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Welcome to Physics 112N Professor Charles E. Hyde-Wright Spring 2005 Navigate from http:www.physics.odu.edu, or http:www.physics.odu.edu/hyde/Teaching/Spring05/Phys112_2005.htm Topics to be covered • Electricity and Magnetism (Chapters 19-24) • Light and Optics (Chapters 25, 26, 28) • Modern Physics (Chapter 30) 10 January 2005 Walker, Chapter 19 2 Phys 111: Chapters 1-18 • Description of motion: Kinematics Position (in 1-, 2-, 3- dimensions) Velocity (rate of change of position) Acceleration (rate of change of velocity) • Relationship between Force and Motion Net Force equals mass times acceleration • Description of motion in terms of Energy Kinetic Energy Potential Energy (Gravity, Springs…) Thermal Energy (non conservative forces) • Examples of forces: Contact forces (friction, “normal” force = force perpendicular to surface) Spring Force F = - kx Gravity 10 January 2005 Walker, Chapter 19 3 Gravity • • • • |F| = G M m / r2 Near surface of earth ( h << R ) |F| = G M m /(R+h)2 m [ GM/R2 ] = mg Circular, Elliptical, Parabolic, & Hyperbolic orbits of moons, planets, asteroids, comets, possible visitors from outer space. • Potential Energy: U = - G M m /r Note minus sign, Potential energy decreases as two masses approach: Conservation of energy means Kinetic Energy increases as Potential energy decreaces. 10 January 2005 Walker, Chapter 19 4 Chapter 19 Electric Charges, Forces, and Fields • • • • Fundamental Forces in Physics Gravity (gravitons) Electromagnetism (photons) Weak Interaction (W and Z bosons) Strong Interaction (gluons) All of physics is based on these four forces All four forces have similar equations. 10 January 2005 Walker, Chapter 19 5 Energy in our World • Nuclear Fusion in sun E=mc2 H H H H He + n + n + Energy Thermal Energy at surface converted to visible light energy Fusion • Light Energy Chemical Energy (photosynthesis) • Plants Fossil Fuels Fuel for cars (motion) Fuel for power plants Radiation (electrical energy lighting for your Physics HW). • Plants Food –> Krebs cycle ADP/ATP Energy for thought, motion of muscles HW 10 January 2005 Walker, Chapter 19 6 Electromagnetism in our World • Gravity holds us to the earth. • Electromagnetism dominates every other aspect of our physical world Atoms, Molecules, Solids, & Liquids held together by electrostatics Chemistry Light Virtually all technology: • Electronics, Electric motors, Electric Lighting • Even fire is fundamentally an electromagnetic phenomenon • Profound insights into the physical nature of life. 10 January 2005 Walker, Chapter 19 7 Electrostatic Phenomena • Rubbing things makes an electrostatic charge Spark, Hair standing on end Thunderclouds rub rising microscopic icecrystals against falling hail Clouds charge up • Electrostatic phenomena do not require any obvious macroscopic change (mass, material change) 10 January 2005 Walker, Chapter 19 8 Basic Model of Electrostatics Franklin, Coulomb, 18th Century • When two dissimilar materials are in contact, microscopic particles can be transferred from one to the other Modern view: electrons e-, or ions Ca++… • These particles carry a property (like mass) called electriccharge. Electric charge can be positive or negative Electric charge is a scalar: It is a quantity independent of any direction in space (compare temperature vs. velocity) Positive attracts negative Positive repels positive, Negative repels negative Charge adds linearly: put together charge q1 and charge q2, they act like q3 = q1 + q2. Charge is conserved: 0 = +q + (-q) 10 January 2005 Walker, Chapter 19 9 Insulators & Conductors • Charges placed on an insulator (plastic, wood, ceramic) stay put—in spite of the electric forces on them: Fnet=0 Binding force acts like a microscopic spring. As external electric force pulls on charge on insulator, the binding force pulls back (up to some limit: spring breaks) Charges placed on a metal are free to move in response to electro-magnetic (or other forces): ma = F 10 January 2005 Walker, Chapter 19 10 Electrical Charge All physical quantities must be measured as multiples of a standard Time is measured in multiples of the standard second (now defined by atomic physics phenomena) Distance is measured in multiples of the standard meter (now defined in reference to the speed of light times the second). Mass is measured in multiples of the standard kilogram, housed near Paris, France. The SI unit of electrical charge is the Coulomb The Coulomb (C ) is defined from magnetic phenomena (skip till later). 10 January 2005 Walker, Chapter 19 11 The Structure of an Atom The atom consists of a positively charged nucleus, orbited by negatively charged electrons. The nucleus contains protons (positive) and neutrons (neutral). The orbital lines are an accurate description of the orbits of electrons in a highly excited atom The fuzzy red blob is a better representation of the electron wave in the atomic ground state (see Chap. 30). 10 January 2005 Walker, Chapter 19 12 The Electron One of the fundamental particles found in nature is the electron. • The electron mass is 9.11 10-31 kg. • The electron charge (-e) is -1.6 10-19 C. The symbol e is the magnitude of the electron’s charge • The electron is part of a family of fundamental particles known as leptons. • Electron lifetime > 1023 years (test of charge conservation). Eur. Phys. J. C 3, 1 (1998) 10 January 2005 Walker, Chapter 19 13 The Proton The proton is not a fundamental particle. It has a finite size (10-15 m) and a spectrum of excited states. It is understood to consist of three quarks bound together by a cloud of gluons and quark—anti-quark pairs. • The proton mass is 1.67 10-27 kg. • The proton is 2000 times heavier than the electron, so the vast majority of an atom’s mass resides in the nucleus. • The proton charge (+e) is +1.6 10-19 C. • The proton charge and electron charge are known to be equal and opposite to very high precision. • |qp + qe|/e < 10-21 10 January 2005 Eur. Phys. J. C 3, 1 (1998) Walker, Chapter 19 14 • An object may contain both positive and negative charges. If the object possesses a net charge it is said to be charged. If the object possesses no net charge it is said to be neutral. • An atom is normally neutral, because it possesses an equal number of electrons and protons. However, if one or more electrons are removed from or added to an atom, an ion is formed, which is charged. • Charge is always conserved: charge may be transferred but it is never created or destroyed. However, charges can be created and destroyed in positive and negative pairs, so that the net charge in the universe does not change. 10 January 2005 Walker, Chapter 19 15 Electrical Forces Two charged objects will exert forces on one another. • Unlike charges attract one another. + - • Like charges repel one another. + + • The force decreases with the square of the distance between the charges 10 January 2005 Walker, Chapter 19 16 Polarization An object is polarized when its charges are rearranged so that there is a net charge separation. Charged objects can be attracted to neutral objects because of polarization. 10 January 2005 charged Walker, Chapter 19 neutral & polarized 17 Insulators and Conductors Materials are classified by how easily charged particles can “flow” through them. • If charges flow freely, the material is a conductor (metals, for example) • If charges are unable to move freely, the material is an insulator (glass, for example) • Some materials have properties in between insulators and conductors, these are called semiconductors. 10 January 2005 Walker, Chapter 19 18 Charge Transfer Charge is usually transferred because electrons move from one place to another. But sometimes the flow of both positively or negatively charged ions (atoms or molecules) is important (cells, batteries…). The earth can be viewed as an infinite (conducting) reservoir of electrons. An object in electrical contact with the earth is said to be grounded. What happens when I ground the Van de Graaff generator? [And why do I do this before touching the generator?] 10 January 2005 Walker, Chapter 19 19 Properties of the Mutual Electrical Forces Acting on Two Charges • Each of the two charged object experiences a force that is equal and opposite to the force experienced by the other charge (Newton’s Third Law). • The force is attractive if the charges are unlike and repulsive if the charges are like. • The force is inversely proportional to the square of the separation of the two charges, and is directed along the line joining them (attractive or repulsive). • The force is proportional to the product of the magnitudes of the 2 charges. Remember force is a vector! 10 January 2005 Walker, Chapter 19 20 Coulomb’s Law The magnitude of the force between two point* objects separated by a distance r with charges q1 and q2 is given by Coulomb’s Law: F k q1q2 r 2 q1 and q2 are the values (+ or -) of the two charges where k = 8.99… 109 Nm2/C2 , precision of 10-7 is linked to measurement of electron charge. *or spherical charge distributions, or any objects whose size is much less than the separation distance r The direction of the force on one charge is either toward (negative) or away (positive) from the other charge. 10 January 2005 Walker, Chapter 19 21 Force: vector, magnitude, component | q1 || q2 | • Magnitude (strictly positive) | F | k 2 r F k q1 r 10 January 2005 q1q2 r 2 q2 • Component along direction from q1 to q2 of Force from q1 acting on q2. • If q1q2> 0, force is repulsive (pushes q2 away from q1) • If q1q2< 0, force is attractive (pulls q2 towards q1) Walker, Chapter 19 22 Comments on Coulomb’s Law • 1/r2 Charge is conserved, Gauss’ Law Deviations from 1/r2 are measured to be less than 1 part in 1010 over distance scales from (10-10 m to 1.0 m) • The force is linear in the value of each charge. If an amount of charge 0.2q1 is brought from far away and added to q1, the force on q2 is increased to (q1 + 0.2q1 )q2 1.2q1q2 F k k 2 2 r r • Why k? (Why not k=1?) In Gaussian (or cgs) units, 1.00 esu is defined such that Two charges of 1.00 esu each separated by 1cm exert mutual forces on each other of 1 dyne = 1 gm cm2/sec2 k = 8.99 109 Nm2/C2 = 1.00 dyne (cm)2/esu2. The value of k depends upon our choice of units for Force, Distance and Charge. 10 January 2005 Walker, Chapter 19 23 Subscript labels on Force F k F12 Force on charge q1 from charge q2 F21 Force on charge q2 from charge q1 F21 -F12 : Newton's Third Law : Action - Reaction q1 10 January 2005 F12 F21 Walker, Chapter 19 q1q2 2 r q2 24 Vectors and Scalars • A scalar is a physical quantity with magnitude, but without direction in space. Temperature Mass Energy, Time, Charge … • A Vector is a physical quantity with magnitude and direction in space. Displacement Momentum Velocity, Force 10 January 2005 Walker, Chapter 19 25 Vector Components & Unit Vectors • A vector can be expressed in terms of a coordinate system. • Force vector F = 1.6 N oriented 110° counterclockwise from x-axis. • Force Vector F = (1.6 N)(cos110°) along +x-axis plus (1.6N)(sin110°) along +y-axis F 1.5 Nˆy q110 x -0.55 Nˆx xˆ displacement of 1.0 along x - axis (no units) yˆ displacement of 1.0 along y - axis (no units) F (1.6N)(cos110) xˆ + (1.6N)(sin110) yˆ (1.6 N )(-0.342) xˆ + (1.6N)(0.940) yˆ -0.55 Nxˆ + 1.5 Nyˆ 10 January 2005 Walker, Chapter 19 26 Walker Problem 13, pg. 641 Given that q = +12 mC and d = 16 cm, (a) find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in Figure 19-30. (b) How would your answers to part (a) change if the distance d were tripled? 10 January 2005 Walker, Chapter 19 27 Solution Draw free body for JUST q2 F21 k (12mC )- 24mC 2 (0.16m) in direction from 1 to 2 - 101N xˆ 10 January 2005 F23 Walker, Chapter 19 k (-24mC )+ 36mC (0.16m) 2 in direction from 3 to 2 + 303N xˆ 28 Problem 13, Solution, cont’d F2 (-101N + 303N ) xˆ 202N in + x - direction B) Tripling the separations decreases all forces by a factor of 32=9 F2 = 22.4 N, +x direction 10 January 2005 Walker, Chapter 19 29 Relative Strength of Gravity and Electrostatics • In the hydrogen atom, the electron and proton are separated by 0.5·10-10 m • The ratio of gravitational attraction between the electron and proton divided by the electrostatic attraction is FG/FQ = 10-39 (see text) • This ratio is independent of the separation Both forces are 1/r2. • Why is gravity so much more important in the solar system? 10 January 2005 Walker, Chapter 19 30 Multiple Charges • If there are more than two charges present, the net force on any one charge is given by the vector sum of the forces on that charge from all surrounding charges. This is an example of the Principle of Superposition. F+ - F- + + What is the direction of the net force on each charge (roughly)? 10 January 2005 Walker, Chapter 19 31 Walker (1st edition) Problem 19, pg. 641 (a) Find the direction and magnitude of the net electrostatic force exerted on the point charge q3 in the Figure. Let q = +1.8 mC and d = 22 cm. (b) How would your answers to part (a) change if the distance d were doubled? 10 January 2005 Walker, Chapter 19 32 Solution • • • • • • Force F3,2 on q3 from q2 is repulsive Force F3,1 on q3 from q1 is attractive Force F3,4 on q3 from q4 is repulsive Distance from q2 to q3 is d Distance from q4 to q3 is d Distance from q1 to q3 is (2)d F3, 2 k q2 q3 d 2 k - 2.0q - 3.0q d 2 6k q2 d2 2 -6 Nm 1 . 8 10 C 9 Define F k 2 8.99 10 d C 2 0.22m 2 q2 2 0.602 N F3, 2 6 F 3.61N F3, 2 3.61Nxˆ 10 January 2005 Walker, Chapter 19 33 Solution, cont’d F3, 4 k q3 q4 - 3.0q - 4.0q k d2 12 F 7.22 N d2 12k q2 d2 F3, 4 F3, 4 7.22 Nyˆ q3 q1 - 3.0q q 3 q 2 3 F3,1 k 2 k k F 0.903 N d 2d 2 2 d 2 2 x - component of force F3,1 F3,1x F3,1 cosq31 (0.903N ) cos(180 + 45) -0.638 N FNet (2.97 N ) xˆ + (6.58 N ) yˆ FNet (2.97 N ) 2 + (6.58 N ) 2 52.15 N 2 7.22 N Add the force vectors graphically y - component of force F3,1 F3,1y F3,1 sin q31 (0.903N ) sin(180 + 45) -0.638N F3,1 -0.638 Nxˆ - 0.638 Nyˆ FNet F3,1 + F3, 2 + F3, 4 FNet -0.638 Nxˆ - 0.638 Nyˆ + 3.61Nxˆ + 7.22 Nyˆ FNet (3.61N - 0.638 N ) xˆ + (7.22 N - 0.638 N ) yˆ F3,4 FNet F3,2 F3,1 10 January 2005 Walker, Chapter 19 34 Solution, four charges FNet (2.97 N ) xˆ + (6.58 N ) yˆ FNet 7.22 N • Find angle q from x-axis • Cosq = [FNet,x]/ |FNet| • Cosq 2.97N/7.22N q 65.7 10 January 2005 Walker, Chapter 19 y FNet q x 35 Spherical Charge Distributions In general a spherical charge distribution behaves as if all of its charge were at the center of the sphere. Use the distance to the center of the sphere to calculate the electrostatic force. q2 q1q2 q1 F k 10 January 2005 r 2 Walker, Chapter 19 r 36 Newton: Action at a Distance Faraday: Force Fields • A mass m exerts a gravitational force GmM/r2 on a second mass M separated by a distance r, and vice versa. • Coulomb gave us the same picture for electrostatic forces • Faraday offered a new insight, introducing the Electric Field, which can be thought of as carrying the force from charge q to charge Q. In physics, a field means a physical variable that has a defined value at every point in space. Examples: • Temperature map, Barometric Pressure map (a scalar field) • Wind velocity map (a vector field) • Initially just a mathematical trick, with our understanding of electromagnetic waves and the quantum nature of light, Electric and Magnetic fields are as real as charge and mass. 10 January 2005 Walker, Chapter 19 37 Electric Field • If a test charge q0 experiences a force F at a given location r, the magnitude of the electric field at that location is defined by F E q0 • The electric field is a “what if” concept. What would be the electrostatic force acting on a charge q0 if it were placed at position r? • The electric field can also be thought of as a disturbance in space caused by nearby charges. • The electrostatic force experienced by a charge is the interaction between the charge and the electric field at that position. • The SI units of electric field are Newtons/Coulomb = N/C 10 January 2005 Walker, Chapter 19 38 Electric Force F(r) from charge Q acting on a test charge q0 at various locations r =(x,y,z): F=kQq0/r2 Electric Field E(r)= F/ q0 q0 Q 10 January 2005 Walker, Chapter 19 39 Electric Field E(r) from charge Q at various locations r: E=kQ/r2 r Q 10 January 2005 Walker, Chapter 19 40 Electric Field E ( x, y, z ) at • A vector every point in space that tells us the magnitude and direction of the force Fq qE ( x, y, z ) a charge q will experience if the charge q is placed at the position (x,y,z). • If q<0, then the force F on q is opposite E. • To measure E = F/q, q must be small enough that it doesn’t change the distribution of charges that created the electric field in the first place. 10 January 2005 Walker, Chapter 19 41 Electric Field Direction The direction of the electric field is defined to be the direction of the force that would be experienced if the test charge is positive. Because the field has a direction, it must be a vector. E q0 q0 E 10 January 2005 + Walker, Chapter 19 42 Electric Field (cont.) The electric field is the force per charge at a given location. If you know the electric field, then the force on a charge can easily be found using F = qE Example: A charge q of 8 mC experiences a uniform electric field of 1000 N/C to the right. (a) What is the force on the charge? (b) What would the force be if the charge were –8 mC? q Note: In problems like this we do not need to know what charges created the electric field. 10 January 2005 Walker, Chapter 19 E = 1000 N/C 43 Electric Field of a Point Charge From Coulomb’s Law, the magnitude of the force experienced by a test charge q0 a distance r from a charge q is qq F k r 0. 2 Since the definition of the electric field is F E , q0 q0 the magnitude of the electric field from a point charge is given by q Ek 10 January 2005 r . 2 Walker, Chapter 19 q 44 Walker Problem 28, pg. 642 What is the magnitude of the electric field produced by a charge of magnitude 10.0 mC at a distance of (a) 1.00 m and (b) 2.00 m? Q Ek 2 r k = 8.99 ·109 N m2/C2 10 January 2005 Walker, Chapter 19 45 Electric Field & Polarization • What is the magnitude of an electric field strong enough to polarize the molecules in the air to the point that electrons are pulled out of the air (ionization produces a spark)? Several Million Newton/Coulomb. Several Million Volt/meter 10 January 2005 Walker, Chapter 19 46 Electric Fields in Nuclear Physics • What is the electric field at the surface of a proton? (radius 10-15 m, charge 1.6·10-19 C) E = (8.99 ·109 N m2/C2)(1.6·10-19 C)/(10-15 m) 2 E=(14.4) 109-19+30 N/C Q Ek 2 E=1.44 · 1019 N/C r That’s big! 10 January 2005 Walker, Chapter 19 47 Electric Fields in Atomic/Molecular physics • What is the electric field from the hydrogen nucleus (proton) at a distance of one atomic radius (r=0.5Å=0.5·10-10m) E = k q / r2 E = (8.99 ·109 N m2/C2)(1.6·10-19 C)/(0.5·10-10 m) 2 E = (58)(109-19+20) ( N/C) E = 5.8 ·1011 N/C • Smaller, but still very large. 10 January 2005 Walker, Chapter 19 48 Superposition Just like with forces, electric fields must be added as vectors. The electric field from several charges is the vector sum of the electric field from each charge. Example: Consider two identical negative charges as shown. At which lettered point is the magnitude of the electric field greatest? Least? a 10 January 2005 b - c Walker, Chapter 19 - d 49 Superposition E2 E1 - - E Q2 = Q 1 Q1<0 E E2 E1 10 January 2005 Walker, Chapter 19 50 Walker Problem 66, pg. 644 An object of mass m = 3.7 g and charge q = +44 mC is attached to a string and placed in a uniform electric field that is inclined at an angle of 30.0° with the horizontal. The object is in static equilibrium when the string is horizontal. Find (a) the magnitude of the electric field and (b) the tension in the string. 10 January 2005 Walker, Chapter 19 51 Walker Problem 66, pg. 644 • Free Body Diagram • Net force = 0 • S Fx=0: qEsin30o – mg = 0 qE T mg m = 3.7E-3 kg, q = 44.E-6 C E = mg/(q sin30o) = (3.7E-3 kg)(9.8m/s2)/(0.5*44.E-6 C) E = 1.65E+3 (kg·m/s2)/C = 1.65E+3 N/C • S Fy=0: qEcos30o – T = 0 T = (44.E-6 C) (1.65E+3 N/C)0.866 = 6.3E-2 N 10 January 2005 Walker, Chapter 19 52 Electric Field Lines In order to visualize the electric field in space it is convenient to draw Electric field-lines (see Fig. 19-13). The field lines are directional [curved] lines that everywhere point in the direction of the electric field at that point. + - + Dipole 10 January 2005 Walker, Chapter 19 53 Field Line Properties • The electric field is tangent to the field line at any point in space. • The strength of the electric field is proportional to the density of field lines (areal density measured perpendicular to field line). • The field lines always begin on positive charges or at infinity and end on negative charges or at infinity. • No two field lines can ever cross. • The number of field lines leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. 10 January 2005 Walker, Chapter 19 54 Electric Field Lines Note that twice as many field lines originate from the +2q charge than the +q or –q charges. 10 January 2005 Walker, Chapter 19 55 Lecture 2, Quiz 1 1. The net charge inside the green blob is: a) Positive b) Zero c) Negative Hint: Are there more Electric Field lines entering, or leaving the blob, or is it equal? 10 January 2005 Walker, Chapter 19 56 Lecture 2, Quiz 2 2. The net charge inside the green blob is: a) Positive b) Zero c) Negative Hint: Are there more Electric Field lines entering, or leaving the blob, or is it equal? 10 January 2005 Walker, Chapter 19 57 Lecture 2, Quiz 3 3. The net charge inside the green blob is: a) Positive b) Zero c) Negative Hint: Are there more Electric Field lines entering, or leaving the blob, or is it equal? 10 January 2005 Walker, Chapter 19 58 Walker Problem 37, pg. 642 The electric field lines surrounding three charges are shown in the Figure. The center charge is q2 = -10.0 mC. (a) What are the signs of q1 and q3? (b) Find q1. (c) Find q3. 10 January 2005 Walker, Chapter 19 59 Parallel-Plate Capacitor Two parallel conducting plates with opposite charge, separated by a distance d, is known as a parallel-plate capacitor. The electric field is uniform between the plates (except near the edges, not shown). Uniform means the electric field magnitude and direction are the same everywhere (in gap). This is because of, not in spite of Coulombs 1/r2 law!! 10 January 2005 Walker, Chapter 19 60 Electrostatic Equilibrium Recall that charges within a conductor are free to move around easily. If the charges within a conductor are not in motion, then the system is said to be in electrostatic equilibrium. 10 January 2005 Walker, Chapter 19 61 Properties of Electrostatic Equilibrium • In the presence of electrostatic forces, the charges on the conductor move around until the following static conditions are achieved: The electric field is zero everywhere inside a conductor. The excess charge on a conductor resides entirely on its surfaces. The electric field just outside a charged conductor is perpendicular to its surface. • On irregularly shaped objects, the charge accumulates at sharp points, and the electric field is most intense at sharp points. 10 January 2005 Walker, Chapter 19 62 Electric Flux We define electric flux F as the product of the surface area A times the component Ecosq of the electric field perpendicular to the surface. In general, F = EAcosq. a F EA b F = 0 (c) F = EAcosq 10 January 2005 q is the angle between the electric field and the line perpendicular to the surface. Walker, Chapter 19 63 Gauss’s Law Consider an arbitrary (imaginary) closed surface (called a Gaussian surface) enclosing a total charge q. The electric flux through the surface is q F 0 0 41k 8.8510-12 C2 /N m2 This integral property is a consequence of the 1/r2 Coulomb Law, and is valid for any irregular surface, no matter how complicated the electric field produced by internal or external charges. 10 January 2005 Walker, Chapter 19 64 Example Three point charges are arranged as shown. q1 = +4 mC, q2 = -6 mC and q3 = -4 mC. Find the electric flux through the three Gaussian surfaces labeled a, b and c. a b q 1 c q3 q2 10 January 2005 Walker, Chapter 19 65 Walker Problem 49, pg. 643 A thin wire of infinite extent has a charge per unit length of l. Using the cylindrical Gaussian surface shown in the Figure, show that the electric field produced by this wire at a radial distance r has a magnitude given by l E 2 0r 10 January 2005 Walker, Chapter 19 66 Walker Problem 49, pg. 643 solution By symmetry, Electric force on a test charge is directed radially outward (if l>0). Closed Gaussian surface consists of the cylinder and its two end caps. Electric flux through end caps is zero because E is parallel to surface. Electric flux through cylinder wall: F=Area · E(r ) F = 2 r L E(r ) Net Flux = 0 + 0 + 2 r L E(r ) = (charge enclosed)/0 = L l /0 10 January 2005 Walker, Chapter 19 E (r ) 1 l l 2k 2 0 r r 67 Charges on (and in) a conductor • Charge on a conductor is free to move under the influence of its mutual repulsion. • Are the charges in a) or b) “farther apart”? The quantitative meaning to this question is “Which configuration gives the lowest value for the electrostatic energy?” (See Chap 20.) • It is a property of the 1/r2 law (not just repulsion) that all the excess charge on a conductor ends up on the SURFACE. This can be an inside, as well as outside surface!! 10 January 2005 Walker, Chapter 19 68 Quiz 1 Jan 10, 2005 • Two charges Q1 and Q2 are separated by a distance of 0.010 m. The Electrostatic force of Q1 on Q2 is 2.0e-5 N. • At what distance of separation between Q1 and Q2 would the force be 1.0e-5N? a) 0.02 m d) 0.007m 10 January 2005 b) 0.014 m e) 0.005 m Walker, Chapter 19 c) 0.01 m 69 Quiz 1 12 January 2004 Name…………………… • In the diagram at right, F1 is the electrostatic force of Q1 acting on charge q=1.0E-9C . • Draw a vector with its tail at q to represent the magnitude and direction of the electrostatic force F2 of Q2 acting on charge q (the length of your vector should roughly describe the relative magnitudes of F2 and F1. • Draw a vector with its tail at q to represent the magnitude and direction of the net force FNet acting on q from both Q1 and Q2 • Label your vectors F1 and FNet Q2 = -1.0E-6 C • Note: F F +F Net 10 January 2005 1 Q1 = +1.0E-6 C q F1 2 Walker, Chapter 19 70 Quiz 2 Sketch the electric field lines generated by these two charges. Hint: Consider the electric flux through the three gaussian surfaces defined by the three dashed lines. 2 February 2004 Name…………………… +4mC 10 January 2005 -2mC Walker, Chapter 19 71 Preparation for Lab 2 (Chapter 21) • Electric Current in wire equals steady flow of charge (not equilibrium!). • Unit of measure is Coulomb per second = Amp • 1.00 C/s = 1.0 A • Think of electric current like flow of water in pipe. • Voltage = Electrostatic Potential difference of power supply or battery (e.g. AA=1.5 V) How hard the current is being forced around circuit. Think of difference in height of two ends of a water pipe. Water flows with greater force when the height difference is greater. • Resistance R = measure of how hard you have to push to obtain current (flow). R = V/I Pump Think of long thin pipe (high resistance to flow) versus short broad pipe (low resistance to flow). 10 January 2005 Walker, Chapter 19 72 Equivalence of Gauss’ Law and Coulomb’s Law • Coulomb: Electric field at a distance r from a point charge Q: E E(r) = k Q / = Q / (4 0 For Q>0, E>0: E points away from Q For Q<0, E<0: E points towards Q. r2 r2) • Gauss: Electric flux through an imaginary closed spherical shell a distance r from Q Flux = E(r)•(Surface area of shell)= E(r) 4 r2 Q r • Outward flux is positive • Inward flux is negative Gauss: Flux = Q/ 0. E(r) = Q / (4 0 r2) 10 January 2005 Walker, Chapter 19 73 Gauss’ Law and the Parallel Plate Capacitor • Consider a rectangular Gaussian surface penetrating into the metal of a parallel plate capacitor: Total Charge on left plate = Q, right plate = -Q Total area or each plate = A Surface charge density = s = Q/A Surface area of face of Gaussian surface parallel to plate = a. Charge enclosed by Gaussian surface: sa Flux through portion of Gaussian surface inside metal = 0 (E=0). Flux through top and bottom surfaces outside metal = 0 (Electric field parallel to surface). Flux through face of Gaussian surface parallel to plate (outside) = Ea. Gauss’ Law: sa/0 = Ea + + + + a + + + + + + + - • Uniform Electric Field in gap: E = s/0 10 January 2005 Walker, Chapter 19 74