Electric Potential
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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. -
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. -
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. -
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions. -
Introduction to Electrical and Computer Engineering International
Introduction to Electrical and Computer Engineering Basic Circuits and Simulation Electrical & Computer Engineering Basic Circuits and Simulation (1 of 22) International System of Units (SI) • Length: meter (m) • SI Prefixes (power of 10) • Mass: kilogram (kg) – 1012 Tera (T) • Time: second (s) – 109 Giga (G) – 106 Mega (M) • Current: Ampere (A) – 103 kilo (k) • Voltage: Volt (V) – 10-3 milli (m) • Temperature: Degrees – 10-6 micro (µ) Kelvin (ºK) – 10-9 nano (n) – 10-12 pico (p) Electrical & Computer Engineering Basic Circuits and Simulation (2 of 22) 1 SI Examples • A few examples: • 1 Gbit = 109 bits, or 103106 bits, or one thousand million bits – 10-5 s = 0.00001 s; use closest SI prefix • 1×10-5 s = 10 × 10-6 s or 10 μs or • 1×10-5 s = 0.01 × 10-3 s or 0.01 ms Electrical & Computer Engineering Basic Circuits and Simulation (3 of 22) Typical Ranges Voltage (V) Current (A) • 10-8 Antenna of radio • 10-12 Nerve cell in brain receiver (10 nV) • 10-7 Integrated circuit • 10-3 EKG – voltage memory cell (0.1 µA) produced by heart • 10×10-3 Threshold of • 1.5 Flashlight battery sensation in humans • 12 Car battery • 100×10-3 Fatal to humans • 110 House wiring (US) • 1-2 Typical Household • 220 House wiring (Europe) appliance • 107 Lightning bolt (10 MV) • 103 Large industrial appliance • 104 Lightning bolt Electrical & Computer Engineering Basic Circuits and Simulation (4 of 22) 2 Electrical Quantities • Electric Charge (positive or negative) – (Coulombs, C) - q – Electron: 1.602 x 10 • Current (Ampere or Amp, A) – i or I – Rate of charge flow, – 1 1 Electrical & Computer Engineering Basic Circuits and Simulation (5 of 22) Electrical Quantities (continued) • Voltage (Volts, V) – w=energy required to move a given charge between two points (Joule, J) – – 1 1 1 Joule is the work done by a constant 1 N force applied through a 1 m distance. -
Electromagnetic Fields and Energy
MIT OpenCourseWare http://ocw.mit.edu Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. Please use the following citation format: Haus, Hermann A., and James R. Melcher, Electromagnetic Fields and Energy. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed [Date]). License: Creative Commons Attribution-NonCommercial-Share Alike. Also available from Prentice-Hall: Englewood Cliffs, NJ, 1989. ISBN: 9780132490207. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms 8 MAGNETOQUASISTATIC FIELDS: SUPERPOSITION INTEGRAL AND BOUNDARY VALUE POINTS OF VIEW 8.0 INTRODUCTION MQS Fields: Superposition Integral and Boundary Value Views We now follow the study of electroquasistatics with that of magnetoquasistat ics. In terms of the flow of ideas summarized in Fig. 1.0.1, we have completed the EQS column to the left. Starting from the top of the MQS column on the right, recall from Chap. 3 that the laws of primary interest are Amp`ere’s law (with the displacement current density neglected) and the magnetic flux continuity law (Table 3.6.1). � × H = J (1) � · µoH = 0 (2) These laws have associated with them continuity conditions at interfaces. If the in terface carries a surface current density K, then the continuity condition associated with (1) is (1.4.16) n × (Ha − Hb) = K (3) and the continuity condition associated with (2) is (1.7.6). a b n · (µoH − µoH ) = 0 (4) In the absence of magnetizable materials, these laws determine the magnetic field intensity H given its source, the current density J. -
Electric Potential
Electric Potential • Electric Potential energy: b U F dl elec elec a • Electric Potential: b V E dl a Field is the (negative of) the Gradient of Potential dU dV F E x dx x dx dU dV F UF E VE y dy y dy dU dV F E z dz z dz In what direction can you move relative to an electric field so that the electric potential does not change? 1)parallel to the electric field 2)perpendicular to the electric field 3)Some other direction. 4)The answer depends on the symmetry of the situation. Electric field of single point charge kq E = rˆ r2 Electric potential of single point charge b V E dl a kq Er ˆ r 2 b kq V rˆ dl 2 a r Electric potential of single point charge b V E dl a kq Er ˆ r 2 b kq V rˆ dl 2 a r kq kq VVV ba rrba kq V const. r 0 by convention Potential for Multiple Charges EEEE1 2 3 b V E dl a b b b E dl E dl E dl 1 2 3 a a a VVVV 1 2 3 Charges Q and q (Q ≠ q), separated by a distance d, produce a potential VP = 0 at point P. This means that 1) no force is acting on a test charge placed at point P. 2) Q and q must have the same sign. 3) the electric field must be zero at point P. 4) the net work in bringing Q to distance d from q is zero. -
9 AP-C Electric Potential, Energy and Capacitance
#9 AP-C Electric Potential, Energy and Capacitance AP-C Objectives (from College Board Learning Objectives for AP Physics) 1. Electric potential due to point charges a. Determine the electric potential in the vicinity of one or more point charges. b. Calculate the electrical work done on a charge or use conservation of energy to determine the speed of a charge that moves through a specified potential difference. c. Determine the direction and approximate magnitude of the electric field at various positions given a sketch of equipotentials. d. Calculate the potential difference between two points in a uniform electric field, and state which point is at the higher potential. e. Calculate how much work is required to move a test charge from one location to another in the field of fixed point charges. f. Calculate the electrostatic potential energy of a system of two or more point charges, and calculate how much work is require to establish the charge system. g. Use integration to determine the electric potential difference between two points on a line, given electric field strength as a function of position on that line. h. State the relationship between field and potential, and define and apply the concept of a conservative electric field. 2. Electric potential due to other charge distributions a. Calculate the electric potential on the axis of a uniformly charged disk. b. Derive expressions for electric potential as a function of position for uniformly charged wires, parallel charged plates, coaxial cylinders, and concentric spheres. 3. Conductors a. Understand the nature of electric fields and electric potential in and around conductors. -
13. Maxwell's Equations and EM Waves. Hunt (1991), Chaps 5 & 6 A
13. Maxwell's Equations and EM Waves. Hunt (1991), Chaps 5 & 6 A. The Energy of an Electromagnetic Field. • 1880s revision of Maxwell: Guiding principle = concept of energy flow. • Evidence for energy flow through seemingly empty space: ! induced currents ! air-core transformers, condensers. • But: Where is this energy located? Two equivalent expressions for electromagnetic energy of steady current: ½A J ½µH2 • A = vector potential, J = current • µ = permeability, H = magnetic force. density. • Suggests energy located outside • Suggests energy located in conductor. conductor in magnetic field. 13. Maxwell's Equations and EM Waves. Hunt (1991), Chaps 5 & 6 A. The Energy of an Electromagnetic Field. • 1880s revision of Maxwell: Guiding principle = concept of energy flow. • Evidence for energy flow through seemingly empty space: ! induced currents ! air-core transformers, condensers. • But: Where is this energy located? Two equivalent expressions for electrostatic energy: ½qψ# ½εE2 • q = charge, ψ = electric potential. • ε = permittivity, E = electric force. • Suggests energy located in charged • Suggests energy located outside object. charged object in electric field. • Maxwell: Treated potentials A, ψ as fundamental quantities. Poynting's account of energy flux • Research project (1884): "How does the energy about an electric current pass from point to point -- that is, by what paths and acording to what law does it travel from the part of the circuit where it is first recognizable as electric and John Poynting magnetic, to the parts where it is changed into heat and other forms?" (1852-1914) • Solution: The energy flux at each point in space is encoded in a vector S given by S = E × H. -
Topic 2.3: Electric and Magnetic Fields
TOPIC 2.3: ELECTRIC AND MAGNETIC FIELDS S4P-2-13 Compare and contrast the inverse square nature of gravitational and electric fields. S4P-2-14 State Coulomb’s Law and solve problems for more than one electric force acting on a charge. Include: one and two dimensions S4P-2-15 Illustrate, using diagrams, how the charge distribution on two oppositely charged parallel plates results in a uniform field. S4P-2-16 Derive an equation for the electric potential energy between two oppositely ∆ charged parallel plates (Ee = qE d). S4P-2-17 Describe electric potential as the electric potential energy per unit charge. S4P-2-18 Identify the unit of electric potential as the volt. S4P-2-19 Define electric potential difference (voltage) and express the electric field between two oppositely charged parallel plates in terms of voltage and the separation ⎛ ∆V ⎞ between the plates ⎜ε = ⎟. ⎝ d ⎠ S4P-2-20 Solve problems for charges moving between or through parallel plates. S4P-2-21 Use hand rules to describe the directional relationships between electric and magnetic fields and moving charges. S4P-2-22 Describe qualitatively various technologies that use electric and magnetic fields. Examples: electromagnetic devices (such as a solenoid, motor, bell, or relay), cathode ray tube, mass spectrometer, antenna Topic 2: Fields • SENIOR 4 PHYSICS GENERAL LEARNING OUTCOME SPECIFIC LEARNING OUTCOME CONNECTION S4P-2-13: Compare and contrast the Students will… inverse square nature of Describe and appreciate the gravitational and electric fields. similarity and diversity of forms, functions, and patterns within the natural and constructed world (GLO E1) SUGGESTIONS FOR INSTRUCTION Entry Level Knowledge Notes to the Teacher The definition of gravitational fields around a point When examining the gravitational field of a mass, mass it is useful to view the mass as a point mass, irrespective of its size. -
Voltage and Electric Potential.Doc 1/6
10/26/2004 Voltage and Electric Potential.doc 1/6 Voltage and Electric Potential An important application of the line integral is the calculation of work. Say there is some vector field F (r )that exerts a force on some object. Q: How much work (W) is done by this vector field if the object moves from point Pa to Pb, along contour C ?? A: We can find out by evaluating the line integral: = ⋅ A Wab ∫F(r ) d C Pb C Pa Say this object is a charged particle with charge Q, and the force is applied by a static electric field E (r ). We know the force on the charged particle is: FE(rr) = Q ( ) Jim Stiles The Univ. of Kansas Dept. of EECS 10/26/2004 Voltage and Electric Potential.doc 2/6 and thus the work done by the electric field in moving a charged particle along some contour C is: Q: Oooh, I don’t like evaluating contour integrals; isn’t there W =⋅F r d A ab ∫ () some easier way? C =⋅Q ∫ E ()r d A C A: Yes there is! Recall that a static electric field is a conservative vector field. Therefore, we can write any electric field as the gradient of a specific scalar field V ()r : E (rr) = −∇V ( ) We can then evaluate the work integral as: =⋅A Wab Qd∫E(r ) C =−QV∫ ∇()r ⋅ dA C =−QV⎣⎡ ()rrba − V()⎦⎤ =−QV⎣⎡ ()rrab V()⎦⎤ Jim Stiles The Univ. of Kansas Dept. of EECS 10/26/2004 Voltage and Electric Potential.doc 3/6 We define: VabVr( a) − Vr( b ) Therefore: Wab= QV ab Q: So what the heck is Vab ? Does it mean any thing? Do we use it in engineering? A: First, consider what Wab is! The value Wab represents the work done by the electric field on charge Q when moving it from point Pa to point Pb. -
At Equilibrium Under Electrostatic Conditions, Any Excess Charge Resides on the Surface of a Conductor
The Electric Field Inside a Conductor: Shielding At equilibrium under electrostatic conditions, any excess charge resides on the surface of a conductor. At equilibrium under electrostatic conditions, the electric field is zero at any point within a conducting material. The conductor shields any charge within it from electric fields created outside the conductor. The Electric Field Inside a Conductor: Shielding The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions. Chapter 17 Electric Potential Potential Energy The work done by the gravitational field on the ball in going from A to B equals the difference between the gravitational potential energy at A (GPEA) and the gravitational potential energy at B (GPEB) WBA = mghA − mghB = GPE A − GPEB Potential Energy Analogous situation between the work done by the gravitational field on the ball and the work done by the electric field on the charge. Potential Energy The work done by the electric field on the charge in going from A to B equals the difference between the electric potential energy at A (EPEA) and the electric potential energy at B (EPEB) WBA = EPE A − EPEB Note that the electric force is a conservative force just like the gravitational force so the work done by it is independent of the path taken between A and B. The Electric Potential Difference W EPE EPE BA = A − B qo qo qo The potential energy per unit charge is called the electric potential. The Electric Potential Difference DEFINITION OF ELECTRIC