Preclass est9
How much money will a typical person (not you :-)
from this class earn in their entire lifetime? (in 2007 dollars)?
(Don’t just guess, try to estimate the answer)
A) $2-4 Million
B) $20-40 Million
C) $200-400 Million
D) $2-4 Billion
E) How could I possibly know this?
1
CAPA #13 tonight
New online participation survey is still up! (But not for much longer)
Reading: 34.6 (don't stress about the math, focus on the concepts!)
New pretest available for next Tuesday.
_________________________
Last: Inductors, and AC circuits
Today: Maxwell's equations
Next: More of Maxwell!
Vrms = V peak / 2
Pave = Ppeak /2
(P = I V, as usual)
!
2
Why does almost everyone use AC Voltage?
1. Ease of generating.
Recall a rotating coil in a B-field creates an AC induced
(First large scale test at Niagara Falls)
2. AC is easy to change from one peak Voltage level to
another. (Transformers!)
3
1
Light bulbs and appliances with motors (vacuum cleaners,
blenders, …) use AC Voltage to operate.
But devices with electronic circuits (TV’s, computers, phones,
…) need DC Voltage (constant) to function.
The “power supply” in TV’s, computers, etc. convert AC
Voltage from the wall into DC Voltage (typically 2-15 Volts)
that the circuitry needs.
4
CT 33.36
A 600 Watt hairdryer is attached to 120 VAC
circuit. What is the peak current through the
hairdryer (to within 5%)?
A: 0 A B) 5 A
E) Other
C) 7 A
D) 10 A
rms = peak / 2
(P = I V)
!
5
CT 33.37
The instantaneous power consumed by my De-luxe Toaster
Oven looks like this as a function of time:
6
2
CT 33.38
1200 W
Which of the following is correct?
P ave
V rms
I rms
A: 1200 W 120 V 10 A (=1200/120)
B: 1200 W 170 V
7 A (=1200/170)
C: 600 W
120 V
5 A (= 600/120)
D: 600 W
170 V
3.5 A (=600/170)
E: None of the above is right.
7
CT 33.39
What is "T" in the picture (in the USA)?
A: 1/30 s
B: 1/60 s
C: 1/120 s
D: Other
8
AC Voltage is used to distribute power to homes (rather than
DC Voltage).
9
3
Electrical power is transmitted from power plants to cities
with big aluminum power cables.
Much energy is wasted because of resistance in the cables,
the cables heat up (i2R losses). To reduce this waste, power
is transmitted at very high voltage (100 kV to 1 MV !)
P (from plant to city) = iV = constant
Set by the needs of the city and the capacity of the plant.
10
DC versus AC
Lots of good books on the science
and the people involved.
11
12
4
Magnetic Energy Density
Recall that for a capacitor C, there is stored potential
energy in the electric field.
1
U = CV 2
2
The energy is stored in the electric field and the density
is:
uE =
v
U
1
= ! 0 | E |2
Volume 2
13
For an inductor L, with current i, there is stored energy in
the magnetic field.
U=
1 2
Li
2
The energy density in the magnetic field is:
uB =
U
1 1 v 2
=
|B|
Volume 2 µ 0
14
Clicker Question
The same current i flows through solenoid 1 and solenoid 2.
Solenoid 2 is twice as long and has twice as many turns as
solenoid 1, and has twice the diameter. (Hint) for a solenoid
B = µo n i )
What is the ratio of the magnetic energy contained in
solenoid 2 to that in solenoid 1, that is, what is U 2
U1
I
A) 2
B) 4
1
C) 8
D) 16
2
I
E) None of these.
15
5
It takes work to get current flowing through an inductor.
You must work against the back EMF which opposes any
change in the current.
That work = potential energy stored = U = ½ Li2
And is thus stored in the inductor’s magnetic field.
16
EMF around a (stationary) closed loop is defined as:
#=
v v
E
! " dl
Loop
And thus Faraday’s Law can be written as:
v
v
! E " dl
Loop
=#
d
dt
v
v
! B " dA
surf
17
A changing B-field creates a new kind of E-field.
B
If B is decreasing  E-field is CCW
E
If B is increasing  E-field is Clockwise
B
E
18
6
The (non-Coulomb) E-field is very different from the Coulomb
E-field created by single electric charges.
E
B
q
v v
#V = " $ E ! dl = 0
$=
E
v v
E
# " dl ! 0
Loop
19
If there are only stationary charges, no currents, then there
are no B-fields.
In this case there is no Magnetic Flux in this situation only!
#=
v
v
" E ! dl
= 0 (special case only)
Loop
20
CT 33.12
A solenoid has an increasing current causing an
increasing B-field inside. An end-on view of the solenoid is
shown. What is the direction of the force on an electron
(shown below the solenoid)?
I
A
B
D
C
E: 0
B(in)
electron
21
7
CT 33.14
A long solenoid (radius R) contains a uniform B field that
increases steadily, B(t) = c t.
Consider the dashed “Amperian loop”.
What is " E • dL around the loop?
R
A: zero
B: 2πrE
C: 2πRE
!
D: π r^2 E
E: π R^2 E
B
r
22
CT 33.14b
What is
"" B • dA
through the the dashed curve?
A: zero
!
B: 2πrB
C: 2πRB
D: π r^2 B
E: π R^2 B
R
B
r
23
CT 33.14c
Let’s put this together. Recall B = ct.
d#
d
Faraday says $ E • dl = " = " $$ B • dA
dt
dt
Recall the left side is 2πrE
2
Recall ! ## B • dA = " r B
So… how does E depend on r?
A: E=0 B: E ~ 1/r
C: E ~ r D: E~ r^2
E: Other
!
R
B
r
24
8
Electromagnetism in Full
v
v
$ E # dl
v
v
v
v
! B # dl
d! B
dt
= µ 0ienc + µ 0$ 0
! E " dA =
v
="
v
d" E
dt
Qenc
#0
! B " dA = 0
25
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