a solenoid calculate the magnetic energy of an inductor 3 Magnetic forces 4 FORCE ON A MOVING CHARGE FORCE ON A CURRENT-CARRYING WIRE

Recall that an electric field exerts a force on charges 5

picture shows the vector force for Q>0, so F and E are in the

= Q E The charge can be stationary or moving VDO 62: force on a

magnetic field Duration: 0:55 min https://youtu.

moving charge 7 Recall that the direction of v B to the

magnetic flux density A charge Q (+ or ) v The force exerted by

2 Recall that an electric field exerts a force on charges 5 Moving charges in magnetic field experience a force 6 This picture shows the vector force for Q>0, so F and E are in the same direction E Electric field intensity A charge Q (+ or ) F = Q E The charge can be stationary or moving VDO 62: force on a current-carrying wire under the magnetic field Duration: 0:36 min VDO 136: Force acting on moving changes in the magnetic field Duration: 0:55 min A magnetic field, however, exerts a force on a moving charge 7 Recall that the direction of v B to the right-hand rule 8 is according B v (velocity of the charge) v B magnetic flux density A charge Q (+ or ) v The force exerted by the magnetic field on a moving charge is B F = Qv B VDO 64: cross product of v and B Duration: 1:07 min (trimmed 0:00-1:12)

For example, the direction of force will be as follows (continued) 9 10 a

2v B F v B จ ดจะเคล อนท อย างไร เม อเล อนแม เหล กเข าหาม น?

0:16-0:56) be/18-qdfolbvk จ ด = ตำแหน งท อ เล กตรอนเคล อนท ออกจากจอ v B

3 For example, the direction of force will be as follows (continued) 9 10 a positive charge Q=2C = F v + 2v B B v a negative charge Q = 2 C v B B = 2v B F v B จ ดจะเคล อนท อย างไร เม อเล อนแม เหล กเข าหาม น? (VDO titles: Magnetic force on moving electrons) (continued) จ ดจะเคล อนท อย างไร เม อเล อนแม เหล กเข าหาม น? v B VDO 138: Question (90 ) Duration: 0:19 min (trim 0:00-0:19) S N VDO 139: Answer (90 ) Duration: 0:40 min (trim 0:16-0:56) จ ด = ตำแหน งท อ เล กตรอนเคล อนท ออกจากจอ v B (ก) ข น (จ) อย ท เด ม (ค) ลง (ข) ขวา (ง) ซ าย (ข) ขวา (ง) ซ าย (ก) ข น (จ) อย ท เด ม (ค) ลง VDO 139: Answer (180 ) Duration: 0:25 min (trim 1:16-2:21)

be/slmv2illuam The above is known as Lorentz force equation A current-carrying wire in a magnetic field experience force (cont d) Which direction the wire will move?

4 VDO 56: Motion of charge in magnetic field (circular and helix) 13 The force on a moving charge under both electric field and magnetic field is a sum v (velocity of the charge) B E A charge Q (+ or ) of forces exerted by each field F = Q( E + v B) Duration: 1:34 min The above is known as Lorentz force equation A current-carrying wire in a magnetic field experience force (cont d) Which direction the wire will move? uniform B S I L B + V L N Current is a flow of electrons Force on a straight wire in a uniform F = I L B current vector that points in the direction of current and has the magnitude of the wire length B is (a) (b) Inward into the screen Outward from the screen VDO 185: force on a wire Duration: 0:45 min (trimmed 0:03 0:48 min) At 0.18 min, the flow of electricity means the flow of current

(cont d) When the current flows in the opposite direction, the direction of force is reversed 17 The force serves to rotate a loop in a DC motor 18 S B L N VDO 185: force on a

be/xi7o8cmpi0e Magnetic Materials 19 MAGNETIZATION PERMEABILITY THE NATURE OF MAGNETIC MATERIALS Q Under an influence of an external magnetic field, how does a material such as

5 (cont d) When the current flows in the opposite direction, the direction of force is reversed 17 The force serves to rotate a loop in a DC motor 18 S B L N VDO 185: force on a wire (another direction of current) Duration: 0:35 min (trimmed 0:45 1:20 min) VDO 119: Simple DC motor circuit Duration: 0:20 min Magnetic Materials 19 MAGNETIZATION PERMEABILITY THE NATURE OF MAGNETIC MATERIALS Q Under an influence of an external magnetic field, how does a material such as iron become magnet? A A material becomes magnet because their dipole moments align approximately in one direction. In the following slides, we will explain this answer in detail. 20

In a simple model, an electron moves in orbit of the nucleus and spins around itself 21 Orbital movement and spin of electrons are analogous to movements of charges 22 orbiting electron spinning

which causes magnetism or dipole moments Orbital movement causes the orbital dipole moment Spinning causes the spin dipole moment A magnetic domain is a small region where the dipole moments point in

6 In a simple model, an electron moves in orbit of the nucleus and spins around itself 21 Orbital movement and spin of electrons are analogous to movements of charges 22 orbiting electron spinning electron orbiting electron =) orbital dipole moment spinning electron =) spin dipole moment electron electron nucleus nucleus Similar to the earth, which moves around the sun and spins around itself which causes magnetism or dipole moments Orbital movement causes the orbital dipole moment Spinning causes the spin dipole moment A magnetic domain is a small region where the dipole moments point in the same direction Magnetic domains can be seen visually by the Kerr microscopy technique A magnetic domain a dipole moment (vector) due to an orbital or a spinning electron Each magnetic domain has the size of around 10-6 m A piece of magnetic materials such as magnets may have millions of magnetic domains

Each domain has the net dipole moment or the vector sum of all dipole moments in the domain In magnetic materials, net moments will align in the

domains under no external magnetic field H Magnetic domains under the magnetic field VDOs: Magnetic domains under the external magnetic field

be/qgwredkpq6e These VDOs do not consider an effect known as the hysteresis effect.

In a material, magnetization (a vector) appears in a relationship of B and H.

7 Each domain has the net dipole moment or the vector sum of all dipole moments in the domain In magnetic materials, net moments will align in the same direction if we apply an external magnetic field 25 a piece of iron 26 Streamlines of H the net dipole moment in a magnetic domain Magnetic domains under no external magnetic field H Magnetic domains under the magnetic field VDOs: Magnetic domains under the external magnetic field VDO 25: demonstration Duration: 1:15 min 27 VDO 142: animation Duration: 0:52 min (trim 0:10 to 1:02) These VDOs do not consider an effect known as the hysteresis effect. The purpose of this VDOs is to illustrate a basic concept of magnetized domains. In a material, magnetization (a vector) appears in a relationship of B and H. dipole moment in a domain free space (vacuum) a material H 28 Recall: in free space (vacuum), we have a relationship B = µ 0 H (free space) Magnetic flux density Magnetic field intensity In a material (such iron), the relationship is B = µ 0 ( H + M) (generic material) Magnetization (the vector sum of all the magnetic dipole moments)

8 The magnetization M is proportional to the magnetic field intensity H, i.e., M = m H. 29 Materials are divided into 3 groups according to the basis of their magnetic susceptibilities 30 material s magnetic susceptibility (no unit, dimensionless) gold water vacuum air aluminum cobalt iron (99.96% pure) Magnetic susceptibility of various materials Source: (p. 137, S. M. Wenthworth, 2005) m measures how well the dipole moments align themselves under an external magnetic field Positive value = dipole moments align with the external field Zero = dipole moments do not align with the external field Negative =dipole moments in the opposite direction of the external field paramagnetic materials: gold water air aluminum cobalt iron (99.96% pure) diamagnetic materials: ferromagnetic materials: Their m s are negative Their m s are positive Their m s are positive and small and large The relationship between B and. in a material is then... H B = µ 0 (1 + m ) H 31 Inductance = µ 0 µ r H = µ H 32 INDUCTORS relative permeability: µ r =(1+ m ) permeability: µ = µ r µ 0 INDUCTANCE OF A SOLENOID

Inductors are common electronic components 33 A simple way to

you wrap the wire in a straight line, you have a solenoid If

definition of inductance (or self-inductance) Definition:

(H) current flowing in the inducting structure (A) Nth turn d

9 Inductors are common electronic components 33 A simple way to make an inductor is to wrap a wire tightly in circles 34 If you wrap the wire in a straight line, you have a solenoid If you wrap the wire as a donut, you have a toroid Here is the definition of inductance (or self-inductance) Definition: Inductance is the ratio of two terms: 35 Inductance of a solenoid is st turn magnetic flux linkage (Wb) L = I Inductance (H) current flowing in the inducting structure (A) Nth turn d permeability of the material at the core L = µn 2 S d N = Number of turns cross-section area of the core length of the solenoid

10 Inductor stores magnetic energy 37 Inductance L current I The magnetic energy stored in an inductor is W H = 1 2 LI2 Here are new symbols in this lecture Symbol Name Unit Abbreviation v M L m µ r µ W H 38 v velocity meter/second m/s magnetization ampere/meter A/m magnetic susceptibility - - relative permeability - - permeability henry/meter H/m inductance henry H magnetic flux linkage weber Wb magnetic energy joule J Summary Magnetic forces Lorentz force equation Review of cross product Force on a straight current-carrying wire Magnetic materials Magnetization Relative permeability Permeability Inductance Definition Inductance of a solenoid Magnetic energy stored in an inductor 39

Physics 202, Lecture 14

Physics 202, Lecture 14 Today s Topics Sources of the Magnetic Field (Ch. 27) Review of Biot-Savart Law Ampere s Law Magnetism in Matter Magnetic Fields (Biot-Savart): Summary Current loop, distance on