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Announcements Careers in Physics Event: Dr. Jeffrey Phillips from EPRI will discuss working in the field of energy production. 11 AM today Olin Lounge Seminar: Dr. Jeffrey Phillips, Electric Power Research Institute Integrated Coal Gasification Combined Cycle Power Plants : A Cleaner Coal-to-Electricity Option 4:00 PM Olin 101 Thursday Pick up the handout Announcements II Office Hrs: None after class today; email for an appointment today Semester Quiz I is on 02/03/05. Lectures 1-5; Ch 3,22-24 One {letter-sized} page of notes allowed Hints: Review {and master} HW, and reading quizzes Study lecture notes, and do optional problems for extra practice Electric Flux and Gauss’ Law E E dA E cos dA E En •The electric flux through a closed surface is given by Gauss’ Law •Usually you can pick your surface so that the integration doesn’t need to be done •We must distinguish between field and flux! E E dA 4 k q e Special optional Readings For those of you who are interested, “Div, Grad, Curl and all that” in Ch 2 has a more quantitative analysis of Gauss’ law. The handout is from the beginning of that chapter and has a more quantitative treatment of unit normals and surface integrals than we did in class. You will not need to know this for the course, but it might aid your understanding. Gauss’s Law charge q charge 2q charge -q charge -2q Which other charge(s) do we have to include in a gaussian surface so as to contain the +2q charge and have flux equal to: Zero ? +3q/e0? A) -2q C) q -2q/e0 ? B) -q D) impossible IMPOSSIBLE Today’s Reading Quiz charge q charge 2q charge -q charge -2q Consider Gauss's law: Which of the following is true? E must be the electric field due to the enclosed charge If a charge is placed outside the surface, then it cannot affect E on the surface On the surface E is everywhere parallel to dA If q = 0 then E = 0 everywhere on the Gaussian surface If the charge inside consists of an electric dipole, then the integral is zero. Example A) q/eo B) -q/eo C) 0 Figure 24-29. •What is the flux through the first surface? •What is the flux through the second surface? •What is the flux through the third surface? •What is the flux through the fourthsurface? •What is the flux through the fifth surface? D) 2q/eo Applying Gauss’s Law •Can be used to determine total flux through a surface in simple cases •Must have a great deal of symmetry to use easily Charge in an infinite triangular channel What is flux out of one side? charge q E q e0 q S 3e 0 S 1 S 2 S 3 E1 E 2 3 S 0 Applying Gauss’s Law L R r •Infinite cylinder radius R charge density •What is the electric field inside and outside the cylinder? •Draw a cylinder with the desired radius inside the cylindrical charge •Electric Field will point directly out from the axis qin V AE 2 rLE e0 e0 r E 2e 0 r L e0 2 Applying Gauss’s Law L R r •Infinite cylinder radius R charge density •What is the electric field inside and outside the cylinder? •Draw a cylinder with the desired radius outside the cylindrical charge •Electric Field will point directly out from the center AE 2 rLE R2 E 2e 0 r qin e0 V e0 R L e0 2 Applying Gauss’s Law r E 3e 0 Sphere volume: V = 4a3/3 R r Sphere area: A = 4a2 •Sphere radius R charge density . What is E-field inside? •Draw a Gaussian surface inside the sphere of radius r What is the magnitude of the electric field inside the sphere at radius r? A) R3/3e0r2 B) r2/3e0R C) R/3e0 D) r/3e0 AE 4 r E 2 V e0 4 r 3e 0 3 qin e0 Conductors in Equilbirum •A conductor has charges that can move freely •In equilibrium the charges are not moving •Therefore, there are no electric fields in a conductor in equilibrium F qE ma =0 qin e 0 e 0 E dA =0 •The interior of a conductor never has any charge in it •Charge on a conductor is always on the surface Electric Fields near Conductors •No electric field inside the conductor •Electric field outside cannot be tangential – must be perpendicular •Add a gaussian pillbox that penetrates the surface Area A 0 0 AE Surface charge qin e0 A E nˆ e0 e0 •Electric field points directly out from (or in to) conductor Conductors shield charges No net charge •What is electric field outside the spherical conductor? Charge q •Draw a Gaussian surface •No electric field – no charge •Inner charge is hidden – except Charge -q Charge +q E •Charge +q on outside to compensate •Charge distributed uniformly qrˆ 4e 0 r 2 Conductors shield charges Charge q Charge -q Charge +q •Charge is induced on the inner and outer surfaces of the conducting shell, which hides the interior charge •How would the situations change if the charge inside were on a conductor? Example Suppose that the radius of the central wire is 26 µm, the radius of the cylinder 1.3 cm, and the length of the tube 16 cm. If the electric field at the cylinder's inner wall is 2.7 x 104 N/C •What is the charge enclosed on the wire? •We know all the physical dimensions! •We know how the field lines point out from a wire •We know the field on the interior of the cylinder Example Suppose that the radius of the central wire is 26 µm, the radius of the cylinder 1.3 cm, and the length of the tube 16 cm. If the electric field at the cylinder's inner wall is 2.7 x 104 N/C •EA=q/eo=E(2rl)+0+0 •What if we know the charge density, l, and not the field? •EA=q/eo=E(2rl)+0+0=ll/eo Practice Problem I A cube with 1.40 m edges is oriented as shown in the figure Suppose there is a charge situated in the middle of the cube. • What is the magnitude of the flux through the whole cube? • What is the magnitude of the flux through any one side? A) q/eo B) q/4eo C) 0 D) q/6eo Practice Problem II A cube with 1.40 m edges is oriented as shown in the figure Suppose the cube sits in a uniform electric field of 10i ? • What is the magnitude of the flux through the whole cube? • What is the magnitude of the flux through the top side? • How many sides have nonzero flux? A) q/eo B) q/4eo C) 0 D) q/6eo A) 2 D) 1 B) 4 C) 0