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; 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 EnEn 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!

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 2qcharge qcharge -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/  0? -2q/  0 ? IMPOSSIBLE A)-2qC) q B)-q D) impossible

Today’s Reading Quiz 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. charge -q charge 2qcharge qcharge -2q

Example What is the flux through the first surface? Figure 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? A)q/  o D) 2q/  o B)-q/  o C)0

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 q Charge in an infinite triangular channel What is flux out of one side?

Applying Gauss’s Law Infinite cylinder radius R charge density  What is the electric field inside and outside the cylinder? L R Electric Field will point directly out from the axis r Draw a cylinder with the desired radius inside the cylindrical charge

Applying Gauss’s Law Infinite cylinder radius R charge density  What is the electric field inside and outside the cylinder? L R Electric Field will point directly out from the center r Draw a cylinder with the desired radius outside the cylindrical charge

Applying Gauss’s Law Sphere radius R charge density . What is E-field inside? R Sphere volume: V = 4  a 3 /3 Sphere area: A = 4  a 2 Draw a Gaussian surface inside the sphere of radius r r What is the magnitude of the electric field inside the sphere at radius r? A)  R 3 /3  0 r 2 B)  r 2 /3  0 R C)  R/3  0 D)  r/3  0

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 = 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 Surface charge  Area A Add a gaussian pillbox that penetrates the surface Electric field points directly out from (or in to) conductor

Conductors shield charges No net charge Charge q What is electric field outside the spherical conductor? Draw a Gaussian surface No electric field – no charge Inner charge is hidden – except Charge -q Charge +q on outside to compensate Charge distributed uniformly Charge +q

Conductors shield charges 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? Charge -q Charge +q

Example 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 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 10 4 N/C

Example EA=q/  o =E(2  rl)+0+0 What if we know the charge density,, and not the field? EA=q/  o =E(2  rl)+0+0= l/  o 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 10 4 N/C

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/  o D) q/6  o B)q/4  o C)0

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/  o D) q/6  o B)q/4  o C)0 A)2D) 1 B)4 C)0