Physics 12201320 Electromagnetism Optics and wave phenomena Lecture

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

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

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

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

A second way to determine direction: Law Lenz’s

Mutual Inductance Units: henry [H] = [Wb/A] = [Vs/A] = [J/A 2]

Self Inductance

For M = 240 m. H and N 2 =5 turns, what needs N 1 to be if L = 1 cm and A= 1 cm 2?

Magnetic Field Energy

Energy stored in an inductor: What L is needed to store 1 k. Wh energy in coil with 1 A, 1 k. A, 1 m. A? L = 2 U/I 2

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

The L-C Circuit

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 d 2 q/dt 2 + 1/LC q = 0 ‘harmonic oscillator’ q = Q cos(wt+f) i = dq/dt = - w. Q sin(wt+f) From further analogy between mechanic oscillators like springs, we find:

Ex 30. 35 C 60 m. F charged by connecting 12 V battery. Then C disconnected from battery and hooked up to L=1. 5 H 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?

Finally, the LRC series circuit:

Ex 30. 41 L=0. 285 H, C= 0. 46 m. F, w’= (6 LC)-0. 5 What is R? Group Task

Alternating Currents (AC) v = V cos wt i 2 = I 2 cos 2 wt Note: cos 2 wt = ½ (1+ cos 2 wt) i 2 = I 2 ½ (1+cos 2 wt) The average of cos(anything) is zero <i 2>avg = I 2/2 and <i>= irms = I/20. 5

Ex PC: 2. 7 A from 120 V 60 Hz a) Average current – zero b) Average of square of current is not zero: c) Current amplitude I

Resistance, Reactance v. R = VR cos wt = i. R = (IR) cos wt

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

Similarly, with ‘capacitive reactance’ XC = 1/w. C

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

i in phase with VR

Power in Ac Circuits:

Resonance in AC Circuits

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

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

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

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.

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:

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

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.

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.