Juan Alberto Garcia the University of Texas at El Paso

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Juan Alberto Garcia The University of Texas at El Paso Is that all there is about E&M then??? F*@# no!! Electricity and Magnetism… no more! Electromagnetism!! • Hans Christian Ørsted ‐ Professor at Copenhagen ‐ Discovered (in 1820) one connection!! ‐ This one ‐ Well actually.. • One problem… he didn’t follow his experiment, but he published it tough. ! =D • Meanwhile in the Faraday world.. Devy kept Faraday performing tasks that were not desired by him.. • 1821 Ampère published his research…. Ampère • Force between two wires with electricity • They attract or repel each other .. Depending on the direction of the current!! • Led to the foundation of Electrodynamics • It was not until 1831 that Faraday finally started working in E&M and explained… • .. • Induction!!!! But First!!, Flux • Magnetic Flux A A B B Induction • Explained by Faraday! (this guy) • That is faraday’s law… well the easy form.. • It means the following…. • Well this is better… Lenz’s Law • Corollary of Faraday’s Law and Ohm’s Law • The emf induced in an electric circuit always acts in such a direction that the current it drives around the circuit opposes the change in magnetic flux which produces the emf. Maxwell • And then.. There was Maxwell • On Physical Lines of Force, March 1861 , Published 20 equations with 20 variables which were a compilation of what was know at the time. • Then on A Treatise on Electricity and Magnetism in 1873 he published what are known as the Maxwell’s Equations. Maxwell’s Equations • 4 PDE’s that describe the “Fields.” • They are in descending order (in free space): • Gauss’s law for E‐fields • Gauss’s law for B‐fields • Faraday’s Law • Ampère’s Law And then, there was light… • Turns out Maxwell’s Equations describe fields that Oscillate through space. • Furthermore he calculated the speed of this waves to be…. • 310,740,000 m/s • Can anyone tell me what speed is this?? • Not quite .. There were experimental and numerical errors at the time, the actual value is 299,792,458 m/s .. The speed of light!! The speed of light • This led to the work of .. • That’s another talk.. ☺ Enough.. For now. • The Motor • And some other cool stuff....

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Electro Magnetic Fields Lecture Notes B.Tech
ELECTRO MAGNETIC FIELDS LECTURE NOTES B.TECH (II YEAR – I SEM) (2019-20) Prepared by: M.KUMARA SWAMY., Asst.Prof Department of Electrical & Electronics Engineering MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY (Autonomous Institution – UGC, Govt. of India) Recognized under 2(f) and 12 (B) of UGC ACT 1956 (Affiliated to JNTUH, Hyderabad, Approved by AICTE - Accredited by NBA & NAAC – ‘A’ Grade - ISO 9001:2015 Certified) Maisammaguda, Dhulapally (Post Via. Kompally), Secunderabad – 500100, Telangana State, India ELECTRO MAGNETIC FIELDS Objectives: • To introduce the concepts of electric field, magnetic field. • Applications of electric and magnetic fields in the development of the theory for power transmission lines and electrical machines. UNIT – I Electrostatics: Electrostatic Fields – Coulomb’s Law – Electric Field Intensity (EFI) – EFI due to a line and a surface charge – Work done in moving a point charge in an electrostatic field – Electric Potential – Properties of potential function – Potential gradient – Gauss’s law – Application of Gauss’s Law – Maxwell’s first law, div ( D )=ρv – Laplace’s and Poison’s equations . Electric dipole – Dipole moment – potential and EFI due to an electric dipole. UNIT – II Dielectrics & Capacitance: Behavior of conductors in an electric field – Conductors and Insulators – Electric field inside a dielectric material – polarization – Dielectric – Conductor and Dielectric – Dielectric boundary conditions – Capacitance – Capacitance of parallel plates – spherical co‐axial capacitors. Current density – conduction and Convection current densities – Ohm’s law in point form – Equation of continuity UNIT – III Magneto Statics: Static magnetic fields – Biot‐Savart’s law – Magnetic field intensity (MFI) – MFI due to a straight current carrying filament – MFI due to circular, square and solenoid current Carrying wire – Relation between magnetic flux and magnetic flux density – Maxwell’s second Equation, div(B)=0, Ampere’s Law & Applications: Ampere’s circuital law and its applications viz.
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Magnetism Known to the Early Chinese in 12Th Century, and In
Magnetism Known to the early Chinese in 12th century, and in some detail by ancient Greeks who observed that certain stones “lodestones” attracted pieces of iron. Lodestones were found in the coastal area of “Magnesia” in Thessaly at the beginning of the modern era. The name of magnetism derives from magnesia. William Gilbert, physician to Elizabeth 1, made magnets by rubbing Fe against lodestones and was first to recognize the Earth was a large magnet and that lodestones always pointed north-south. Hence the use of magnetic compasses. Book “De Magnete” 1600. The English word "electricity" was first used in 1646 by Sir Thomas Browne, derived from Gilbert's 1600 New Latin electricus, meaning "like amber". Gilbert demonstrates a “lodestone” compass to ER 1. Painting by Auckland Hunt. John Mitchell (1750) found that like electric forces magnetic forces decrease with separation (conformed by Coulomb). Link between electricity and magnetism discovered by Hans Christian Oersted (1820) who noted a wire carrying an electric current affected a magnetic compass. Conformed by Andre Marie Ampere who shoes electric currents were source of magnetic phenomena. Force fields emanating from a bar magnet, showing Nth and Sth poles (credit: Justscience 2017) Showing magnetic force fields with Fe filings (Wikipedia.org.) Earth’s magnetic field (protects from damaging charged particles emanating from sun. (Credit: livescience.com) Magnetic field around wire carrying a current (stackexchnage.com) Right hand rule gives the right sign of the force (stackexchnage.com) Magnetic field generated by a solenoid (miniphyiscs.com) Van Allen radiation belts. Energetic charged particles travel along B lines Electric currents (moving charges) generate magnetic fields but can magnetic fields generate electric currents.
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F = BIL (F=Force, B=Magnetic Field, I=Current, L=Length of Conductor)
Magnetism Joanna Radov Vocab: -Armature- is the power producing part of a motor -Domain- is a region in which the magnetic field of atoms are grouped together and aligned -Electric Motor- converts electrical energy into mechanical energy -Electromagnet- is a type of magnet whose magnetic field is produced by an electric current -First Right-Hand Rule (delete) -Fixed Magnet- is an object made from a magnetic material and creates a persistent magnetic field -Galvanometer- type of ammeter- detects and measures electric current -Magnetic Field- is a field of force produced by moving electric charges, by electric fields that vary in time, and by the 'intrinsic' magnetic field of elementary particles associated with the spin of the particle. -Magnetic Flux- is a measure of the amount of magnetic B field passing through a given surface -Polarized- when a magnet is permanently charged -Second Hand-Right Rule- (delete) -Solenoid- is a coil wound into a tightly packed helix -Third Right-Hand Rule- (delete) Major Points: -Similar magnetic poles repel each other, whereas opposite poles attract each other -Magnets exert a force on current-carrying wires -An electric charge produces an electric field in the region of space around the charge and that this field exerts a force on other electric charges placed in the field -The source of a magnetic field is moving charge, and the effect of a magnetic field is to exert a force on other moving charge placed in the field -The magnetic field is a vector quantity -We denote the magnetic field by the symbol B and represent it graphically by field lines -These lines are drawn ⊥ to their entry and exit points -They travel from N to S -If a stationary test charge is placed in a magnetic field, then the charge experiences no force.
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Magnetic Flux and Flux Linkage
Magnetic Flux and Flux Linkage To be able to calculate and explain the magnetic flux through a coil of wire To be able to calculate the magnetic flux linkage of a coil of wire To be able to calculate the magnetic flux linkage of a rotating coil Magnetic Flux, Magnetic flux is a measure of how many magnetic field lines are passing through an area of A m2. The magnetic flux through an area A in a magnetic field of flux density B is given by: BA This is when B is perpendicular to A, so the normal to the area is in the same direction as the field lines. Magnetic Flux is measured in Webers, Wb The more field pass through area A, the greater the concentration and the stronger magnetic field. This is why a magnet is strongest at its poles; there is a high concentration of field lines. We can see that the amount of flux flowing through a loop of wire depends on the angle it makes with the field lines. The amount of flux passing through the loop is given by: θ is the angle that the normal to the loop makes with the field lines. Magnetic Flux Density We can now see why B is called the magnetic flux density. If we rearrange the top equation for B we get: B So B is a measure of how many flux lines (field lines) passes through each unit area (per m2). A A flux density of 1 Tesla is when an area of 1 metre squared has a flux of 1 Weber.
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Lecture 8: Magnets and Magnetism Magnets
Lecture 8: Magnets and Magnetism Magnets •Materials that attract other metals •Three classes: natural, artificial and electromagnets •Permanent or Temporary •CRITICAL to electric systems: – Generation of electricity – Operation of motors – Operation of relays Magnets •Laws of magnetic attraction and repulsion –Like magnetic poles repel each other –Unlike magnetic poles attract each other –Closer together, greater the force Magnetic Fields and Forces •Magnetic lines of force – Lines indicating magnetic field – Direction from N to S – Density indicates strength •Magnetic field is region where force exists Magnetic Theories Molecular theory of magnetism Magnets can be split into two magnets Magnetic Theories Molecular theory of magnetism Split down to molecular level When unmagnetized, randomness, fields cancel When magnetized, order, fields combine Magnetic Theories Electron theory of magnetism •Electrons spin as they orbit (similar to earth) •Spin produces magnetic field •Magnetic direction depends on direction of rotation •Non-magnets → equal number of electrons spinning in opposite direction •Magnets → more spin one way than other Electromagnetism •Movement of electric charge induces magnetic field •Strength of magnetic field increases as current increases and vice versa Right Hand Rule (Conductor) •Determines direction of magnetic field •Imagine grasping conductor with right hand •Thumb in direction of current flow (not electron flow) •Fingers curl in the direction of magnetic field DO NOT USE LEFT HAND RULE IN BOOK Example Draw magnetic field lines around conduction path E (V) R Another Example •Draw magnetic field lines around conductors Conductor Conductor current into page current out of page Conductor coils •Single conductor not very useful •Multiple winds of a conductor required for most applications, – e.g.
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Ee334lect37summaryelectroma
EE334 Electromagnetic Theory I Todd Kaiser Maxwell’s Equations: Maxwell’s equations were developed on experimental evidence and have been found to govern all classical electromagnetic phenomena. They can be written in differential or integral form. r r r Gauss'sLaw ∇ ⋅ D = ρ D ⋅ dS = ρ dv = Q ∫∫ enclosed SV r r r Nomagneticmonopoles ∇ ⋅ B = 0 ∫ B ⋅ dS = 0 S r r ∂B r r ∂ r r Faraday'sLaw ∇× E = − E ⋅ dl = − B ⋅ dS ∫∫S ∂t C ∂t r r r ∂D r r r r ∂ r r Modified Ampere'sLaw ∇× H = J + H ⋅ dl = J ⋅ dS + D ⋅ dS ∫ ∫∫SS ∂t C ∂t where: E = Electric Field Intensity (V/m) D = Electric Flux Density (C/m2) H = Magnetic Field Intensity (A/m) B = Magnetic Flux Density (T) J = Electric Current Density (A/m2) ρ = Electric Charge Density (C/m3) The Continuity Equation for current is consistent with Maxwell’s Equations and the conservation of charge. It can be used to derive Kirchhoff’s Current Law: r ∂ρ ∂ρ r ∇ ⋅ J + = 0 if = 0 ∇ ⋅ J = 0 implies KCL ∂t ∂t Constitutive Relationships: The field intensities and flux densities are related by using the constitutive equations. In general, the permittivity (ε) and the permeability (µ) are tensors (different values in different directions) and are functions of the material. In simple materials they are scalars. r r r r D = ε E ⇒ D = ε rε 0 E r r r r B = µ H ⇒ B = µ r µ0 H where: εr = Relative permittivity ε0 = Vacuum permittivity µr = Relative permeability µ0 = Vacuum permeability Boundary Conditions: At abrupt interfaces between different materials the following conditions hold: r r r r nˆ × (E1 − E2 )= 0 nˆ ⋅(D1 − D2 )= ρ S r r r r r nˆ × ()H1 − H 2 = J S nˆ ⋅ ()B1 − B2 = 0 where: n is the normal vector from region-2 to region-1 Js is the surface current density (A/m) 2 ρs is the surface charge density (C/m ) 1 Electrostatic Fields: When there are no time dependent fields, electric and magnetic fields can exist as independent fields.
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Physics, Chapter 32: Electromagnetic Induction
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 32: Electromagnetic Induction Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 32: Electromagnetic Induction" (1958). Robert Katz Publications. 186. https://digitalcommons.unl.edu/physicskatz/186 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 32 Electromagnetic Induction 32-1 Motion of a Wire in a Magnetic Field When a wire moves through a uniform magnetic field of induction B, in a direction at right angles to the field and to the wire itself, the electric charges within the conductor experience forces due to their motion through this magnetic field. The positive charges are held in place in the conductor by the action of interatomic forces, but the free electrons, usually one or two per atom, are caused to drift to one side of the conductor, thus setting up an electric field E within the conductor which opposes the further drift of electrons. The magnitude of this electric field E may be calculated by equating the force it exerts on a charge q, to the force on this charge due to its motion through the magnetic field of induction B; thus Eq = Bqv, from which E = Bv.
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Teacher Notes Science Nspired
The Magnetic Field of a Coil TEACHER NOTES SCIENCE NSPIRED Science Objectives Students will understand the relationship between magnetic flux density and the strength of the electrical current. Students will determine the value of the magnetic constant. Vocabulary Magnetic flux density Electric Current TI-Nspire™ Technology Skills: Download a TI-Nspire About the Lesson document This lesson demonstrates the proportional relationship between Open a document the magnetic flux density at the center of a long, electrically Move between pages charged coil and the strength of the electrical current. This is a Collect data using probe more advanced experiment for high school students. As a result, students will: Tech Tip: Create a closed circuit Access free tutorials at Determine a relationship from a graph. http://education.ti.com/calculator Calculate the value for the magnetic constant. s/pd/US/Online- Calculate percent error of the experimental value from the Learning/Tutorials given true value. Lesson Files: Student Activity TI-Nspire™ Navigator™ Magnetic_Field_of_a_Coil_St udent.doc Send out the .tns file. Magnetic_Field_of_a_Coil_St Monitor student progress using Class Capture. udent.pdf Use Live Presenter to spotlight student answers. TI-Nspire document Enter items as appropriate for use of TI-Navigator. Magnetic_Field_of_a_Coil.tns Activity Materials Magnetic_Field_of_a_Coil.tns document TI-Nspire™ Technology Magnetic Field Sensor Data Collection Interface (i.e., EasyLink) Coil with 1,000 turns Ammeter (moving coil rectifier) Low-voltage power supply ©2013 Texas Instruments Incorporated 1 education.ti.com The Magnetic Field of a Coil TEACHER NOTES SCIENCE NSPIRED Discussion Points and Possible Answers Move to pages 1.2 – 1.4. Have students answer questions 1 - 2 on the handheld, the activity sheet, or both.
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Chapter 23 Magnetic Flux and Faraday's Law of Induction
Chapter 23 Magnetic Flux and Faraday’s Law of Induction 23.1 Induced EMF 23.2 Magnetic Flux 23.3 Faraday’s Law of Induction 23.4 Lenz’s Law 23.5 Mechanical Work and Electrical Energy 23.6 Generators and Motors 23.7 Inductance 23.9 Energy Stored in a Magnetic Field 23.10 Transformers 1 Current electricity produces Magnetic fields, So can 2 Magnetic fields produce electricity? 1 Oersted, 1820 2 Faraday, 1931 Faradays discoveries are the basis of our modern electrical civilization. Faraday (and Henry) noticed that a MOVING magnet near a wire loop caused a blip on his galvanometer. Figure 23–1 Magnetic induction ! Basic setup of Faraday’s experiment on magnetic induction. When the position of the switch on the primary circuit is changed from open to closed or from closed to open, an emf is induced in the secondary circuit. The induced emf causes a current in the secondary circuit, and the current is detected by the ammeter. If the current in the primary circuit does not change, no matter how large it may be, there is no induced current in the secondary circuit. Figure 23–2 Induced current produced by a moving magnet ! A coil experiences an induced current when the magnetic field passing through it varies. (a) When the magnet moves toward the coil the current is in one direction. (b) No current is induced while the magnet is held still. (c) When the magnet is pulled away from the coil the current is in the other direction. Also, changing the shape of a loop in or relative to a magnetic field would cause a blip on an ammeter.
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Maxwell's Equations for Magnetostatics
11/14/2004 Maxwells equations for magnetostatics.doc 1/4 Maxwell’s Equations for Magnetostatics From the point form of Maxwell’s equations, we find that the static case reduces to another (in addition to electrostatics) pair of coupled differential equations involving magnetic flux density B ()r and current density J (r ): ∇ ⋅=BBJ()r 0 ∇x( r) =µ0 ( r ) Recall from the Lorentz force equation that the magnetic flux density B ()r will apply a force on current density J ()r flowing in volume dv equal to: dF= ( J(rx) B ( r))dv Current density J ()r is of course expressed in units of Amps/meter2. The units of magnetic flux density B ()r are: Newton⋅ seconds Weber Tesla Coulomb⋅ meter meter2 Jim Stiles The Univ. of Kansas Dept. of EECS 11/14/2004 Maxwells equations for magnetostatics.doc 2/4 * Recall the units for electric flux density D (r ) are Colombs/m2. Compare this to the units for magnetic flux density—Webers/m2. * We can say therefore that the units of electric flux are Coulombs, whereas the units of magnetic flux are Webers. * The concept of magnetic flux is much more important and useful than the concept of electric flux, as there is no such thing as magnetic charge. We will talk much more later about the concept of magnetic flux! Now, let us consider specifically the two magnetostatic equations. * First, we note that they specify both the divergence and curl of magnetic flux density B (r ), thus completely specifying this vector field. * Second, it is apparent that the magnetic flux density B (r ) is not conservative (i.e,∇=xrBJ( ) µ0 ( r) ≠ 0).
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Magnetic Fields
Experiment 3: Magnetic Fields Nate Saffold [email protected] Office Hour: Mondays, 5:30PM-6:30PM @ Pupin 1216 INTRO TO EXPERIMENTAL PHYS-LAB 1494/2699 Outline ● Today we will deal with magnetic fields only ● The physics of interest to understand the experiment is: ● Interplay between electric currents and magnetic fields: ❖ Currents experience magnetic force (Lorentz law) ❖ Current generate magnetic fields (Biot-Savart law) ● The experiment will be mainly focused on: ● Determining the magnetic field of an electromagnet using the Lorentz force ● Study the induced e.m.f. of a magnetic field through a coil of known geometry PHYS 1493/1494/2699: Exp. 3 – Magnetic Fields 3 Magnetic fields ● What creates a magnetic field? Answer: Moving charges! ● Question: How do we define the magnetic field? ● While the electric field has a nice definition that only involves its sources ( ), this is not the case for magnetic fields ● They can only be defined operatively through the force they exert on a moving charge (Lorentz force): ● Right-hand rule: Given a charge q moving with velocity v, the magnetic field is whatever we have to plug into this equation to find the right magnitude and direction of the exerted force PHYS 1493/1494/2699: Exp. 3 – Magnetic Fields 4 Lorentz Force ● From the previous slide, a charged particle entering a magnetic field with some velocity will feel a Lorentz force: Symbol for field directed into the plane PHYS 1493/1494/2699: Exp. 3 – Magnetic Fields 5 Lorentz Force ● From the previous slide, a charged particle entering a magnetic field with some velocity will feel a Lorentz force: Symbol for field directed into the plane PHYS 1493/1494/2699: Exp.
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1 Induction Experiments 2 Magnetic Flux 3 Faraday's
Physics 1214 | Chapter 21: Electromagnetic Induction | 02/15 1 Induction Experiments emf or electromotive force: (from Chapter 19) the influence that moves charge from lower to higher potential. induced current: changing magnetic field causing a current in a circuit. induced emf : the emf that is present to cause a current. 2 Magnetic Flux Magnetic flux through a plane surface in a constant magnetic field For a plane surface with area A in a uniform magnetic field B~ , both B? and φ are the same at all points on the surface. The magnetic flux ΦB through the surface is ΦB = B?A = BA cos φ. If B~ happens to be perpendicular to the surface, then cos φ = 1 and the previous equation reduces to ΦB = BA: Unit: The SI unit magnetic flux is the unit magnetic field (1 T) times the unit of area (1 m2): (1 T)(1 m2) =[1 N/(A · m)](1 m2)= 1 N · m/A. This unit is call 1 weber (1 Wb). 1 weber = 1 Wb = 1 T · m2 = 1 N · m/A. magnetic flux density ∆Φ B = B ∆A 1 T = 1 Wb/m2 3 Faraday's Law The common element in ALL induction effects is changing magnetic flux through a circuit. Faraday's law of induction The magnitude of the induced emf in a circuit equals the absolute value of the time rate of change of the magnetic flux through the circuit. In symbols, Faraday's law is ∆ΦB E = : ∆t In this definition, E is the magnitude of the emf and is always positive.
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