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Transcript
Lecture 14.1 : Electromagnetic Fields Lecture Outline: E & B Transformations The Displacement Current Textbook Reading: Ch. 34.1 - 34.3 April 16, 2013 1 Announcements •Homework #11 due on Monday, April 22, at 9pm. •Quiz #5 on Thursday will cover Ch. 33 material (33.1-33.9). •Online Evaluation e-mails will be sent to you on Monday, April 22. ‣Please fill out the evaluation form...it is completely confidential. May 8 is deadline. ‣Evaluations are read by myself, as well as the Chair of the Physics Department. ‣Evaluations are VERY useful in helping to improve the course. ‣Remember that PHY212 and PHY222 (lab) are separate courses! 2 Last Lecture... Maxwell proposed that a changing electric field induces a magnetic field (mirror idea to Faraday’s law, which says changing magnetic field induces an electric field). 3 Last Lecture... Inductors are devices in circuits that can be used to store energy in magnetic fields (similar to Capacitors storing energy in electric fields). They have interesting behavior when placed in circuits. Inductance Φm L≡ I 1 henry = 1 H ≡ 1 Wb/A = 1 Tm2 /A 4 Last Lecture... If the current through an inductor is changing, a potential difference develops across the inductor. Induced current Induced field � � � � � dΦm � � dI � � = L� � ∆VL = �� � dt � dt � We choose same sign convention as in resistors...voltage decreases in direction of current flow. 5 Last Lecture... We worked out the potential energy stored in the magnetic field of an inductor: 1 2 UL = A·�·B 2µ0 We could convert this to an energy density by dividing out the volume of the inductor. This result is actually very general. 1 2 uB = B 2µ0 Recall for Electric Fields: 1 uE = � 0 E 2 2 6 The Can Crusher Demo 5K20.65 Eddy Currents 7 Clicker Question #1 Sharon runs past Bill while holding a positive charge q. In Bill’s reference frame, there is (or are) A. B. C. D. Only an electric field. Only a magnetic field. An electric and a magnetic field. No fields. 8 Clicker Question #2 Sharon runs past Bill while holding a positive charge q. In Sharon’s reference frame, there is (or are) A. B. C. D. Only an electric field. Only a magnetic field. An electric and a magnetic field. No fields. 9 E & B Transformations Our current understanding of electric and magnetic fields can lead to some confusing scenarios: •As Brittney runs by Alec, he sees a moving charge and hence a magnetic field, while Brittney doesn’t see any magnetic field. •If Alec creates a magnetic field that Brittney runs through, he expects a magnetic force on the charge, while she does not. 10 E & B Transformations Recall that inertial reference frames move at constant velocity with respect to one another. Newton’s laws are valid in inertial frames. �vCA = �vCB + �vBA d�vCA d�vCB d�vBA = + dt dt dt �aCA = �aCB Observers in either frame agree on the acceleration of particle C, so they agree on the net force acting on the particle. 11 E & B Transformations Alec creates a region with zero electric field, and magnetic field BA. He observes a particle with velocity vCA traveling through this region to experience force FA. Brittney runs alongside the charge. What does she observe? 12 E & B Transformations Alec creates a region with zero electric field, and magnetic field BA. He observes a particle with velocity vCA traveling through this region to experience force FA. 13 E & B Transformations More generally, a charge can move through E and B fields with velocity vCA . We can imagine an observer moving at the same velocity as the charge. �B = E � A + �vCA × B �A E Note: Frame B still can’t say anything about possible magnetic fields since they are at rest with respect to the charge. 14 E & B Transformations What about transforming magnetic fields between frames? 15 Clicker Question #3 Experimenters on earth have created the magnetic field shown. A rocket flies through the field, from right to left. Which are the field (or fields) in the rocket’s reference frame? 16 E & B Transformations A warning about “relativity” and Einstein... Fields at q2 due to q1: 1 q 1 � EA = ĵ 4π�0 r2 µ0 q1 vCA � BA = k̂ 2 4π r 17 Clicker Question #4 The E & B fields in frame A are shown. Which diagram shows the fields in frame B? 18 The Displacement Current Recall Ampere’s Law: � � · d�s = µ0 Ithrough B 19 The Displacement Current No rule saying we have to pick surface S1. We could also choose to evaluate Ampere’s Law through S2, which is bounded by the same curve. 20 The Displacement Current Consider the circuit below with a capacitor and a battery. It appears we will get very different values for Ithrough depending on which surface we use. 21 The Displacement Current We need to modify Ampere’s Law to account for what’s happening in surface S2. This surface sees a changing electric flux. 22 Reminders •Read Ch. 34. •Quiz #5 on Thursday. 23