Transcript Physics 1220/1320

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 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:
Lenz’s Law
Mutual
Inductance
Units: henry
[H] = [Wb/A]
= [Vs/A]
= [J/A2]
Self
Inductance
For M = 240 mH and N2 =5 turns, what needs N1 to be if L = 1cm
and A= 1cm2?
Magnetic Field Energy
Energy stored in an inductor:
What L is needed to store 1 kWh energy
in 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
Loop rule:
E – iR – 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 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:
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?
Finally, the LRC series circuit:
Ex 30.41 L=0.285H, C= 0.46 mF, w’= (6LC)-0.5
What is R?
Group Task
1
R2
1
1 
1
1
 1
w 
 2 
 R 2  4L2 


  R  2L
LC 4L
6LC
LC 6LC
 LC 6LC 
2
 R  2(0.285 H)
1
1

 45.4  .
4
4
(0.285H) (4.60 10 F) 6(0.285H) (4.60 10 F)
Alternating Currents (AC)
v = V cos wt
i2 = I2 cos2 wt
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
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
with ‘inductive reactance’ XL = wL
In other words: that little trick creates
an ohm-like equation
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 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/MaxwellEquations.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.