As customary, choice (a) is the correct answer in all the following problems.
|
|
- Elvin Douglas
- 7 years ago
- Views:
Transcription
1 PHY2049 Summer 2012 Instructor: Francisco Rojas Exam 1 As customary, choice (a) is the correct answer in all the following problems. Problem 1 A uniformly charge (thin) non-conucting ro is locate on the central axis a istance b from the center of an uniformly charge non-conucting isk. The length of the ro is L an has a linear charge ensity λ. The isk has raius a an a surface charge ensity σ. The total force among these two objects is (1) F = λσ (L+ a 2 +b 2 (b+l) 2 +a 2 )ˆk (2) F = λσa2 L ˆk 4ɛ 0 b 2 (3) F = λσa2 L ˆk 8ɛ 0 b 2 (4) F ( = σ 1 (5) F = λσl2 L 2 +a 2ˆk L L 2 +a 2 )ˆk We saw in class that the electric fiel create at any point along the central axis is given by E(z) = σ ( z 1 )ˆk a 2 +z 2 Breaking up the ro into an infinite number of infinitesimally small point charges q, we have that the net force on each tiny charge is F = q E(z). Summing up all these 1
2 contributions, an using the fact that q = λz gives F = q σ ( 1 b+l ( z 1 Problem 2 = λσ ˆk = λσ ˆk b z a 2 +z 2 )ˆk (1) (z a 2 +z 2 ) b+l ) z a 2 +z 2 b = λσ ( L a 2 +(b+l) 2 + a 2 +b 2 )ˆk (4) A uniformly charge (thin) non-conucting shell (hollow sphere) of raius R with the total positive charge Q is place at a istance away from an infinite non-conucting sheet carrying a uniformly istribute positive charge with a ensity σ. The istance is measure from shell s center (point O). What is the magnitue of the total electric fiel at the center of the shell? (2) (3) (1) σ (2) Q 4πɛ 0 R 2 + σ (3) Q 4πɛ 0 R 2 + σ ɛ 0 (4) Q 4πɛ 0 R 2 (5) Q 4πɛ 0 R + σ ɛ 0 This is problem is very easy to solve if one recalls the superposition principle. The total electric fiel at any point in space is equal to the sum of the iniviual contributions from each source. The electric fiel prouce by the sphere in its interior is always zero 1. The electric fiel prouce by a non-conucting infinitely long sheet is σ everywhere in space. Therefore, the sum of these two contributions at the center of the sphere is simply σ. 1 This can be seen as a consequence of Gauss Law for this spherically symmetric situation 2
3 Problem 3 A roun wastepaper basket with a 0.15 m raius opening is in a uniform electric fiel of 300 N/C, perpenicular to the opening. The total flux through the sies an bottom, in N m 2 /C, is: (1) - 21 (2) 4.2 (3) 0 (4) 280 (5) can t tell without knowing the areas of the sies an bottom Because the electric fiel is a constant everywhere, the electric flux through any close surface is zero. Thus, we can write Φ = E A = 0 Decomposing the entire surface of the basket into the sies, bottom, an top, yiels Φ = E A = E A+ E A+ E A = 0 sies bottom top thus Therefore sies E A+ sies E A = bottom E A+ bottom top E A (5) = EA top (6) = Eπr 2 (7) = = 300π (8) = 21 (9) E A = 21N/Cm 2 3
4 Problem 4 An electric fiel given by E = 10î 5(y 2 + 5)ĵ pierces the Gaussian cube of the figure, where the cube is 2 m on a sie. (E is in newtons per coulomb an y is in meters.) What is the net electric flux through the entire cube? (1) -80 N/C m 2 (2) 80 N/C m 2 (3) 0 (4) 20 N/C m 2 (5) -20 N/c m 2 We can break up the entire close surface into the six sies of the cube. The front an back sies o not contribute since E lies on the x,y plane, thus it is parallel to these sies. Also, the x component E x = 10 of the electric fiel is constant. This implies that the contributions from this component woul cancel in each other out among all sies. The same will happen with the constant part in E y = 5y Therefore, we en up with Problem 5 Φ = 5 y 2 xz +5 y 2 xz = 5 (2) 2 A = 5 (2) = 80 y=2 y=0 A graph of the x component of the electric fiel as a function of x in a region of space is shown in the figure. The scale of the vertical axis is set by E xs = 16.0 N/C. The y an z components of the electric fiel are zero in this region. If the electric potential at the origin is 10 V, what is the electric potential (in V) at x = 4.0 m? (1) 26 (2) -6 (3) 36 (4) 0 (5) 42 4
5 By efinition we have b V b V a = E s a Where a an b are just two points in which we measure the electric potential V. Since we are given that V(x = 0) = 10 V, we might as well use that as our point a, an x = 4 as b to fin V b. Since the y an z components of the electric fiel are zero everywhere, we have E s = E x x, an E x is given by the plot as a function of x. Therefore, we can write V b = V a b a E x x (10) But the integral above is simply the area uner the curve E x vs. x. We just nee to be careful with the sign of that area since it is negative in the range 0 x 3, an positive in the range x > 4. Thus, V(x = 4) = V(x = 0) 4 0 E x x (11) = 10 ( 24+8) = 26 (12) Problem 6 In the figure, a charge particle (either an electron or a proton; you nee to fin out which it is) is moving rightwar between two parallel charge plates. The plate potentials are V 1 = 25 V an V 2 = 35 V. The particle is slowing own from an initial spee of m/s at the left plate. What is its spee, in m/s, just as it reaches plate 2? (1) (2) (3) not possible to know without knowing the plates separation (4) (5) If we use conservation of energy (potential plus kinetic), this problem is really straighforwar. The potential energy of the particle when it starts from plate 1 is U 1 = qv 1 an 5
6 when it arrives at plate 2 is U 2 = qv 2. (Recall that the electric potential is a continuous function in space, therefore a particle very close to the plates will be at an electric potential equal to the one on the plate 2 ). Therefore, conservation of energy reas U 1 +K 1 = U 2 +K 2 (13) qv mv2 1 = qv mv2 2 (14) Solving for v 2 gives v 2 = v q m (V 1 V 2 ) (15) But now it comes a crucial point. What m o we use? The mass of a proton or that of an electron? This is very important since their masses iffer by a factor of almost 2000! To clarify this, we recall that E = V. This implies that the electric fiel, at a certain point in space, points in the opposite irection of V at that location. Imagine we raw an x axis going from plate 1 to plate 2. Since the electric fiel is constant everywhere between the plates, i.e. E = (Ex,0,0) where E x = constant, the potential V(x) is a monotonic function of x in going from one plate to the other. Thus, since the potential at plate 1 is V 1 = 25 V an ecreases to V 2 = 35 V at plate 2, V is negative along the entire range of x. In other wors, V points to negative irection of x (left). Therefore, from E = V we arrive at the conclusion that E points in the positive irection on x (right). Now, since the particle is slowing own, the total force on it must be in the opposite irection of motion. Since the particle is traveling to the right, the net force ought to point to the left. From F = q E, we see that this is only possible if q is negative since E points to the right. Therefore, the particle is an electron. Using then the electron s mass m e = kgs, an charge q = C, we have v 2 = v q m (V 1 V 2 ) = m/s (16) 2 Notice that since E = V, the electric potential V must be a continuous function. Otherwise it woul imply an infinite E. 6
7 Problem 7 The figure shows a parallel-plate capacitor of plate area A an plate separation 2. The left half of the gap is fille with material of ielectric constant κ 1 = 12; the top of the right half is fille with material of ielectric constant κ 2 = 20; the bottom of the right half is fille with material of ielectric constant κ 3 = 30. What is the capacitance in terms of ɛ 0, A, an? (1) 9 ɛ 0A (2) 62 ɛ 0A (3) 18 ɛ 0A (4) 31 ɛ 0A (5) none of these Assuming that the separation between the plates is much smaller than their extension, we can ignore fringe effects at the eges of the plates an at the junction of the two materials. Since the plates of a capacitor are mae of conucting material, the plates are equipotential surfaces. This an the first statement allows us to consier this system as mae of capacitor three capacitors C 1,C 2 an C 3 where C 2 an C 3 are in series, an this combination is in parallel with C 1. Thus With C eq = C 1 + C 2C 3 C 2 +C 3 (17) C 1 = κ 1 ɛ 0 A/2 2 C 2 = κ 2 ɛ 0 A/2 an C 3 = κ 3 ɛ 0 A/2 (18) we have C eq = ɛ 0A 2 = 9 ɛ 0A ( κ1 2 + κ ) 2κ 3 κ 2 +κ 3 (19) (20) 7
8 Problem 8 In the figure shown, a potential iference of V = 10 V is applie across the arrangement of capacitors with capacitances of C 1 = C 2 = 4µF, an C 3 = 6µF. What is the charge q 2 on capacitor C 2? (1) 20µC (2) 40µC (3) 60µC (4) 80µC (5) 10µC Capacitors C 1 an C 2 are in series, thus, share the same charge. If V 1 an V 2 are the voltages across each of them, we have V = V 1 +V 2 (21) 10 = Q/C 1 +Q/C 2 (22) Since C 1 = C 2 C = 4µF, we get Q = CV 2 = 20µC (23) Problem 9 What is the minimum mechanical work that has to be one on the charge q = 1µC in orer to bring it from point a to point b? In figure, the soli sphere of charge Q = 2µC with a raius R = 2m is hel fixe in space. Point a is locate at 12m from the center of the sphere an point b at 10m as shown. (1) J (2) J (3) J (4) J (5) J 8
9 Since both charges have the same sign, an we are bringing the charge q closer to Q, we immeiately know that we have to make a positive work ue to the electric repulsion. Inee, the work is W = q(v b V a ) = q ( kq kq ) r b r a = ( ) (24) (25) = J (26) Problem 10 The figure shows a non-conucting (thin) isk with a hole. The raius of the isk is b an the raius of the hole is a. A total charge Q is uniformly istribute on its surface. Assuming that the electric potential at infinity is zero, what is the electric potential at the center of the isk? (1) 2kQ b+a 2kQ (2) b a (3) 2kQ (4) 0 (5) kq b 2 a 2 b 2 We saw in class that the potential prouce by a charge isk of raius R, at a istance z from it, along its central axis was σ ( ) z 2ɛ 2 +R 2 z 0 By supersposition, we can think of the potential create by isk with the hole as the sum of two isks, with the same but opposite surface ensities: V(z) = σ ( ) z 2ɛ 2 +b 2 z 0 = σ ( z 2 +b 2 z 2 +a 2 ) Since we are only intereste at the center, we have σ ( z 2 +a 2 z ) (27) (28) (29) V(0) = σ (b a) (30) The total area of the isk with the hole is A = π(b 2 a 2 ), thus σ = Q π(b 2 a 2 ) 9
10 Finally V(0) = 1 (b a) 2kQ(b a) = (b a)(b+a) = 2kQ b+a Q π(b 2 a 2 ) (31) (32) (33) Problem 11 A wire segment of length L has constant linear charge ensity λ > 0. Which of the following expressions gives the magnitue of the electric fiel a istance D from the center of the wire (see figure)? L/2 (1) kλd L/2 (4) 0 (5) kλd x (D 2 +x 2 ) 3/2 (2) kλd L/2 L/2 x D +x L 0 x D 2 +x 2 L x (3) kλd D 2 +x 2 0 Putting the ro along the x axis with its center at the origin, the problem boils own to compute E at the point (x,y) = (0,D) The contribution from the segment x is E q = k D 2 +x 2 = kλ x D 2 +x 2 (34) 10
11 Also, we see immeiately that the x-component of the total electric fiel will be zero ue to mutual cancellations among mirror-symmetric segments of the ro. Thus, we only nee the y-component, therefore E y = E D D 2 +x = kλd x 2 (D 2 +x 2 ) 3/2 (35) To get the total electric fiel, we simply a up all of these contributions, hence Problem 12 E y = L/2 x E y = kλd L/2 (D 2 +x 2 ) 3/2 (36) A charge Q is place in the center of a shell of raius R. The flux of electric fiel through the shell surface is Φ 0. What is the new flux through the shell surface, if its raius is ouble? (1) Φ 0 (2) 2Φ 0 (3) 4Φ 0 (4) Φ 0 /2 (5) Φ 0 /4 Gauss law states that the electric flux through a close surface is Φ E s = Q enc (37) ɛ 0 from where we see that the flux only cares about the total charge enclose by the surface. By increasing the raius of the sphere we are merely increasing the size of the surface, but the enclose charge remains the same. Therefore the new flux is just the ol Φ 0. 11
12 Problem 13 Two very small spheres have equal masses m, carry charges of the same sign an value q, an hang on strings of length L as shown in figure. Due to the repulsive force, the spheres are separate by some istance. Fin this istance. Assume that L so that you can use the approximation tanα sinα α (1) 3 2L q2 k mg (2) 3 L q2 k mg (3) 2L q2 k mg (4) L q2 k Lq mg (5) 2 k 2mg To achieve equilibrium, we see from the figure that we nee Now, combining these two equations as T cosα = mg an T sinα = F e (38) tanα = F e mg (39) 12
13 an using the Coulomb s force among the two small spheres F e = kq 2 / 2, gives tanα = kq2 2 mg (40) Finally, for small values for α, tanα sinα = /2 L, we have from where we obtain Problem 14 /2 L kq2 2 mg 3 2L kq2 mg (41) (42) In figure, how much charge is store on the parallel-plate capacitors by the 10 V battery? One is fille with air, an the other is fille with a ielectric for which κ = 2.0; both capacitors have a plate area of m 2 an a plate separation of 1.00 mm. (1) 0.53 nc (2) 0.35 nc (3) 1.06 nc (4) 0.53 µc (5) 0.35 µc The charge store on capacitor C 1 is q 1 = C 1 V = κ ɛ 0A V = = an on capacitor C 2 is q 2 = C 2 V = ɛ 0A V = = Thus, the total is q tot = = 0.53nC 13
( )( 10!12 ( 0.01) 2 2 = 624 ( ) Exam 1 Solutions. Phy 2049 Fall 2011
Phy 49 Fall 11 Solutions 1. Three charges form an equilateral triangle of side length d = 1 cm. The top charge is q = - 4 μc, while the bottom two are q1 = q = +1 μc. What is the magnitude of the net force
More informationCHAPTER 24 GAUSS S LAW
CHAPTER 4 GAUSS S LAW 4. The net charge shown in Fig. 4-40 is Q. Identify each of the charges A, B, C shown. A B C FIGURE 4-40 4. From the direction of the lines of force (away from positive and toward
More informationExam 1 Practice Problems Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8 Spring 13 Exam 1 Practice Problems Solutions Part I: Short Questions and Concept Questions Problem 1: Spark Plug Pictured at right is a typical
More informationExam 2 Practice Problems Part 1 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Exam Practice Problems Part 1 Solutions Problem 1 Electric Field and Charge Distributions from Electric Potential An electric potential V ( z
More informationChapter 22: Electric Flux and Gauss s Law
22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we
More informationCalculating Viscous Flow: Velocity Profiles in Rivers and Pipes
previous inex next Calculating Viscous Flow: Velocity Profiles in Rivers an Pipes Michael Fowler, UVa 9/8/1 Introuction In this lecture, we ll erive the velocity istribution for two examples of laminar
More informationScalar : Vector : Equal vectors : Negative vectors : Proper vector : Null Vector (Zero Vector): Parallel vectors : Antiparallel vectors :
ELEMENTS OF VECTOS 1 Scalar : physical quantity having only magnitue but not associate with any irection is calle a scalar eg: time, mass, istance, spee, work, energy, power, pressure, temperature, electric
More informationChapter 22: The Electric Field. Read Chapter 22 Do Ch. 22 Questions 3, 5, 7, 9 Do Ch. 22 Problems 5, 19, 24
Chapter : The Electric Field Read Chapter Do Ch. Questions 3, 5, 7, 9 Do Ch. Problems 5, 19, 4 The Electric Field Replaces action-at-a-distance Instead of Q 1 exerting a force directly on Q at a distance,
More informationCHAPTER 26 ELECTROSTATIC ENERGY AND CAPACITORS
CHAPTER 6 ELECTROSTATIC ENERGY AND CAPACITORS. Three point charges, each of +q, are moved from infinity to the vertices of an equilateral triangle of side l. How much work is required? The sentence preceding
More informationHW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.
HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 22.P.053 The figure below shows a portion of an infinitely
More informationElectromagnetism Laws and Equations
Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2
More informationi( t) L i( t) 56mH 1.1A t = τ ln 1 = ln 1 ln 1 6.67ms
Exam III PHY 49 Summer C July 16, 8 1. In the circuit shown, L = 56 mh, R = 4.6 Ω an V = 1. V. The switch S has been open for a long time then is suenly close at t =. At what value of t (in msec) will
More informationLecture L25-3D Rigid Body Kinematics
J. Peraire, S. Winall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L25-3D Rigi Boy Kinematics In this lecture, we consier the motion of a 3D rigi boy. We shall see that in the general three-imensional
More informationHomework 8. problems: 10.40, 10.73, 11.55, 12.43
Hoework 8 probles: 0.0, 0.7,.55,. Proble 0.0 A block of ass kg an a block of ass 6 kg are connecte by a assless strint over a pulley in the shape of a soli isk having raius R0.5 an ass M0 kg. These blocks
More informationReview & Summary. Questions. Checkpoint 4
QUESTIONS 677 Checkpoint 4 The figure shows two large, parallel, nonconucting sheets with ientical (positive) uniform surface charge ensities, an a sphere with a uniform (positive) volume charge ensit.
More informationReview Questions PHYS 2426 Exam 2
Review Questions PHYS 2426 Exam 2 1. If 4.7 x 10 16 electrons pass a particular point in a wire every second, what is the current in the wire? A) 4.7 ma B) 7.5 A C) 2.9 A D) 7.5 ma E) 0.29 A Ans: D 2.
More informationChapter 18. Electric Forces and Electric Fields
My lecture slides may be found on my website at http://www.physics.ohio-state.edu/~humanic/ ------------------------------------------------------------------- Chapter 18 Electric Forces and Electric Fields
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. 8.02 Spring 2013 Conflict Exam Two Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 802 Spring 2013 Conflict Exam Two Solutions Problem 1 (25 points): answers without work shown will not be given any credit A uniformly charged
More informationThe Electric Field. Electric Charge, Electric Field and a Goofy Analogy
. The Electric Field Concepts and Principles Electric Charge, Electric Field and a Goofy Analogy We all know that electrons and protons have electric charge. But what is electric charge and what does it
More informationHalliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
More informationAnswers to the Practice Problems for Test 2
Answers to the Practice Problems for Test 2 Davi Murphy. Fin f (x) if it is known that x [f(2x)] = x2. By the chain rule, x [f(2x)] = f (2x) 2, so 2f (2x) = x 2. Hence f (2x) = x 2 /2, but the lefthan
More informationHW7 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.
HW7 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 24.P.021 (a) Find the energy stored in a 20.00 nf capacitor
More informationSolution. Problem. Solution. Problem. Solution
4. A 2-g ping-pong ball rubbed against a wool jacket acquires a net positive charge of 1 µc. Estimate the fraction of the ball s electrons that have been removed. If half the ball s mass is protons, their
More informationTEACHER S CLUB EXAMS GRADE 11. PHYSICAL SCIENCES: PHYSICS Paper 1
TEACHER S CLUB EXAMS GRADE 11 PHYSICAL SCIENCES: PHYSICS Paper 1 MARKS: 150 TIME: 3 hours INSTRUCTIONS AND INFORMATION 1. This question paper consists of 12 pages, two data sheets and a sheet of graph
More informationInductors and Capacitors Energy Storage Devices
Inuctors an Capacitors Energy Storage Devices Aims: To know: Basics of energy storage evices. Storage leas to time elays. Basic equations for inuctors an capacitors. To be able to o escribe: Energy storage
More informationCandidate Number. General Certificate of Education Advanced Level Examination June 2014
entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 214 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Wednesday
More informationFRICTION, WORK, AND THE INCLINED PLANE
FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More informationThe potential (or voltage) will be introduced through the concept of a gradient. The gradient is another sort of 3-dimensional derivative involving
The potential (or voltage) will be introduced through the concept of a gradient. The gradient is another sort of 3-dimensional derivative involving the vector del except we don t take the dot product as
More informationChapter 22 Magnetism
22.6 Electric Current, Magnetic Fields, and Ampere s Law 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
More informationFigure 27.6b
Figure 27.6a Figure 27.6b Figure 27.6c Figure 27.25 Figure 27.13 When a charged particle moves through a magnetic field, the direction of the magnetic force on the particle at a certain point is A. in
More informationChapter 4. Electrostatic Fields in Matter
Chapter 4. Electrostatic Fields in Matter 4.1. Polarization A neutral atom, placed in an external electric field, will experience no net force. However, even though the atom as a whole is neutral, the
More informationChapter 23 Electric Potential. Copyright 2009 Pearson Education, Inc.
Chapter 23 Electric Potential 23-1 Electrostatic Potential Energy and Potential Difference The electrostatic force is conservative potential energy can be defined. Change in electric potential energy is
More informationPre-lab Quiz/PHYS 224 Magnetic Force and Current Balance. Your name Lab section
Pre-lab Quiz/PHYS 224 Magnetic Force and Current Balance Your name Lab section 1. What do you investigate in this lab? 2. Two straight wires are in parallel and carry electric currents in opposite directions
More informationPhys222 Winter 2012 Quiz 4 Chapters 29-31. Name
Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region
More informationPhysics 202, Lecture 3. The Electric Field
Physics 202, Lecture 3 Today s Topics Electric Field Quick Review Motion of Charged Particles in an Electric Field Gauss s Law (Ch. 24, Serway) Conductors in Electrostatic Equilibrium (Ch. 24) Homework
More informationNotes on tangents to parabolas
Notes on tangents to parabolas (These are notes for a talk I gave on 2007 March 30.) The point of this talk is not to publicize new results. The most recent material in it is the concept of Bézier curves,
More informationVector surface area Differentials in an OCS
Calculus and Coordinate systems EE 311 - Lecture 17 1. Calculus and coordinate systems 2. Cartesian system 3. Cylindrical system 4. Spherical system In electromagnetics, we will often need to perform integrals
More informationExercises on Voltage, Capacitance and Circuits. A d = (8.85 10 12 ) π(0.05)2 = 6.95 10 11 F
Exercises on Voltage, Capacitance and Circuits Exercise 1.1 Instead of buying a capacitor, you decide to make one. Your capacitor consists of two circular metal plates, each with a radius of 5 cm. The
More informationPhysics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings
1 of 11 9/7/2012 1:06 PM Logged in as Julie Alexander, Instructor Help Log Out Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings Course Home Assignments Roster Gradebook Item Library
More informationChapter 18 Static Equilibrium
Chapter 8 Static Equilibrium 8. Introduction Static Equilibrium... 8. Lever Law... Example 8. Lever Law... 4 8.3 Generalized Lever Law... 5 8.4 Worked Examples... 7 Example 8. Suspended Rod... 7 Example
More informationPhysics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb:
Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6 Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions 24 multiple choice questions. You may need to do some calculation.
More informationCenter of Gravity. We touched on this briefly in chapter 7! x 2
Center of Gravity We touched on this briefly in chapter 7! x 1 x 2 cm m 1 m 2 This was for what is known as discrete objects. Discrete refers to the fact that the two objects separated and individual.
More informationElectromagnetism - Lecture 2. Electric Fields
Electromagnetism - Lecture 2 Electric Fields Review of Vector Calculus Differential form of Gauss s Law Poisson s and Laplace s Equations Solutions of Poisson s Equation Methods of Calculating Electric
More informationGiven three vectors A, B, andc. We list three products with formula (A B) C = B(A C) A(B C); A (B C) =B(A C) C(A B);
1.1.4. Prouct of three vectors. Given three vectors A, B, anc. We list three proucts with formula (A B) C = B(A C) A(B C); A (B C) =B(A C) C(A B); a 1 a 2 a 3 (A B) C = b 1 b 2 b 3 c 1 c 2 c 3 where the
More informationCLASS TEST GRADE 11. PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism
CLASS TEST GRADE 11 PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism MARKS: 45 TIME: 1 hour INSTRUCTIONS AND INFORMATION 1. Answer ALL the questions. 2. You may use non-programmable calculators.
More informationMagnetic Field and Magnetic Forces
Chapter 27 Magnetic Field and Magnetic Forces PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 27 Magnets
More informationElectric Fields in Dielectrics
Electric Fields in Dielectrics Any kind of matter is full of positive and negative electric charges. In a dielectric, these charges cannot move separately from each other through any macroscopic distance,
More informationCOURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st
COURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st WEEKLY PROGRAMMING WEE K SESSI ON DESCRIPTION GROUPS GROUPS Special room for LECTU PRAC session RES TICAL (computer classroom, audiovisual
More informationMeasurement of Capacitance
Measurement of Capacitance Pre-Lab Questions Page Name: Class: Roster Number: Instructor:. A capacitor is used to store. 2. What is the SI unit for capacitance? 3. A capacitor basically consists of two
More informationE/M Experiment: Electrons in a Magnetic Field.
E/M Experiment: Electrons in a Magnetic Field. PRE-LAB You will be doing this experiment before we cover the relevant material in class. But there are only two fundamental concepts that you need to understand.
More informationReview D: Potential Energy and the Conservation of Mechanical Energy
MSSCHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.01 Fall 2005 Review D: Potential Energy and the Conservation of Mechanical Energy D.1 Conservative and Non-conservative Force... 2 D.1.1 Introduction...
More informationLecture L22-2D Rigid Body Dynamics: Work and Energy
J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L - D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L-3 for
More informationElectromagnetism Extra Study Questions Short Answer
Electromagnetism Extra Study Questions Short Answer 1. The electrostatic force between two small charged objects is 5.0 10 5 N. What effect would each of the following changes have on the magnitude of
More informationExample Optimization Problems selected from Section 4.7
Example Optimization Problems selecte from Section 4.7 19) We are aske to fin the points ( X, Y ) on the ellipse 4x 2 + y 2 = 4 that are farthest away from the point ( 1, 0 ) ; as it happens, this point
More informationChapter 6 Circular Motion
Chapter 6 Circular Motion 6.1 Introduction... 1 6.2 Cylindrical Coordinate System... 2 6.2.1 Unit Vectors... 3 6.2.2 Infinitesimal Line, Area, and Volume Elements in Cylindrical Coordinates... 4 Example
More informationChapter 15, example problems:
Chapter, example problems: (.0) Ultrasound imaging. (Frequenc > 0,000 Hz) v = 00 m/s. λ 00 m/s /.0 mm =.0 0 6 Hz. (Smaller wave length implies larger frequenc, since their product,
More information2 A bank account for electricity II: flows and taxes
PHYS 189 Lecture problems outline Feb 3, 2014 Resistors and Circuits Having introduced capacitors, we now expand our focus to another very important component of a circuit resistors. This entails more
More informationChapter 9 Circular Motion Dynamics
Chapter 9 Circular Motion Dynamics 9. Introduction Newton s Second Law and Circular Motion... 9. Universal Law of Gravitation and the Circular Orbit of the Moon... 9.. Universal Law of Gravitation... 3
More informationMidterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m
Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of
More informationReading: Ryden chs. 3 & 4, Shu chs. 15 & 16. For the enthusiasts, Shu chs. 13 & 14.
7 Shocks Reaing: Ryen chs 3 & 4, Shu chs 5 & 6 For the enthusiasts, Shu chs 3 & 4 A goo article for further reaing: Shull & Draine, The physics of interstellar shock waves, in Interstellar processes; Proceeings
More informationPhysics 53. Gravity. Nature and Nature's law lay hid in night: God said, "Let Newton be!" and all was light. Alexander Pope
Physics 53 Gravity Nature and Nature's law lay hid in night: God said, "Let Newton be!" and all was light. Alexander Pope Kepler s laws Explanations of the motion of the celestial bodies sun, moon, planets
More informationLines. We have learned that the graph of a linear equation. y = mx +b
Section 0. Lines We have learne that the graph of a linear equation = m +b is a nonvertical line with slope m an -intercept (0, b). We can also look at the angle that such a line makes with the -ais. This
More informationELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES
ELECTRIC FIELD LINES AND EQUIPOTENTIAL SURFACES The purpose of this lab session is to experimentally investigate the relation between electric field lines of force and equipotential surfaces in two dimensions.
More informationLagrange s equations of motion for oscillating central-force field
Theoretical Mathematics & Applications, vol.3, no., 013, 99-115 ISSN: 179-9687 (print), 179-9709 (online) Scienpress Lt, 013 Lagrange s equations of motion for oscillating central-force fiel A.E. Eison
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationPhysics 201 Homework 8
Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the
More informationPhysics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationHalliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
More informationTwo-Body System: Two Hanging Masses
Specific Outcome: i. I can apply Newton s laws of motion to solve, algebraically, linear motion problems in horizontal, vertical and inclined planes near the surface of Earth, ignoring air resistance.
More informationLast Name: First Name: Physics 102 Spring 2006: Exam #2 Multiple-Choice Questions 1. A charged particle, q, is moving with speed v perpendicular to a uniform magnetic field. A second identical charged
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationCandidate Number. General Certificate of Education Advanced Level Examination June 2010
entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 1 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Friday 18
More informationExamples of magnetic field calculations and applications. 1 Example of a magnetic moment calculation
Examples of magnetic field calculations and applications Lecture 12 1 Example of a magnetic moment calculation We consider the vector potential and magnetic field due to the magnetic moment created by
More informationMagnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.
Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.
More information11 CHAPTER 11: FOOTINGS
CHAPTER ELEVEN FOOTINGS 1 11 CHAPTER 11: FOOTINGS 11.1 Introuction Footings are structural elements that transmit column or wall loas to the unerlying soil below the structure. Footings are esigne to transmit
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationChapter 27 Magnetic Field and Magnetic Forces
Chapter 27 Magnetic Field and Magnetic Forces - Magnetism - Magnetic Field - Magnetic Field Lines and Magnetic Flux - Motion of Charged Particles in a Magnetic Field - Applications of Motion of Charged
More informationA METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS
A METHOD OF CALIBRATING HELMHOLTZ COILS FOR THE MEASUREMENT OF PERMANENT MAGNETS Joseph J. Stupak Jr, Oersted Technology Tualatin, Oregon (reprinted from IMCSD 24th Annual Proceedings 1995) ABSTRACT The
More informationPhysics 112 Homework 5 (solutions) (2004 Fall) Solutions to Homework Questions 5
Solutions to Homework Questions 5 Chapt19, Problem-2: (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in Figure P19.2, as shown. (b) Repeat
More informationStack Contents. Pressure Vessels: 1. A Vertical Cut Plane. Pressure Filled Cylinder
Pressure Vessels: 1 Stack Contents Longitudinal Stress in Cylinders Hoop Stress in Cylinders Hoop Stress in Spheres Vanishingly Small Element Radial Stress End Conditions 1 2 Pressure Filled Cylinder A
More informationMechanics 1: Conservation of Energy and Momentum
Mechanics : Conservation of Energy and Momentum If a certain quantity associated with a system does not change in time. We say that it is conserved, and the system possesses a conservation law. Conservation
More informationWORK DONE BY A CONSTANT FORCE
WORK DONE BY A CONSTANT FORCE The definition of work, W, when a constant force (F) is in the direction of displacement (d) is W = Fd SI unit is the Newton-meter (Nm) = Joule, J If you exert a force of
More information6/2016 E&M forces-1/8 ELECTRIC AND MAGNETIC FORCES. PURPOSE: To study the deflection of a beam of electrons by electric and magnetic fields.
6/016 E&M forces-1/8 ELECTRIC AND MAGNETIC FORCES PURPOSE: To study the deflection of a beam of electrons by electric and magnetic fields. APPARATUS: Electron beam tube, stand with coils, power supply,
More informationThe small increase in x is. and the corresponding increase in y is. Therefore
Differentials For a while now, we have been using the notation dy to mean the derivative of y with respect to. Here is any variable, and y is a variable whose value depends on. One of the reasons that
More informationDIFFRACTION AND INTERFERENCE
DIFFRACTION AND INTERFERENCE In this experiment you will emonstrate the wave nature of light by investigating how it bens aroun eges an how it interferes constructively an estructively. You will observe
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) If the voltage at a point in space is zero, then the electric field must be A) zero. B) positive.
More informationAP2 Magnetism. (c) Explain why the magnetic field does no work on the particle as it moves in its circular path.
A charged particle is projected from point P with velocity v at a right angle to a uniform magnetic field directed out of the plane of the page as shown. The particle moves along a circle of radius R.
More informationExam 2 Practice Problems Part 2 Solutions
Problem 1: Short Questions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8. Exam Practice Problems Part Solutions (a) Can a constant magnetic field set into motion an electron, which is initially
More informationPhysics 1120: Simple Harmonic Motion Solutions
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured
More information1. A wire carries 15 A. You form the wire into a single-turn circular loop with magnetic field 80 µ T at the loop center. What is the loop radius?
CHAPTER 3 SOURCES O THE MAGNETC ELD 1. A wire carries 15 A. You form the wire into a single-turn circular loop with magnetic field 8 µ T at the loop center. What is the loop radius? Equation 3-3, with
More informationThe Force Table Introduction: Theory:
1 The Force Table Introduction: "The Force Table" is a simple tool for demonstrating Newton s First Law and the vector nature of forces. This tool is based on the principle of equilibrium. An object is
More informationCode number given on the right hand side of the question paper should be written on the title page of the answerbook by the candidate.
Series ONS SET-1 Roll No. Candiates must write code on the title page of the answer book Please check that this question paper contains 16 printed pages. Code number given on the right hand side of the
More information1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D
Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be
More informationForces between charges
Forces between charges Two small objects each with a net charge of Q (where Q is a positive number) exert a force of magnitude F on each other. We replace one of the objects with another whose net charge
More informationCurso2012-2013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.
1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.
More informationMath 230.01, Fall 2012: HW 1 Solutions
Math 3., Fall : HW Solutions Problem (p.9 #). Suppose a wor is picke at ranom from this sentence. Fin: a) the chance the wor has at least letters; SOLUTION: All wors are equally likely to be chosen. The
More informationAP1 Oscillations. 1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a spring-block oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More information