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Physics 1220/1320

Electromagnetism & Optics and wave phenomena. Physics 1220/1320. Lecture Magnetism, chapter 27-32. Electromagnetic Induction. Field strength, Shape, Location, Orientation If any of these change, I is induced. Faraday’s Law. F B =int[ B •d A ] For uniform B: F B = B • A.

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Physics 1220/1320

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  1. Electromagnetism & Optics and wave phenomena Physics 1220/1320 Lecture Magnetism, chapter 27-32

  2. Electromagnetic Induction • Field strength, • Shape, • Location, • Orientation • If any of these • change, I is • induced

  3. Faraday’s Law FB=int[B•dA] For uniform B: FB= B•A

  4. Direction of Induced EMF Note: only CHANGE in flux causes the emf, not the presence of flux http://www.uwsp.edu/physastr/kmenning/flash/AF_3101.swf

  5. A second way to determine direction: Lenz’s Law

  6. Mutual Inductance Units: henry [H] = [Wb/A] = [Vs/A] = [J/A2]

  7. Self Inductance

  8. For M = 240 mH and N2 =5 turns, what needs N1 to be if L = 1cm and A= 1cm2?

  9. Magnetic Field Energy

  10. Energy stored in an inductor: What L is needed to store 1 kWh energy in coil with 1A, 1kA, 1mA? L = 2U/I2

  11. What is the effect of L on a circuit? a- The R-L Circuit i = E/R (1-e-(R/L)t) i = I0 e-(R/L)t Loop rule: E – iR – L di/dt = 0  During discharge:

  12. The L-C Circuit

  13. We find that instead of the exponential behavior of the RL circuit, in the LC circuit i oscillates! Loop rule: -L di/dt – q/C = 0 or d2q/dt2 + 1/LC q = 0 ‘harmonic oscillator’ q = Q cos(wt+f) i = dq/dt = - wQ sin(wt+f) From further analogy between mechanic oscillators like springs, we find:

  14. Ex 30.35 C 60mF charged by connecting 12V battery. Then C disconnected from battery and hooked up to L=1.5H a) w and T of oscillations? b) Initial charge on C? c) How much energy initially in C? d) Charge on C after 23 ms? Signs on plates are opposite to those at t=0 e) i in L at that time?

  15. Finally, the LRC series circuit:

  16. Ex 30.41 L=0.285H, C= 0.46 mF, w’= (6LC)-0.5 What is R? Group Task

  17. Alternating Currents (AC) v = V cos wt • i2 = I2 cos2wt • Note: cos2wt = ½ (1+ cos2wt) •  i2 = I2 ½ (1+cos2wt) • The average of cos(anything) is zero • <i2>avg = I2/2 and <i>= irms = I/20.5

  18. Ex PC: 2.7A from 120V 60Hz • Average current – zero • b) Average of square of current is not zero: • c) Current amplitude I

  19. Resistance, Reactance vR = VR cos wt = iR = (IR) cos wt

  20. with ‘inductive reactance’ XL= wL In other words: that little trick creates an ohm-like equation

  21. Similarly, with ‘capacitive reactance’ XC = 1/wC

  22.  The LRC Series Circuit 2 cases: XL > XC or XC > XL ‘Same ohm-trick’  “Impedance”

  23. i in phase with VR

  24. Power in Ac Circuits:

  25. Resonance in AC Circuits

  26. So far, we have avoided a complication in our understanding of circuitry: It turns out that Ampere’s law is ____________ :

  27. The hindsight approach for electromagnetism is to start with the Maxwell Equations: (here in their less useful integral form)

  28. In their more useful differential form, they become: divergence, curl, http://scienceworld.wolfram.com/physics/MaxwellEquations.html

  29. In sum, it turns out that all radiation propagates in form of electromagnetic waves, where E and B are just two aspects of the same thing: A moving electric charge which creates a dipole moment.

  30. A general description of such a propagating wave is: For waves in (through) matter , we get correction factors: The energy and momentum of these waves can be described by a characteristic vector:

  31. A whole set of phenomena we are familiar with boil down to being em-waves:

  32. In modern physics, much attention is paid to the fact that this view (‘classical physics’) of the world breaks down in the realm of the very small and the very large. Classical Physics is not abandoned altogether, it’s field of relevance is simply found to be limited. It exists as a limiting case of GR and QP as a macroscopic approximation of the true behaviors. In its realm, CP gives remarkably precise information.

  33. Quantum Physics recognizes that the distinction between matter and energy is artificial for light, a famous paradox occurs, the wave-particle duality, ie it can be shown that light must be both at the same time (so called ‘two-slit’ experiment) General Relativity recognizes that there is an absolute maximum speed, the speed of light and that space itself is curved by the presence of heavy objects (so the Euclidian statement that a straight line is the shortest distance between two points is ultimately not true (albeit very close to reality for distances not very much larger than lightyears). Much of the effort in Modern Physics is devoted to find new exotic phenomena in materials which exploit QP (most recently: nano science and modern optics (quantum computation, data encryption, teleportation). A great unknown is the ‘how to’ of unifying the two great theories of physics, QP and GR.

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