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•dA]

For uniform B:FB= B•A

Direction of Induced EMFNote: 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:Lenz’s Law

MutualInductance

Units: henry[H] = [Wb/A] = [Vs/A] = [J/A2]

SelfInductance

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

Magnetic Field Energy

Energy stored in an inductor:

What L is needed to store 1 kWh energyin coil with 1A, 1kA, 1mA?

L = 2U/I2

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

During discharge:

Loop rule: E – iR – L di/dt = 0

The L-C Circuit

We find that instead of the exponential behavior of the RLcircuit, 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 analogybetween mechanic oscillatorslike springs, we find:

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=0e) i in L at that time?

Finally, the LRC series circuit:

Ex 30.41 L=0.285H, C= 0.46 mF, w’= (6LC)-0.5

What is R?

Group Task

LCLCLR

LCLCLR

LCL

R

LC 6

112

6

114

6

1

4

1 222

22

. 4.45F)10(4.60H)6(0.285

1

F)10(4.60H)(0.285

1)H285.0(2

44

R

Alternating Currents (AC)v = V cos wt

i2 = I2 cos2 wtNote: 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

Ex PC: 2.7A from 120V 60Hz

a) Average current – zero

b) Average of square of current is not zero:

c) Current amplitude I

Resistance, Reactance

vR = VR cos wt = iR = (IR) cos wt

In other words: that little trick createsan ohm-like equation

with ‘inductive reactance’ XL = wL

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

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 ourunderstanding of circuitry:

It turns out that Ampere’s lawis ____________

:

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

http://scienceworld.wolfram.com/physics/MaxwellEquations.html

In their more useful differential form, they become:

divergence,        curl,

In sum, it turns out that all radiation propagates in form of electromagneticwaves, where E and B are just two aspects of the same thing: A movingelectric 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 acharacteristic vector:

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

In modern physics, much attention is paid to the factthat this view (‘classical physics’) of the world breaksdown in the realm of the very small and the very large.

Classical Physics is not abandoned altogether, it’s fieldof 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 matterand energy is artificial

for light, a famous paradox occurs, the wave-particleduality, ie it can be shown that light must be bothat the same time (so called ‘two-slit’ experiment)

General Relativity

recognizes that there is an absolute maximum speed,the speed of lightand that space itself is curved bythe 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 newexotic phenomena in materials which exploit QP (most recently:nano science and modern optics (quantum computation, dataencryption, teleportation). A great unknown is the ‘how to’ of unifying the two great theories of physics, QP and GR.