Where k = 1. The electric field produced by a point charge is given by
|
|
- Clinton Alexander
- 5 years ago
- Views:
Transcription
1 Ch 21 review: 1. Electric charge: Electric charge is a property of a matter. There are two kinds of charges, positive and negative. Charges of the same sign repel each other. Charges of opposite sign attract. Charge is conserved. 2. Coulomb s law: For charges q 1 and q 2 separated by a distance r, the magnitude of the electric force on either charge is given by F = 1 q 1 q 2 4πε r 2 Where k = 1 4πε = N m 2 /C 2 ; and ε = C 2 /N m 2. The force on each charge is along the line joining the two charges repulsive if the two charges have the sign, attractive if they have opposite signs. 3. Electric field: A charged body produces an electric field in the space around it. The electric field is force per unit charge exerted on a test charge at any point. E = F q The electric field produced by a point charge is given by E = 1 q 4πε r 2 r The electric field of any combination of charges is the vector sum of the fields produced by the individual charges. 4. Electric field lines: Electric field lines provide a graphical representation of electric fields. At any point on a field line, the tangent to the line is in the direction of the field at that point. The number of lines per unit area is proportional to the magnitude of the field at the point. 5. Electric dipole: An electric dipole is a pair of electric charges of equal magnitude q but opposite sign, separated by a distance d. The electric dipole moment p has magnitude p = qd. The direction of p is from negative toward positive charge. In an electric field E, an electric dipole experiences a torque τ = p E τ = pe sin φ 6. How to set up an integral: For a given charge distribution, the total electric field at a point is the vector sum of the fields at this point due to each point charge in the charge distribution. If the charges are continuously distributed along a line, over a surface, or through a volume, i.e. the charges cannot be considered as discrete point charges, it requires to integrate over the charge distribution to calculate the total electric field. Here is the general guideline how hot set up an integral for this type of problems. a. Make a drawing showing the distribution of the charges and your choice of coordinate system. 1
2 b. Divide the charge distribution into infinitesimal segments. Try to use symmetry and do it in a way such that one of the electric field components can be cancelled. c. Calculate the electric field due to an infinitesimal segment and express the electric field in terms of variables so that the expression can be generalize to all segments. d. Construct an integral based on this expression and integrate over the whole charge distribution. e. Calculate the integral to find the total electric field. Ch 22 review: 1. Electric flux: Electric flux is a measure of the flow of electric field through a surface. It is equal to the product of an area element and the perpendicular component of E, integrated over a surface. Φ E = E cos φ da = E da = E da 2. Gauss s law: Gauss s law states that the total electric flux through a closed surface, which can be written as the surface integral of the component of E normal to the surface, equals a constant times the total charge Qencl enclosed by the surface. Gauss s law is logically equivalent to Coulomb s law, but its use greatly simplifies problems with a high degree of symmetry. Φ E = E da = Q encl ε 3. Charges on a conductor: when excess charge is placed on a conductor, the charge resides entirely on the surface and electric field is zero everywhere in the conductor. Ch 23 review: 1. Electric potential energy: The electric force caused by any collection of charges at rest is a conservative force. The work W done by the electric force on a charged particle moving in an electric field can be represented by the change in a potential-energy function U. The electric potential energy for two point charges q and q depends on their separation r. The electric potential energy for a charge q in the presence of a collection of charges q1, q2, q3 depends on the distance from q to each of these other charges. W U U U a b a b 1 qq two point charges 4 r 2
3 U q q q q 4 r r r q qi i r i q in presence of other point charges 2. Electric potential: Potential, denoted by V, is potential energy per unit charge. The potential difference between two points equals the amount of work that would be required to move a unit positive test charge between those points. The potential V due to a quantity of charge can be calculated by summing (if the charge is a collection of point charges) or by integrating (if the charge is a distribution). The potential can also be calculated if the electric field is known. U 1 q V q 4 r U 1 qi V q 4 i r 1 dq V 4 r b i due to a point charge V V Ed l = E cos dl a b a due to a collection of point charges due to a charge distribution b a 3. Equipotential surfaces: An equipotential surface is a surface on which the potential has the same value at every point. At a point where a field line crosses an equipotential surface, the two are perpendicular. When all charges are at rest, the surface of a conductor is always an equipotential surface and all points in the interior of a conductor are at the same potential. When a cavity within a conductor contains no charge, the entire cavity is an equipotential region and there is no surface charge anywhere on the surface of the cavity. 4. Finding electric field from electric potential: If the potential V is known as a function of the coordinates x, y, and z, the components of electric field E at any point are given by partial derivatives of V. V x y V E E Ez V x y z ˆ V ˆ V ˆ V E = i j k vector form x y z 3
4 Ch 24 review: 1. Capacitors and capacitance: A capacitor is any pair of conductors separated by an insulating materials. The capacitance is Q C V A For a parallel-plate capacitor: C = ε d r For a spherical capacitor: C = 4πε a r b r b r a For a cylindrical capacitor: C = 2πε L ln ( r b ); C/L = 2πε ln ( r b ra 2. Capacitors in series and parallel: For capacitors in series, each capacitor has the same amount of charge. The equivalent capacitance C eq satisfies 1 C eq = 1 C C C 3 + For capacitors in parallel, each capacitor has the same potential difference. The equivalent capacitance is ab ra ) C eq = C 1 + C 2 + C Energy in a capacitor: The energy U required to charge a capacitor C to a potential difference V and a charge Q is equal to the energy stored in the capacitor. The energy stored in a capacitor is 2 Q 1 2 U 1 2CV 2QV 2C The energy density of an electric field is u 1 2 E 2 4. Dielectric: When a dielectric material is inserted between the plates, an induced charge of the opposite sign appears on each surface of the dielectric. The induced charge is a result of redistribution of positive and negative charge within the dielectric materials, a phenomenon called polarization. The permittivity is defined as ε = Kε. The capacitance with the dielectric is A A C KC K (parallel-plate capacitor filled with dielectric) d d Ch 25 review: 1. Current and current density: Current is the amount of charge flowing through a specified area. 4
5 I = dq dt = n q v da The current density is current per unit cross-sectional area: J = nqv d 2. Resistivity: The resistivity ρ of a material is the ratio of the magnitude of electric field and current density. ρ = E J Resistivity usually increases with temperature; for small temperature changes this variation is represented approximately by ρ(t) = ρ [1 + α(t T )] 3. Resistors: The potential difference V across a sample of material that obeys Ohm s law is proportional to the current through the sample. V = IR And the resistance R is R = ρl A 4. Circuits and emf: A complete circuit with a continuous current-carrying path and a source of electromotive force can carry a steady current. The terminal potential difference is V ab = E Ir 5. Energy and power in circuits: A circuit element with a potential difference and a current puts energy into a circuit if the correction direction is from lower to higher potential in the device, and it takes energy out of the circuit if the current is opposite. The power equals the product of the potential difference and the current. P = V ab I (general circuit element) P = V ab I = I 2 R = V ab 2 (power into a resistor) R Ch 26 review: 1. Resistors in series and parallel: When several resistors are connected in series, the current through all resistors is the same, the equivalent resistance is R eq = R 1 + R 2 + R 3 + When several resistors are connected in parallel, the potential difference across all resistors is the same, the equivalent resistance satisfies 1 R eq = 1 R R R 3 + 5
6 2. Kirchhoff s rules: Kirchhoff s junction rule states that the algebraic sum of the currents into any junction must be zero. Kirchhoff s loop rule states that the algebraic sum of potential differences around any loop must be zero. I = (Junction rule) V = (Loop rule) 3. R-C circuits: When a capacitor is charged by a battery in series with a resistor or discharges through a resistor, the current and capacitor charge are not constant. During the charging: q = CE (1 e RC) t = Q f (1 e RC) t During the discharging: i = dq dt = E R e t/rc = I e t/rc i = dq dt = Q q = Q e t/rc t RC e RC = I e t/rc The time constant τ = RC is a measure of how quickly the capacitor charges or discharges. Ch 27 review: 1. Magnets: Permanent magnet has two poles: north and south. North and south poles always appear in pairs. Opposite poles attract and like poles repel. 2. Magnetic forces: A particle with charge q moving with velocity v in a magnetic field B experiences a force F that is perpendicular to both v and B. F = qv B 3. Magnetic field lines and flux: A magnetic field can be represented graphically by magnetic field lines. At each point a magnetic field line is tangent to the direction of B at that point. The field magnitude is large where field lines are close together, and vice versa. Magnetic flux through an area is defined in analogous way to electric flux. The SI unite of magnetic flux is the weber (1 Wb = 1 T m 2 ). The net magnetic flux through any closed surface is zero (Gauss s law for magnetism). Magnetic field lines always close on themselves. Φ B = B da = B cos φ da = B da B da = (closed surface) 4. Motion in a magnetic field: The magnetic force is always perpendicular to v, a particle moving under the action of a magnetic field alone moves with constant speed. In a uniform field, a particle with initial velocity perpendicular to the field moves in a circle with radius R given by 6
7 R = mv q B The time to complete a full circle is given by T = 2πR The cyclotron frequency is f = 1 T = B q 2πm v = 2πm q B. Crossed electric and magnetic fields can be used as a velocity selector. 6. Magnetic force on a conductor: A straight segment of a conductor carrying current I in a uniform magnetic field B experiences a force given by F = Il B A similar relationship give the force df on an infinitesimal current carrying segment dl: df = Idl B 7. Magnetic torque: A current loop with area A and current I in a uniform magnetic field B experiences no net magnetic force, but does experience a magnetic torque. τ = IBA sin φ Ch 28 review: Define the magnetic dipole moment μ = IA, then τ = μ B U = μ B = μb cos φ 1. Magnetic field of a moving charge: The magnetic field B created by a charge q moving with velocity v is given by B = μ qv r 4π r 2 2. Magnetic field of a current-carrying conductor: The law of Biot and Savart gives the magnetic field db created by an element dl of a conductor carrying current I. db = μ Idl r 4π r 2 3. Magnetic field of a long, straight, current-carrying conductor: The magnetic field B at a distance r from a long, straight conductor carrying a current I is given by B = μ I 2πr The magnetic field lines are circles coaxial with the wire, with directions given by the right-hand rule. 4. Magnetic force between current-carrying conductors: Two long, parallel, currentcarrying conductors attract if the currents are in the same direction and repel if the currents are in opposite direction. The magnetic force per unit length between the conductors is given by 7
8 F L = μ II 2πr 5. Magnetic field of a current loop: The magnetic field along the axis of a circular conducting loop of radius a carrying current I is given by Ch 29 review: B x = μ Ia 2 2(x 2 +a 2 ) 3/2 (a circular loop) Bx = μ NI 2a 1. Faraday s law: Faraday s law states that the induced emf in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. E = dφ B dt 2. Lenz s law: Lenz s law states that an induced current of emf always tends to oppose or cancel out the change that caused it. It is often easier to use Lenz s law to determine the direction of the induced current or emf. 3. Motional emf: If a conductor moves in a magnetic field, a motional emf is induced. For a conductor with length L moves in a uniform B field, L and v are both perpendicular to B and to each other, then E = vbl 4. Induced electric fields: When an emf is induced by a changing magnetic flux through a stationary conductor, there is an induced electric field of nonelectrostatic origin. Ch 32 review: E dl = dφ B dt 1. Maxwell s equations and electromagnetic waves: Maxwell s equations predict the existence of electromagnetic waves that propagate in vacuum at the speed of light c. Electromagnetic waves are transverse; the E and B fields are perpendicular to the direction of propagation and to each other. Faraday s law and Ampere s law give relationships between the magnitudes of E and B. In a plane wave, E and B are uniform over any plane perpendicular to the propagation direction. E = cb; c = 1 ε μ 2. Sinusoidal electromagnetic waves: A sinusoidal plane electromagentical wave traveling in vacuum in the +x-direction can be described by E (x, t) = j E max cos(kx ωt); B (x, t) = k B max cos(kx ωt) 3. Energy in electromagnetic waves: The energy flow rate (power per unit area) in an electromagnetic wave in vacuum is given by the Poyting vector. The magnitude of the time-averaged value of the Poynting vector is called the intensity I of the wave. 8
9 S = 1 μ E B I = S av = E maxb max 2μ = E 2 max 2μ c = 1 2 ε 2 E μ max = 1 2 ε 2 ce max Ch 32 review: 1. The nature of light: Light is an electromagnetic wave. A wave front is a surface of constant phase. A ray is a line along the direction of propagation, perpendicular to the wave fronts. The speed of light in vacuum is c. Light always travels more slowly in a medium with index of refraction n. n = c ; λ = λ v n 2. Reflection and refraction: At a smooth interface between two optical materials, the incident, reflected, and refracted rays and the normal to the interface all lie in a single plane called the plane of incidence. The angles of incidence, reflection, and refraction satisfy the law of reflection and the law of refraction. θ r = θ a n a sin θ a = n b sin θ b 3. Total internal reflection: When a ray travels in a material of greater index of refraction n a toward a material of smaller index n b, total internal reflection occurs at the interface when the angle of incidence exceeds a critical angle θ crit sinθ crit = n b n a 4. Polarization of light: The direction of polarization of a linearly polarized electromagnetic wave is the direction of the electric field. A polarizer passes waves that are linearly polarized along its polarizing axis and blocks wave polarized perpendicular to that axis. When polarized light of intensity I max is incident on a polarizer, the transmitted intensity is I = I max cos 2 φ Ch 34 review: 1. Reflection and refraction at a plane surface: When rags diverge from an object point P and are reflected or refracted, the directions of the outgoing rays are the same as though they had diverged from a point P called the image point. It they actually converge at P and diverge again beyond it, P is a real image of P; if they only appear to have diverged from P, it is a virtual image. Images can be either erect or inverted. 9
10 8. Lateral magnification: The lateral magnification m in any reflecting or refracting situation is defined as the ratio of the image height y to object height y. When m is positive, the image is erect; when m is negative, the image is inverted. 9. Focal point and focal length: The focal point of a mirror is the point where parallel rays converge after reflection from a concave mirror, or the point from which they appear to diverge after reflection from a convex mirror. The distance from the focal point to the vertex is called the focal length, denoted as f. 1. Object and image relationship: The object distance s and image distance s are related for a given imaging system. Plane mirror: 1 s + 1 s = (i.e. s = s ); m = s s = 1 Spherical mirror: = 2 = 1 s ; m = s s R f s Spherical refracting surface: n a + n b = n b n a ; m = n as s s R n b s 11. Sign rules: The following sign rules are used with all plane and spherical reflecting and refracting surfaces. s > when the object is on the incoming side of the surface (a real object); s < otherwise. s > when the image is on the outgoing side of the surface ( a real image); s < otherwise. R > when the center of curvature is on the outgoing side of the surface; R < otherwise. m > when the image is erect; m < when inverted. 12. Graphical methods for mirrors: Use the following principal rays A ray parallel to the axis A ray through (or proceeding toward) the focal point A ray along the radius 1
11 A ray to the vertex 13. Thin lenses: A thin lens with a positive focal length is called a converging lens or positive lens. A thin lens with a negative focal length is called a diverging lens or negative lens. The object-image relationship is the same for a converging lens as for a diverging lens, providing that the correct signs are used. 1 s + 1 s = 1 f m = s s (object-image relationship) (lateral magnification) 14. Graphical methods for lenses: Use the following principle rays A ray parallel to the axis A ray through the center of the lens A ray through (or proceeding toward) the first focal point Ch 35 review: 1. Interference: The overlap of waves from two coherent sources of monochromatic light forms an interference pattern. The interference pattern is determined by the principle of superposition, which states that the total wave displacement at any point is the sum of the displacements from the separate waves. 2. Two-source interference of light: When two sources are in phase, constructive interference occurs where the difference in path length from the two sources is zero or an integer number of wavelengths, i.e. d sin θ = mλ, (m =, ±1, ±2, ); destructive interference occurs where the path difference is a half-integer number of wavelengths, i.e. d sin θ = (m )λ, (m =, ±1, ±2, ). For small angles, the position of the mth bright fringe on the a screen is given by y m = R mλ d 11
Describe the forces and torques exerted on an electric dipole in a field.
Learning Outcomes - PHYS 2015 Electric charges and forces: Describe the electrical nature of matter; Explain how an object can be charged; Distinguish between electrical conductors and insulators and the
More informationwe can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron.
Physics II we can said that matter can be regarded as composed of three kinds of elementary particles; proton, neutron (no charge), and electron. Particle Symbol Charge (e) Mass (kg) Proton P +1 1.67
More informationSUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r.
SUMMARY Phys 53 (University Physics II) Compiled by Prof. Erickson q 1 q Coulomb s Law: F 1 = k e r ˆr where k e = 1 4π =8.9875 10 9 N m /C, and =8.85 10 1 C /(N m )isthepermittivity of free space. Generally,
More informationn Higher Physics 1B (Special) (PHYS1241) (6UOC) n Advanced Science n Double Degree (Science/Engineering) n Credit or higher in Physics 1A
Physics in Session 2: I n Physics / Higher Physics 1B (PHYS1221/1231) n Science, dvanced Science n Engineering: Electrical, Photovoltaic,Telecom n Double Degree: Science/Engineering n 6 UOC n Waves n Physical
More informationPhysics / Higher Physics 1A. Electricity and Magnetism Revision
Physics / Higher Physics 1A Electricity and Magnetism Revision Electric Charges Two kinds of electric charges Called positive and negative Like charges repel Unlike charges attract Coulomb s Law In vector
More informationPhysics 208, Spring 2016 Exam #3
Physics 208, Spring 206 Exam #3 A Name (Last, First): ID #: Section #: You have 75 minutes to complete the exam. Formulae are provided on an attached sheet. You may NOT use any other formula sheet. You
More informationExam 4 Solutions. a. 1,2,and 3 b. 1 and 2, not 3 c. 1 and 3, not 2 d. 2 and 3, not 1 e. only 2
Prof. Darin Acosta Prof. Greg Stewart April 8, 007 1. Which of the following statements is true? 1. In equilibrium all of any excess charge stored on a conductor is on the outer surface.. In equilibrium
More informationFinal on December Physics 106 R. Schad. 3e 4e 5c 6d 7c 8d 9b 10e 11d 12e 13d 14d 15b 16d 17b 18b 19c 20a
Final on December11. 2007 - Physics 106 R. Schad YOUR NAME STUDENT NUMBER 3e 4e 5c 6d 7c 8d 9b 10e 11d 12e 13d 14d 15b 16d 17b 18b 19c 20a 1. 2. 3. 4. This is to identify the exam version you have IMPORTANT
More informationElectricity. Revision Notes. R.D.Pilkington
Electricity Revision Notes R.D.Pilkington DIRECT CURRENTS Introduction Current: Rate of charge flow, I = dq/dt Units: amps Potential and potential difference: work done to move unit +ve charge from point
More informationr r 1 r r 1 2 = q 1 p = qd and it points from the negative charge to the positive charge.
MP204, Important Equations page 1 Below is a list of important equations that we meet in our study of Electromagnetism in the MP204 module. For your exam, you are expected to understand all of these, and
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Spring 2014 Final Exam Equation Sheet. B( r) = µ o 4π
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2014 Final Exam Equation Sheet Force Law: F q = q( E ext + v q B ext ) Poynting Vector: S = ( E B) / µ 0 Force on Current Carrying
More informationMansfield Independent School District AP Physics C: Electricity and Magnetism Year at a Glance
Mansfield Independent School District AP Physics C: Electricity and Magnetism Year at a Glance First Six-Weeks Second Six-Weeks Third Six-Weeks Lab safety Lab practices and ethical practices Math and Calculus
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 Before Starting All of your grades should now be posted
More informationComplement to Physics 259
Complement to Physics 259 P. Marzlin 1 1 Institute for Quantum Information Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada I. INTRODUCTORY REMARKS The purpose
More informationAP Physics C. Magnetism - Term 4
AP Physics C Magnetism - Term 4 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the world
More informationFundamental Constants
Fundamental Constants Atomic Mass Unit u 1.660 540 2 10 10 27 kg 931.434 32 28 MeV c 2 Avogadro s number N A 6.022 136 7 36 10 23 (g mol) 1 Bohr magneton μ B 9.274 015 4(31) 10-24 J/T Bohr radius a 0 0.529
More informationDHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY
DHANALAKSHMI SRINIVASAN INSTITUTE OF RESEARCH AND TECHNOLOGY SIRUVACHUR-621113 ELECTRICAL AND ELECTRONICS DEPARTMENT 2 MARK QUESTIONS AND ANSWERS SUBJECT CODE: EE 6302 SUBJECT NAME: ELECTROMAGNETIC THEORY
More informationAP Physics C. Electricity - Term 3
AP Physics C Electricity - Term 3 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 efore Starting All of your grades should now be posted
More informationPhysics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/
Physics GRE: Electromagnetism G. J. Loges University of Rochester Dept. of Physics & stronomy xkcd.com/567/ c Gregory Loges, 206 Contents Electrostatics 2 Magnetostatics 2 3 Method of Images 3 4 Lorentz
More informationPHY102 Electricity Course Summary
TOPIC 1 ELECTOSTTICS PHY1 Electricity Course Summary Coulomb s Law The magnitude of the force between two point charges is directly proportional to the product of the charges and inversely proportional
More informationElectrical polarization. Figure 19-5 [1]
Electrical polarization Figure 19-5 [1] Properties of Charge Two types: positive and negative Like charges repel, opposite charges attract Charge is conserved Fundamental particles with charge: electron
More informationExam 2 Solutions. Note that there are several variations of some problems, indicated by choices in parentheses.
Exam 2 Solutions Note that there are several variations of some problems, indicated by choices in parentheses. Problem 1 Part of a long, straight insulated wire carrying current i is bent into a circular
More informationPhysics 2102 Gabriela González. Marathon review of the course: 15 weeks in ~60 minutes!
Physics 2102 Gabriela González Marathon review of the course: 15 weeks in ~60 minutes! Fields: electric & magnetic electric and magnetic forces on electric charges potential energy, electric potential,
More informationChapter 1 The Electric Force
Chapter 1 The Electric Force 1. Properties of the Electric Charges 1- There are two kinds of the electric charges in the nature, which are positive and negative charges. - The charges of opposite sign
More informationChapter 1: Electrostatics
1.1 Coulomb s law a) State Coulomb s law, Chapter 1: Electrostatics b) Sketch the electric force diagram and apply Coulomb s law for a system of point charges. 1.2 Electric field a) Define and use electric
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics: Final Exam Review Session Problems Solutions
Department of Physics: 8 Problem 1: Spherical Capacitor 8 Final Exam Review Session Problems Solutions A capacitor consists of two concentric spherical shells The outer radius of the inner shell is a =
More informationQuestions A hair dryer is rated as 1200 W, 120 V. Its effective internal resistance is (A) 0.1 Ω (B) 10 Ω (C) 12Ω (D) 120 Ω (E) 1440 Ω
Questions 4-41 36. Three 1/ µf capacitors are connected in series as shown in the diagram above. The capacitance of the combination is (A).1 µf (B) 1 µf (C) /3 µf (D) ½ µf (E) 1/6 µf 37. A hair dryer is
More informationLouisiana State University Physics 2102, Exam 3 April 2nd, 2009.
PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),
More informationPhysics Will Farmer. May 5, Physics 1120 Contents 2
Physics 1120 Will Farmer May 5, 2013 Contents Physics 1120 Contents 2 1 Charges 3 1.1 Terms................................................... 3 1.2 Electric Charge..............................................
More informationWelcome to PHY2054C. Office hours: MoTuWeTh 10:00-11:00am (and after class) at PS140
Welcome to PHY2054C Office hours: MoTuWeTh 10:00-11:00am (and after class) at PS140 Book: Physics 8 ed. by Cutnell & Johnson, Volume 2 and PHY2054 Lab manual for your labs. One Midterm (July 14) and final
More informationMaxwell s equations and EM waves. From previous Lecture Time dependent fields and Faraday s Law
Maxwell s equations and EM waves This Lecture More on Motional EMF and Faraday s law Displacement currents Maxwell s equations EM Waves From previous Lecture Time dependent fields and Faraday s Law 1 Radar
More informationPHY2049 Fall11. Final Exam Solutions (1) 700 N (2) 350 N (3) 810 N (4) 405 N (5) 0 N
Exam Solutions 1. Three charges form an equilateral triangle of side length d = 2 cm. The top charge is q3 = 3 μc, while the bottom two are q1 = q2 = - 6 μc. What is the magnitude of the net force acting
More informationPhysics by Discovery Standards (2nd Semester)
Physics by Discovery Standards 2017-18 (2nd Semester) 11. Newton's Law of Universal Gravitation UG I can apply the Law of Universal Gravitation Reason about how doubling distance, masses, etc. affect the
More information2426 Required Topics (May 4, 2012 draft) Halliday, FUNDAMENTALS OF PHYSICS, 9e Required topics are in bold text. Optional topics are in normal text.
2426 Required Topics (May 4, 2012 draft) Halliday, FUNDAMENTALS OF PHYSICS, 9e Required topics are in bold text. Optional topics are in normal text. Chapter 21 Electric Charge 21-1 What Is Physics? 21-2
More informationPhysics 112. Study Notes for Exam II
Chapter 20 Electric Forces and Fields Physics 112 Study Notes for Exam II 4. Electric Field Fields of + and point charges 5. Both fields and forces obey (vector) superposition Example 20.5; Figure 20.29
More informationWaves. Decibels. Chapter 21: Dimension
Chapter 20: 20.1 The Wave Model 20.2 One Dimensional 20.3 Sinusoidal 20.4 Sound Light 20.5 Index of Refraction 20.6 Power, Intensity, Decibels 20.7 The Doppler Effect Chapter 21: 21.1 The Principle of
More informationr where the electric constant
0. Coulomb s law a) Explain the concepts of electrons, protons, charged objects, charged up, gaining charge, losing charge, grounding and charge conservation. b) Describe the motion of point charges when
More informationCHAPTER 29: ELECTROMAGNETIC INDUCTION
CHAPTER 29: ELECTROMAGNETIC INDUCTION So far we have seen that electric charges are the source for both electric and magnetic fields. We have also seen that these fields can exert forces on other electric
More informationProfs. P. Avery, A. Rinzler, S. Hershfield. Final Exam Solution
PHY2049 Spring 2010 Profs. P. Avery, A. Rinzler, S. Hershfield Final Exam Solution 1. A proton traveling along the x axis (toward increasing x) has a speed of 1.0 10 5 m/s. At time t = 0 it enters a region
More informationChapter 31. Faraday s Law
Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field dφ B ( I I ) E d s = µ o + d = µ o I+ µ oεo ds E B 2 Induction A loop of wire is connected to a sensitive
More informationPhysics Jonathan Dowling. Final Exam Review
Physics 2102 Jonathan Dowling Physics 2102 Final Exam Review A few concepts: electric force, field and potential Electric force: What is the force on a charge produced by other charges? What is the force
More informationPhysics (2) Dr. Yazid Delenda
PHYS 104 Physics (2) Dr. Yazid Delenda Department of Physics, Faculty of Sciences and Arts at Yanbu, Taibah University - Yanbu Branch, KSA. yazid.delenda@yahoo.com Lecture notes available at http://delenda.wordpress.com/teaching/phys104/
More informationr where the electric constant
1.0 ELECTROSTATICS At the end of this topic, students will be able to: 10 1.1 Coulomb s law a) Explain the concepts of electrons, protons, charged objects, charged up, gaining charge, losing charge, charging
More informationUNIT I ELECTROSTATIC FIELDS
UNIT I ELECTROSTATIC FIELDS 1) Define electric potential and potential difference. 2) Name few applications of gauss law in electrostatics. 3) State point form of Ohm s Law. 4) State Divergence Theorem.
More informationOutline of College Physics OpenStax Book
Outline of College Physics OpenStax Book Taken from the online version of the book Dec. 27, 2017 18. Electric Charge and Electric Field 18.1. Static Electricity and Charge: Conservation of Charge Define
More informationMagnets. Domain = small magnetized region of a magnetic material. all the atoms are grouped together and aligned
Magnetic Fields Magnets Domain = small magnetized region of a magnetic material all the atoms are grouped together and aligned Magnets Ferromagnetic materials domains can be forced to line up by applying
More informationPrinciples of Physics II
Principles of Physics II J. M. Veal, Ph. D. version 18.05.4 Contents 1 Fluid Mechanics 3 1.1 Fluid pressure............................ 3 1. Buoyancy.............................. 3 1.3 Fluid flow..............................
More information2. Waves with higher frequencies travel faster than waves with lower frequencies (True/False)
PHY 2049C Final Exam. Summer 2015. Name: Remember, you know this stuff Answer each questions to the best of your ability. Show ALL of your work (even for multiple choice questions), you may receive partial
More informationPHYS 212 Final Exam (Old Material) Solutions - Practice Test
PHYS 212 Final Exam (Old Material) Solutions - Practice Test 1E If the ball is attracted to the rod, it must be made of a conductive material, otherwise it would not have been influenced by the nearby
More informationFinal Exam: Physics Spring, 2017 May 8, 2017 Version 01
Final Exam: Physics2331 - Spring, 2017 May 8, 2017 Version 01 NAME (Please Print) Your exam should have 11 pages. This exam consists of 18 multiple-choice questions (2 points each, worth 36 points), and
More informationGeneral Physics II Summer Session 2013 Review Ch - 16, 17, 18
95.104 General Physics II Summer Session 2013 Review Ch - 16, 17, 18 A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positivecharged rod held near the ball. The
More informationChapter 27 Magnetic Field and Magnetic Forces
Chapter 27 Magnetic Field and Magnetic Forces Lecture by Dr. Hebin Li Goals for Chapter 27 To study magnets and the forces they exert on each other To calculate the force that a magnetic field exerts on
More informationPhysics for Scientists and Engineers 4th Edition 2017
A Correlation and Narrative Summary of Physics for Scientists and Engineers 4th Edition 2017 To the AP Physics C: Electricity and Magnetism Course Description AP is a trademark registered and/or owned
More informationSUGGESTED LESSON PLANS FOR PHY 097 SEMESTER NOV10 Text Book : PHYSICS FOR SCIENTISTS & ENGINEERS WITH MODERN PHYSICS BY GIANCOLI, FOURTH EDITION
SUGGESTED LESSON PLANS FOR PHY 097 SEMESTER NOV0 Text Book : PHYSICS FOR SCIENTISTS & ENGINEERS WITH MODERN PHYSICS BY GIANCOLI, FOURTH EDITION Week Topics Section Page Hrs Sub-Topics WAVES AND OPTICS,.0
More informationPhysics 202, Lecture 13. Today s Topics. Magnetic Forces: Hall Effect (Ch. 27.8)
Physics 202, Lecture 13 Today s Topics Magnetic Forces: Hall Effect (Ch. 27.8) Sources of the Magnetic Field (Ch. 28) B field of infinite wire Force between parallel wires Biot-Savart Law Examples: ring,
More informationPHYSICS 253 SAMPLE FINAL EXAM. Student Number. The last two pages of the exam have some equations and some physical constants.
PHYSICS 253 SAMPLE FINAL EXAM Name Student Number CHECK ONE: Instructor 1 10:00 Instructor 2 1:00 Note that problems 1-19 are worth 2 points each, while problem 20 is worth 15 points and problems 21 and
More informationAP Physics C. Electricity and Magne4sm Review
AP Physics C Electricity and Magne4sm Review Electrosta4cs 30% Chap 22-25 Charge and Coulomb s Law Electric Field and Electric Poten4al (including point charges) Gauss Law Fields and poten4als of other
More informationReview. Spring Semester /21/14. Physics for Scientists & Engineers 2 1
Review Spring Semester 2014 Physics for Scientists & Engineers 2 1 Notes! Homework set 13 extended to Tuesday, 4/22! Remember to fill out SIRS form: https://sirsonline.msu.edu Physics for Scientists &
More informationChapter 2 Basics of Electricity and Magnetism
Chapter 2 Basics of Electricity and Magnetism My direct path to the special theory of relativity was mainly determined by the conviction that the electromotive force induced in a conductor moving in a
More informationCircuits Capacitance of a parallel-plate capacitor : C = κ ε o A / d. (ρ = resistivity, L = length, A = cross-sectional area) Resistance : R = ρ L / A
k = 9.0 x 109 N m2 / C2 e = 1.60 x 10-19 C ε o = 8.85 x 10-12 C2 / N m2 Coulomb s law: F = k q Q / r2 (unlike charges attract, like charges repel) Electric field from a point charge : E = k q / r2 ( towards
More informationCapacitance, Resistance, DC Circuits
This test covers capacitance, electrical current, resistance, emf, electrical power, Ohm s Law, Kirchhoff s Rules, and RC Circuits, with some problems requiring a knowledge of basic calculus. Part I. Multiple
More informationELECTRO MAGNETIC FIELDS
SET - 1 1. a) State and explain Gauss law in differential form and also list the limitations of Guess law. b) A square sheet defined by -2 x 2m, -2 y 2m lies in the = -2m plane. The charge density on the
More informationLouisiana State University Physics 2102, Exam 2, March 5th, 2009.
PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 2, March 5th, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),
More informationF S E S 1. r 2 r N. t = pe sin f. T S p : E S. U = -p S # E
Coulomb s law: For charges q 1 and q separated by a distance r, the magnitude of the electric force on either F = (1.) 1 ƒq 1 q ƒ 4pP 0 r charge is proportional to the product q 1 q and inversely proportional
More informationCHAPTER 7 ELECTRODYNAMICS
CHAPTER 7 ELECTRODYNAMICS Outlines 1. Electromotive Force 2. Electromagnetic Induction 3. Maxwell s Equations Michael Faraday James C. Maxwell 2 Summary of Electrostatics and Magnetostatics ρ/ε This semester,
More informationPHYS General Physics for Engineering II FIRST MIDTERM
Çankaya University Department of Mathematics and Computer Sciences 2010-2011 Spring Semester PHYS 112 - General Physics for Engineering II FIRST MIDTERM 1) Two fixed particles of charges q 1 = 1.0µC and
More informationSENIOR_ 2017_CLASS_12_PHYSICS_ RAPID REVISION_1_ DERIVATIONS IN FIRST FIVE LESSONS Page 1
INDIAN SCHOOL MUSCAT Department of Physics Class XII Rapid Revision -1 DERIVATIONS IN FIRST FIVE LESSONS 1) Field due to an infinite long straight charged wire Consider an uniformly charged wire of infinite
More informationTHE INDIAN COMMUNITY SCHOOL, KUWAIT
THE INDIAN COMMUNITY SCHOOL, KUWAIT SERIES : I SE / 2016-2017 CODE : N 042 MAX. MARKS : 70 TIME ALLOWED : 3 HOURS NO. OF PAGES : 6 PHYSICS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
More informationChapter 31. Faraday s Law
Chapter 31 Faraday s Law 1 Ampere s law Magnetic field is produced by time variation of electric field B s II I d d μ o d μo με o o E ds E B Induction A loop of wire is connected to a sensitive ammeter
More informationAP PHYSICS 2 Essential Knowledge and Learning Objectives Arranged Topically
with AP PHYSICS 2 Essential Knowledge and Learning Objectives Arranged Topically o Big Ideas o Enduring Understandings o Essential Knowledges o Learning Objectives o Science Practices o Correlation to
More informationAmpere s Law. Outline. Objectives. BEE-Lecture Notes Anurag Srivastava 1
Outline Introduce as an analogy to Gauss Law. Define. Applications of. Objectives Recognise to be analogous to Gauss Law. Recognise similar concepts: (1) draw an imaginary shape enclosing the current carrying
More informationAP Physics C Mechanics Objectives
AP Physics C Mechanics Objectives I. KINEMATICS A. Motion in One Dimension 1. The relationships among position, velocity and acceleration a. Given a graph of position vs. time, identify or sketch a graph
More informationQuiz 4 (Discussion Session) Phys 1302W.400 Spring 2018
Quiz 4 (Discussion ession) Phys 1302W.400 pring 2018 This group quiz consists of one problem that, together with the individual problems on Friday, will determine your grade for quiz 4. For the group problem,
More informationElectromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance
Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic
More informationExam 4 (Final) Solutions
PHY049 Spring 006 Prof. Darin Acosta Prof. Greg Stewart May 1, 006 Exam 4 (Final) Solutions 1. Four charges are arranged into a square with side length a=1 cm as shown in the figure. The charges (clockwise
More informationElectromagnetic Induction (Chapters 31-32)
Electromagnetic Induction (Chapters 31-3) The laws of emf induction: Faraday s and Lenz s laws Inductance Mutual inductance M Self inductance L. Inductors Magnetic field energy Simple inductive circuits
More informationProblem Fig
Problem 9.53 A flexible circular loop 6.50 cm in diameter lies in a magnetic field with magnitude 0.950 T, directed into the plane of the page, as shown. The loop is pulled at the points indicated by the
More informationCBSE PHYSICS QUESTION PAPER (2005)
CBSE PHYSICS QUESTION PAPER (2005) (i) (ii) All questions are compulsory. There are 30 questions in total. Questions 1 to 8 carry one mark each, Questions 9 to 18 carry two marks each, Question 19 to 27
More informationLecture 10 Induction and Inductance Ch. 30
Lecture 10 Induction and Inductance Ch. 30 Cartoon - Faraday Induction Opening Demo - Thrust bar magnet through coil and measure the current Topics Faraday s Law Lenz s Law Motional Emf Eddy Currents LR
More informationExam 2 Solutions. ε 3. ε 1. Problem 1
Exam 2 Solutions Problem 1 In the circuit shown, R1=100 Ω, R2=25 Ω, and the ideal batteries have EMFs of ε1 = 6.0 V, ε2 = 3.0 V, and ε3 = 1.5 V. What is the magnitude of the current flowing through resistor
More informationPHY 131 Review Session Fall 2015 PART 1:
PHY 131 Review Session Fall 2015 PART 1: 1. Consider the electric field from a point charge. As you move farther away from the point charge, the electric field decreases at a rate of 1/r 2 with r being
More informationPHYSICS Course Structure Units Topics Marks Electrostatics Current Electricity III Magnetic Effect of Current & Magnetism
PHYSICS Course Structure Units Topics Marks I Chapter 1 Chapter 2 II Chapter 3 III Chapter 4 Chapter 5 IV Chapter 6 Chapter 7 V Chapter 8 VI Chapter 9 Electrostatics Electric Charges and Fields Electrostatic
More informationUniversity of Colorado at Boulder Summer 2017, Session B Tuesday, July 11 - Friday, August 11. Prof. Mik Sawicki PHYS 1120 COURSE CALENDAR WEEK 1
University of Colorado at Boulder Summer 2017, Session B Tuesday, July 11 - Friday, August 11 1 T 07/11 Introduction and Electric charge 2 W 07/12 Coulomb s Law and Unit1 Electric Field. Unit 2 3 TH 07/13
More informationChapter 28. Direct Current Circuits
Chapter 28 Direct Current Circuits Circuit Analysis Simple electric circuits may contain batteries, resistors, and capacitors in various combinations. For some circuits, analysis may consist of combining
More informationPhysics 182. Assignment 4
Physics 182 Assignment 4 1. A dipole (electric or magnetic) in a non-uniform field will in general experience a net force. The electric case was the subject of a problem on the midterm exam; here we examine
More informationFinal Exam Solutions
Prof. Yasu Takano Prof. Paul Avery Dec. 8, 007 Final Exam Solutions (First answer is correct) 1. (Exam 1) Charges +9Q and 3Q are held in place at positions x = 0 m and x = m, respectively. At what position
More informationnrt V dv = nrt ln(3) = P AV A ln(3) P A dv = P A V 5/ / /3
Problem. a For an isothermal process: W iso = VA 3V A PdV = VA 3V A nrt V dv = nrt ln3 = P AV A ln3 For the adiabatic leg, PV γ =const. Thus, I get that P = P A VA V γ. Since the gas is monatomic, γ =
More informationFinal Exam April 21, a) No books, notes, or other such materials are permitted.
Phys 5 Spring 004 Name: Final Exam April, 004 INSTRUCTIONS: a) No books, notes, or other such materials are permitted. b) You may use a calculator. c) You must solve all problems beginning with the equations
More informationName (Print): 4 Digit ID: Section:
Physics 11 Sample Common Exam 3: Sample 5 Name (Print): 4 Digit ID: Section: Honors Code Pledge: As an NJIT student I, pledge to comply with the provisions of the NJIT Academic Honor Code. I assert that
More informationCBSE Examination Paper
CBSE Examination Paper Time allowed : 3 hours Maximum marks: 70 General Instructions: Same as CBSE Examination Paper SET I 1. Using the concept of force between two infinitely long parallel current carrying
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING QUESTION BANK SUB.NAME : ELECTROMAGNETIC FIELDS SUBJECT CODE : EC 2253 YEAR / SEMESTER : II / IV UNIT- I - STATIC ELECTRIC
More informationPHYSICS PRACTICAL (CBSE) - X
PHYSICS PRACTICAL (CBSE) - X Scientific Terminology / Definitions Absolute refractive index (m) : It is the refractive index of the medium with respect to air or vacuum. Amplitude (A) : It is the maximum
More informationPhysics For Scientists and Engineers A Strategic Approach 3 rd Edition, AP Edition, 2013 Knight
For Scientists and Engineers A Strategic Approach 3 rd Edition, AP Edition, 2013 Knight To the Advanced Placement Topics for C *Advanced Placement, Advanced Placement Program, AP, and Pre-AP are registered
More informationb) (4) How large is the current through the 2.00 Ω resistor, and in which direction?
General Physics II Exam 2 - Chs. 19 21 - Circuits, Magnetism, EM Induction - Sep. 29, 2016 Name Rec. Instr. Rec. Time For full credit, make your work clear. Show formulas used, essential steps, and results
More informationOn my honor, I have neither given nor received unauthorized aid on this examination.
Instructor: Profs. Andrew Rinzler, Paul Avery, Selman Hershfield PHYSICS DEPARTMENT PHY 2049 Final Exam April 24, 200 Name (print, last first): Signature: On my honor, I have neither given nor received
More informationCBSE Annual Examination Question Paper 2013
CBSE Annual Examination Question Paper 2013 PHYSICS (THEY) Time allowed: 3 hours] [Maximum marks: 70 General Instructions: (i) All questions are compulsory. (ii) There are 29 questions in total. Question
More informationPHYS 1444 Section 02 Review #2
PHYS 1444 Section 02 Review #2 November 9, 2011 Ian Howley 1 1444 Test 2 Eq. Sheet Terminal voltage Resistors in series Resistors in parallel Magnetic field from long straight wire Ampére s Law Force on
More informationPhysics Final. Last Name First Name Student Number Signature
A - Phys121 - April 9, 2009 1 Physics 121 - Final Last Name First Name Student Number Signature Answer ALL questions. Show all your work and explain your reasoning for full credit. Neatness and clarity
More informationAISSCE 2016 EXPECTED (SURE SHORT) QUESTIONS WEIGHTAGE-WISE 2016
CLASS: XII AISSCE 2016 Subject: Physics EXPECTED (SURE SHORT) QUESTIONS WEIGHTAGE-WISE 2016 Q3 Section A ( 1 Mark ) A force F is acting between two charges placed some distances apart in vacuum. If a brass
More information