Electromagnetism Laws and Equations
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Charges and Fields of a Conductor • in Electrostatic Equilibrium, Free Charges Inside a Conductor Do Not Move
Charges and fields of a conductor • In electrostatic equilibrium, free charges inside a conductor do not move. Thus, E = 0 everywhere in the interior of a conductor. • Since E = 0 inside, there are no net charges anywhere in the interior. Net charges can only be on the surface(s). The electric field must be perpendicular to the surface just outside a conductor, since, otherwise, there would be currents flowing along the surface. Gauss’s Law: Qualitative Statement . Form any closed surface around charges . Count the number of electric field lines coming through the surface, those outward as positive and inward as negative. Then the net number of lines is proportional to the net charges enclosed in the surface. Uniformly charged conductor shell: Inside E = 0 inside • By symmetry, the electric field must only depend on r and is along a radial line everywhere. • Apply Gauss’s law to the blue surface , we get E = 0. •The charge on the inner surface of the conductor must also be zero since E = 0 inside a conductor. Discontinuity in E 5A-12 Gauss' Law: Charge Within a Conductor 5A-12 Gauss' Law: Charge Within a Conductor Electric Potential Energy and Electric Potential • The electrostatic force is a conservative force, which means we can define an electrostatic potential energy. – We can therefore define electric potential or voltage. .Two parallel metal plates containing equal but opposite charges produce a uniform electric field between the plates. .This arrangement is an example of a capacitor, a device to store charge. • A positive test charge placed in the uniform electric field will experience an electrostatic force in the direction of the electric field. -
Electrostatics Voltage Source
012-07038B Instruction Sheet for the PASCO Model ES-9077 ELECTROSTATICS VOLTAGE SOURCE Specifications Ranges: • Fixed 1000, 2000, 3000 VDC ±10%, unregulated (maximum short circuit current less than 0.01 mA). • 30 VDC ±5%, 1mA max. Power: • 110-130 VDC, 60 Hz, ES-9077 • 220/240 VDC, 50 Hz, ES-9077-220 Dimensions: Introduction • 5 1/2” X 5” X 1”, plus AC adapter and red/black The ES-9077 is a high voltage, low current power cable set supply designed exclusively for experiments in electrostatics. It has outputs at 30 volts DC for IMPORTANT: To prevent the risk of capacitor plate experiments, and fixed 1 kV, 2 kV, and electric shock, do not remove the cover 3 kV outputs for Faraday ice pail and conducting on the unit. There are no user sphere experiments. With the exception of the 30 volt serviceable parts inside. Refer servicing output, all of the voltage outputs have a series to qualified service personnel. resistance associated with them which limit the available short-circuit output current to about 8.3 microamps. The 30 volt output is regulated but is Operation capable of delivering only about 1 milliamp before When using the Electrostatics Voltage Source to power falling out of regulation. other electric circuits, (like RC networks), use only the 30V output (Remember that the maximum drain is 1 Equipment Included: mA.). • Voltage Source Use the special high-voltage leads that are supplied with • Red/black, banana plug to spade lug cable the ES-9077 to make connections. Use of other leads • 9 VDC power supply may allow significant leakage from the leads to ground and negatively affect output voltage accuracy. -
New Realization of the Ohm and Farad Using the NBS Calculable Capacitor
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 38, NO. 2, APRIL 1989 249 New Realization of the Ohm and Farad Using the NBS Calculable Capacitor JOHN Q. SHIELDS, RONALD F. DZIUBA, MEMBER, IEEE,AND HOWARD P. LAYER Abstrucl-Results of a new realization of the ohm and farad using part of the NBS effort. This paper describes our measure- the NBS calculable capacitor and associated apparatus are reported. ments and gives our latest results. The results show that both the NBS representation of the ohm and the NBS representation of the farad are changing with time, cNBSat the rate of -0.054 ppmlyear and FNssat the rate of 0.010 ppm/year. The 11. AC MEASUREMENTS realization of the ohm is of particular significance at this time because The measurement sequence used in the 1974 ohm and of its role in assigning an SI value to the quantized Hall resistance. The farad determinations [2] has been retained in the present estimated uncertainty of the ohm realization is 0.022 ppm (lo) while the estimated uncertainty of the farad realization is 0.014 ppm (la). NBS measurements. A 0.5-pF calculable cross-capacitor is used to measure a transportable 10-pF reference capac- itor which is carried to the laboratory containing the NBS I. INTRODUCTION bank of 10-pF fused silica reference capacitors. A 10: 1 HE NBS REPRESENTATION of the ohm is bridge is used in two stages to measure two 1000-pF ca- T based on the mean resistance of five Thomas-type pacitors which are in turn used as two arms of a special wire-wound resistors maintained in a 25°C oil bath at NBS frequency-dependent bridge for measuring two 100-kQ Gaithersburg, MD. -
Electromagnetism What Is the Effect of the Number of Windings of Wire on the Strength of an Electromagnet?
TEACHER’S GUIDE Electromagnetism What is the effect of the number of windings of wire on the strength of an electromagnet? GRADES 6–8 Physical Science INQUIRY-BASED Science Electromagnetism Physical Grade Level/ 6–8/Physical Science Content Lesson Summary In this lesson students learn how to make an electromagnet out of a battery, nail, and wire. The students explore and then explain how the number of turns of wire affects the strength of an electromagnet. Estimated Time 2, 45-minute class periods Materials D cell batteries, common nails (20D), speaker wire (18 gauge), compass, package of wire brad nails (1.0 mm x 12.7 mm or similar size), Investigation Plan, journal Secondary How Stuff Works: How Electromagnets Work Resources Jefferson Lab: What is an electromagnet? YouTube: Electromagnet - Explained YouTube: Electromagnets - How can electricity create a magnet? NGSS Connection MS-PS2-3 Ask questions about data to determine the factors that affect the strength of electric and magnetic forces. Learning Objectives • Students will frame a hypothesis to predict the strength of an electromagnet due to changes in the number of windings. • Students will collect and analyze data to determine how the number of windings affects the strength of an electromagnet. What is the effect of the number of windings of wire on the strength of an electromagnet? Electromagnetism is one of the four fundamental forces of the universe that we rely on in many ways throughout our day. Most home appliances contain electromagnets that power motors. Particle accelerators, like CERN’s Large Hadron Collider, use electromagnets to control the speed and direction of these speedy particles. -
The Lorentz Force
CLASSICAL CONCEPT REVIEW 14 The Lorentz Force We can find empirically that a particle with mass m and electric charge q in an elec- tric field E experiences a force FE given by FE = q E LF-1 It is apparent from Equation LF-1 that, if q is a positive charge (e.g., a proton), FE is parallel to, that is, in the direction of E and if q is a negative charge (e.g., an electron), FE is antiparallel to, that is, opposite to the direction of E (see Figure LF-1). A posi- tive charge moving parallel to E or a negative charge moving antiparallel to E is, in the absence of other forces of significance, accelerated according to Newton’s second law: q F q E m a a E LF-2 E = = 1 = m Equation LF-2 is, of course, not relativistically correct. The relativistically correct force is given by d g mu u2 -3 2 du u2 -3 2 FE = q E = = m 1 - = m 1 - a LF-3 dt c2 > dt c2 > 1 2 a b a b 3 Classically, for example, suppose a proton initially moving at v0 = 10 m s enters a region of uniform electric field of magnitude E = 500 V m antiparallel to the direction of E (see Figure LF-2a). How far does it travel before coming (instanta> - neously) to rest? From Equation LF-2 the acceleration slowing the proton> is q 1.60 * 10-19 C 500 V m a = - E = - = -4.79 * 1010 m s2 m 1.67 * 10-27 kg 1 2 1 > 2 E > The distance Dx traveled by the proton until it comes to rest with vf 0 is given by FE • –q +q • FE 2 2 3 2 vf - v0 0 - 10 m s Dx = = 2a 2 4.79 1010 m s2 - 1* > 2 1 > 2 Dx 1.04 10-5 m 1.04 10-3 cm Ϸ 0.01 mm = * = * LF-1 A positively charged particle in an electric field experiences a If the same proton is injected into the field perpendicular to E (or at some angle force in the direction of the field. -
Quantum Mechanics Electromotive Force
Quantum Mechanics_Electromotive force . Electromotive force, also called emf[1] (denoted and measured in volts), is the voltage developed by any source of electrical energy such as a batteryor dynamo.[2] The word "force" in this case is not used to mean mechanical force, measured in newtons, but a potential, or energy per unit of charge, measured involts. In electromagnetic induction, emf can be defined around a closed loop as the electromagnetic workthat would be transferred to a unit of charge if it travels once around that loop.[3] (While the charge travels around the loop, it can simultaneously lose the energy via resistance into thermal energy.) For a time-varying magnetic flux impinging a loop, theElectric potential scalar field is not defined due to circulating electric vector field, but nevertheless an emf does work that can be measured as a virtual electric potential around that loop.[4] In a two-terminal device (such as an electrochemical cell or electromagnetic generator), the emf can be measured as the open-circuit potential difference across the two terminals. The potential difference thus created drives current flow if an external circuit is attached to the source of emf. When current flows, however, the potential difference across the terminals is no longer equal to the emf, but will be smaller because of the voltage drop within the device due to its internal resistance. Devices that can provide emf includeelectrochemical cells, thermoelectric devices, solar cells and photodiodes, electrical generators,transformers, and even Van de Graaff generators.[4][5] In nature, emf is generated whenever magnetic field fluctuations occur through a surface. -
Maxwell's Equations
Maxwell’s Equations Matt Hansen May 20, 2004 1 Contents 1 Introduction 3 2 The basics 3 2.1 Static charges . 3 2.2 Moving charges . 4 2.3 Magnetism . 4 2.4 Vector operations . 5 2.5 Calculus . 6 2.6 Flux . 6 3 History 7 4 Maxwell’s Equations 8 4.1 Maxwell’s Equations . 8 4.2 Gauss’ law for electricity . 8 4.3 Gauss’ law for magnetism . 10 4.4 Faraday’s law . 11 4.5 Ampere-Maxwell law . 13 5 Conclusion 14 2 1 Introduction If asked, most people outside a physics department would not be able to identify Maxwell’s equations, nor would they be able to state that they dealt with electricity and magnetism. However, Maxwell’s equations have many very important implications in the life of a modern person, so much so that people use devices that function off the principles in Maxwell’s equations every day without even knowing it. 2 The basics 2.1 Static charges In order to understand Maxwell’s equations, it is necessary to understand some basic things about electricity and magnetism first. Static electricity is easy to understand, in that it is just a charge which, as its name implies, does not move until it is given the chance to “escape” to the ground. Amounts of charge are measured in coulombs, abbreviated C. 1C is an extraordi- nary amount of charge, chosen rather arbitrarily to be the charge carried by 6.41418 · 1018 electrons. The symbol for charge in equations is q, sometimes with a subscript like q1 or qenc. -
Capacitance and Dielectrics Capacitance
Capacitance and Dielectrics Capacitance General Definition: C === q /V Special case for parallel plates: εεε A C === 0 d Potential Energy • I must do work to charge up a capacitor. • This energy is stored in the form of electric potential energy. Q2 • We showed that this is U === 2C • Then we saw that this energy is stored in the electric field, with a volume energy density 1 2 u === 2 εεε0 E Potential difference and Electric field Since potential difference is work per unit charge, b ∆∆∆V === Edx ∫∫∫a For the parallel-plate capacitor E is uniform, so V === Ed Also for parallel-plate case Gauss’s Law gives Q Q εεε0 A E === σσσ /εεε0 === === Vd so C === === εεε0 A V d Spherical example A spherical capacitor has inner radius a = 3mm, outer radius b = 6mm. The charge on the inner sphere is q = 2 C. What is the potential difference? kq From Gauss’s Law or the Shell E === Theorem, the field inside is r 2 From definition of b kq 1 1 V === dr === kq −−− potential difference 2 ∫∫∫a r a b 1 1 1 1 === 9 ×××109 ××× 2 ×××10−−−9 −−− === 18 ×××103 −−− === 3 ×××103 V −−−3 −−−3 3 ×××10 6 ×××10 3 6 What is the capacitance? C === Q /V === 2( C) /(3000V ) === 7.6 ×××10−−−4 F A capacitor has capacitance C = 6 µF and charge Q = 2 nC. If the charge is Q.25-1 increased to 4 nC what will be the new capacitance? (1) 3 µF (2) 6 µF (3) 12 µF (4) 24 µF Q. -
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. -
Transformation Optics for Thermoelectric Flow
J. Phys.: Energy 1 (2019) 025002 https://doi.org/10.1088/2515-7655/ab00bb PAPER Transformation optics for thermoelectric flow OPEN ACCESS Wencong Shi, Troy Stedman and Lilia M Woods1 RECEIVED 8 November 2018 Department of Physics, University of South Florida, Tampa, FL 33620, United States of America 1 Author to whom any correspondence should be addressed. REVISED 17 January 2019 E-mail: [email protected] ACCEPTED FOR PUBLICATION Keywords: thermoelectricity, thermodynamics, metamaterials 22 January 2019 PUBLISHED 17 April 2019 Abstract Original content from this Transformation optics (TO) is a powerful technique for manipulating diffusive transport, such as heat work may be used under fl the terms of the Creative and electricity. While most studies have focused on individual heat and electrical ows, in many Commons Attribution 3.0 situations thermoelectric effects captured via the Seebeck coefficient may need to be considered. Here licence. fi Any further distribution of we apply a uni ed description of TO to thermoelectricity within the framework of thermodynamics this work must maintain and demonstrate that thermoelectric flow can be cloaked, diffused, rotated, or concentrated. attribution to the author(s) and the title of Metamaterial composites using bilayer components with specified transport properties are presented the work, journal citation and DOI. as a means of realizing these effects in practice. The proposed thermoelectric cloak, diffuser, rotator, and concentrator are independent of the particular boundary conditions and can also operate in decoupled electric or heat modes. 1. Introduction Unprecedented opportunities to manipulate electromagnetic fields and various types of transport have been discovered recently by utilizing metamaterials (MMs) capable of achieving cloaking, rotating, and concentrating effects [1–4]. -
Chapter 22 Magnetism
Chapter 22 Magnetism 22.1 The Magnetic Field 22.2 The Magnetic Force on Moving Charges 22.3 The Motion of Charged particles in a Magnetic Field 22.4 The Magnetic Force Exerted on a Current- Carrying Wire 22.5 Loops of Current and Magnetic Torque 22.6 Electric Current, Magnetic Fields, and Ampere’s Law Magnetism – Is this a new force? Bar magnets (compass needle) align themselves in a north-south direction. Poles: Unlike poles attract, like poles repel Magnet has NO effect on an electroscope and is not influenced by gravity Magnets attract only some objects (iron, nickel etc) No magnets ever repel non magnets Magnets have no effect on things like copper or brass Cut a bar magnet-you get two smaller magnets (no magnetic monopoles) Earth is like a huge bar magnet Figure 22–1 The force between two bar magnets (a) Opposite poles attract each other. (b) The force between like poles is repulsive. Figure 22–2 Magnets always have two poles When a bar magnet is broken in half two new poles appear. Each half has both a north pole and a south pole, just like any other bar magnet. Figure 22–4 Magnetic field lines for a bar magnet The field lines are closely spaced near the poles, where the magnetic field B is most intense. In addition, the lines form closed loops that leave at the north pole of the magnet and enter at the south pole. Magnetic Field Lines If a compass is placed in a magnetic field the needle lines up with the field.