Understanding Electric Fields in Conductors: Gauss's Law and Induced Charges, Study notes of Physics

Download Understanding Electric Fields in Conductors: Gauss's Law and Induced Charges and more Study notes Physics in PDF only on Docsity! Physics 212 Lecture 4, Slide 1 Physics 212 Lecture 4 Today's Concepts: Conductors + Using Gauss’ Law Applied to Determine E field in cases of high symmetry Physics 212 Lecture 4, Slide 2 Your comments/Concerns Why the electrical field inside a conductor is zero. I would like to know more about the usage of Gauss's law on different types of conductor and their applications. What kind of problems to expect and how to develop a better understanding of everything covered so far. The concept of nesting shells and spheres was confusing. Specifically, I was unsure about the exact characteristics of the induced electric field. Does it perfectly cancel out the other electric field within the shell? I would like to talk more about infinite lines. The lambda part was confusing to me. I am very baffled on the concept of E fields within conductors and how they exactly work. The math behind Gauss' law confuses me, I'd like to discuss that. all of Gauss's law...I've always been super confused by it. Physics 212 Lecture 4, Slide 5 The net result of this can be viewed in two equivalent ways: And… Do positive charges move in a real metal conductor ? No, but… Conductors (What moves?) 05 Physics 212 Lecture 4, Slide 6 Conductors = charges free to move Claim: E = 0 inside any conductor at equilibrium Why? • At equilibrium, the charges inside conductor are not accelerating • If charges inside conductor are not accelerating, the force on any charge is zero • If the force on any charge inside the conductor is zero, the electric field (E = F/q) must also me zero Claim: Excess charge on conductor only on surface at equilibrium Why? • Apply Gauss’ Law • Take Gaussian surface to be just inside conductor surface E = 0 • E = 0 everywhere inside conductor 0E dA =∫ i • Gauss’ Law: 0 encQE dA ε =∫ i 0encQ = SIMULATION 2 07 “I would like to go over why an electric field inside a conductor is zero” Physics 212 Lecture 4, Slide 7 Charge in Cavity of Conductor Q A particle with charge +Q is placed in the center of an uncharged conducting hollow sphere. How much charge will be induced on the inner and outer surfaces of the sphere? A) inner = –Q, outer = +Q B) inner = –Q/2 , outer = +Q/2 C) inner = 0, outer = 0 D) inner = +Q/2, outer = -Q/2 E) inner = +Q, outer = -Q 10 • Gauss’ Law: 0 encQE dA ε =∫ i 0encQ = Qinner Qouter “Pretty much everything regarding the inner and outer charges of a sphere” Since E=0 in conductor Physics 212 Lecture 4, Slide 10 Preflight 0 10 20 30 40 50 17 In a conductor, the electric field inside of the object must be zero and any excess charge must be located on the shell. out in zero Common reasons for choosing zero (smart but not correct) -q will counterbalance +q causing a total electric field inside the spheres to be 0. The pre-lecture mentioned that it has to be zero but I'm not sure why. The man told us... Smart and correct “The field poi ts away from the positive and towards the negative.” Physics 212 Lecture 4, Slide 11 Gauss’ Law 0 encQE dA ε =∫ i ALWAYS TRUE! In cases with symmetry can pull E outside and get 0ε = enc QE A 19 “To go into more detail about how the Gaussian surfaces affect the calculation of the electric field” In General, integral to calculate flux is difficult…. and not useful! To use Gauss’ Law to calculate E, need to choose surface carefully! 1) Want E to be constant and equal to value at location of interest 2) Or wand E dot A = 0 so doesn’t add to integral Physics 212 Lecture 4, Slide 12 Gauss’ Law Symmetries 0 encQE dA ε =∫ i ALWAYS TRUE! In cases with symmetry can pull E outside and get 0ε = enc QE A Spherical Cylindrical Planar 24π=A r 2 04π ε = enc QE r 2π=A rL 02 λ π ε =E r 22π=A r 02 σ ε =E 22 Different cases for Gaussian surfaces. Do we need to know how to derive those equations? “I don't get how for the cylindrical "ends", there E=0.” Physics 212 Lecture 4, Slide 15 In the three cases shown below, the colored lines represent positive (blue) and negative (red) charged planes. The magnitudes of the charge per unit area on each plane is the same. In which case is the magnitude of the electric field at point P biggest? + -+ Case A Case B + Case C + P P P Preflight 27 0 20 40 60 80 100 Physics 212 Lecture 4, Slide 16 + -+ Case A Case B + Case C + Superposition: 28 Physics 212 Lecture 4, Slide 17 Calculation conductor r1 r2 +5 Point charge +5 Coulomb’s at center of a conducting shell of inner radius r1 and outer radius r2 . The net charge on the conducting shell is -3 Coulomb’s y x 0 encQE dA ε =∫ i What is the induced charge on the inner surface of the conductor? A) -8 C B) -5 C C) -3 C D) -2 C E) 0 31 “some good examples will help”