![Page 1: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/1.jpg)
Magnetic Induction
April 1, 2005
![Page 2: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/2.jpg)
Happenings
Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15th.
Should I do a class on Vectors and how we use them??? [vote]
![Page 3: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/3.jpg)
From The Demo ..
![Page 4: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/4.jpg)
Faraday’s Experiments
??
![Page 5: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/5.jpg)
Insert Magnet into Coil
![Page 6: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/6.jpg)
Remove Coil from Field Region
![Page 7: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/7.jpg)
That’s Strange …..
These two coils are perpendicular to each otherThese two coils are perpendicular to each other
![Page 8: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/8.jpg)
Remember Electric Flux?
Did you really think you were through with this kind of concept???
![Page 9: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/9.jpg)
We discussed the normal component of the Electric Field vector
nEnE )cos(nE
![Page 10: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/10.jpg)
DEFINITION:Element of Flux through a surface
EENORMAL
NORMAL
A E=ENORMAL x A
(a scalar)
![Page 11: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/11.jpg)
“Element” of Flux of a vector
E leaving a surface
dAd
also
d NORMAL
nEAE
AEAE
n is a unit OUTWARD pointing vector.
![Page 12: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/12.jpg)
This flux was LEAVING the closed surface
![Page 13: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/13.jpg)
Definition of TOTAL Definition of TOTAL ELECTRIC FLUX through a ELECTRIC FLUX through a surface:surface:
dA
is surface aLEAVING Field
Electric theofFlux Total
out
surfaced
nE
![Page 14: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/14.jpg)
There is ANOTHER Kind of FLUX
THINK OFMAGNETIC FLUX
as the“AMOUNT of Magnetism”
passing through a surface.Don’t quote me on this!!!
![Page 15: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/15.jpg)
What is this thing called FLUX?
Magnetic Flux is a Scalar
The UNIT of FLUX is the weber 1 weber = 1 T-m2
AB dB
![Page 16: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/16.jpg)
Consider a Loop Magnetic field passing
through the loop is CHANGING.
FLUX is changing. There is an emf
developed around the loop.
A current develops (as we saw in demo)
Work has to be done to move a charge completely around the loop.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
![Page 17: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/17.jpg)
Faraday’s Law (Michael Faraday)
For a current to flow around the circuit, there must be an emf.
(An emf is a voltage) The voltage is found to
increase as the rate of change of flux increases.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
![Page 18: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/18.jpg)
Faraday’s Law (Michael Faraday)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx dt
demf
Law sFaraday'
We will get to the minus sign in a short time.
![Page 19: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/19.jpg)
Faraday’s Law (The Minus Sign)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Using the right hand rule, wewould expect the directionof the current to be in thedirection of the arrow shown.
![Page 20: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/20.jpg)
Faraday’s Law (More on the Minus Sign)
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
The minus sign means that the current goes the other way.
This current will produce a magnetic field that would be coming OUT of the page.
The Induced Current therefore creates a magnetic field that OPPOSES the attempt to INCREASE the magnetic field! This is referred to as Lenz’s Law.
![Page 21: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/21.jpg)
How much work?
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
dt
ddVqW
sE/
ChargeWork/Unit
A magnetic field and an electric field areintimately connected.)
emf
![Page 22: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/22.jpg)
So..
dt
ddVemf
sE
FARADAY’s LAW
![Page 23: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/23.jpg)
Flux
AB dB
The MAGNITUDE of the emf induced in a loopis equal to the negative of the rate at which the magnetic flux
through the loop changes with time.
![Page 24: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/24.jpg)
Flux Can Change
If B changes If the AREA of the loop changes Changes cause emf s and currents and
consequently there are connections between E and B fields
These are expressed in Maxwells Equations
AB dB
![Page 25: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/25.jpg)
Maxwell’s Equations(Next Course .. Just a Preview!)
Gauss
Faraday
![Page 26: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/26.jpg)
Another View Of That damned minus sign again …..SUPPOSE that B begins to INCREASE its MAGNITUDE INTO THE PAGE
The Flux into the page begins to increase.
An emf is induced around a loop
A current will flow That current will create a
new magnetic field. THAT new field will change
the magnetic flux.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
![Page 27: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/27.jpg)
Lenz’s Law
Induced Magnetic Fields always FIGHT to stop what you are trying to do!i.e... Murphy’s Law for Magnets
![Page 28: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/28.jpg)
Example of Nasty Lenz
The induced magnetic field opposes thefield that does the inducing!
![Page 29: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/29.jpg)
![Page 30: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/30.jpg)
Don’t Hurt Yourself!
The current i induced in the loop has the directionsuch that the current’s magnetic field Bi opposes thechange in the magnetic field B inducing the current.
![Page 31: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/31.jpg)
Take a deep breath!!
![Page 32: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/32.jpg)
Lenz’s Law
An induced current has a directionsuch that the magnetic field due tothe current opposes the change in the magnetic flux that induces thecurrent. (The result of the negative sign!) …
OR
The toast will always fall buttered side down!
![Page 33: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/33.jpg)
An Example
The field in the diagramcreates a flux given byB=6t2+7t in milliWebersand t is in seconds.
(a)What is the emf whent=2 seconds?
(b) What is the directionof the current in the resistor R?
![Page 34: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/34.jpg)
This is an easy one …
mVemf
tdt
demf
ttB
31724
seconds 2at t
712
76 2
Direction? B is out of the screen and increasing.Current will produce a field INTO the paper (LENZ). Therefore current goes clockwise and R to left in the resistor.
![Page 35: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/35.jpg)
Figure 31-36 shows two parallel loops of wire having a common axis. The smaller loop (radius r) is above the larger loop (radius R) by a distance x >> R. Consequently, the magnetic field due to the current i in the larger loop is nearly constant throughout the smaller loop. Suppose that x is increasing at the constant rate of dx/dt = v. (a) Determine the magnetic flux through the area bounded by the smaller loop as a function of x. (Hint: See Eq. 30-29.) In the smaller loop, find (b) the induced emf and (c) the direction of the induced current.
v
![Page 36: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/36.jpg)
This combines some stuff and is a good review for the final! Or Not.
B is assumed to be constant through the center of the small loop and caused by the large one.
![Page 37: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/37.jpg)
The calculation of Bz
2/322
20
2/122220
2/122
220
2
4
cos
4coscos
xR
iRB
Rdds
xR
R
xR
idsdB
xR
R
xR
idsdBdB
z
z
z
![Page 38: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/38.jpg)
More Work
In the small loop:
Vx
iRr
dt
demf
x
iRr
xR
iRrBrAB zz
4
20
2
3
20
2
2/322
20
22
2
3
2
)prescribed asAway (Far RFor x
2
dx/dt=v
![Page 39: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/39.jpg)
Which Way is Current in small loop expected to flow??
![Page 40: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/40.jpg)
What Happens Here?
Begin to move handle as shown.
Flux through the loop decreases.
Current is induced which opposed this decrease – current tries to re-establish the B field.
![Page 41: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/41.jpg)
moving the bar
R
BLv
R
emfi
BLvdt
dxBL
dt
demf
BLxBAFlux
sign... minus theDropping
![Page 42: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/42.jpg)
Moving the Bar takes work
v
R
vLBP
vR
vLBP
FvFxdt
d
dt
dWPOWER
R
vLBF
orR
BLvBLBiLF
222
22
22
![Page 43: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/43.jpg)
What about a SOLID loop??
METAL Pull
Energy is LOSTBRAKING SYSTEM
![Page 44: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/44.jpg)
Back to Circuits for a bit ….
![Page 45: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/45.jpg)
Definition
Current in loop produces a magnetic fieldin the coil and consequently a magnetic flux.
If we attempt to change the current, an emfwill be induced in the loops which will tend tooppose the change in current.
This this acts like a “resistor” for changes in current!
![Page 46: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/46.jpg)
Definition of Inductance L
i
NL B
UNIT of Inductance = 1 henry = 1 T- m2/A
is the flux near the center of the coil
![Page 47: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/47.jpg)
Consider a Solenoid
n turns per unit lengthniB
or
nliBl
id enclosed
0
0
0
sBl
![Page 48: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/48.jpg)
So….
AnlL
or
AlnL
ori
niAnl
i
nlBA
i
NL B
2
20
0
lengthunit
inductance/
Depends only on geometry just like C andis independent of current.
![Page 49: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/49.jpg)
Inductive Circuit
Switch to “a”. Inductor seems like a
short so current rises quickly.
Field increases in L and reverse emf is generated.
Eventually, i maxes out and back emf ceases.
Steady State Current after this.
i
![Page 50: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/50.jpg)
Consider a “uniform short” coil
section. ANY across uniform be toassumed is and
section"any " acrossflux theis where
:loops NFor
inductor theof loop single aFor
)(
dt
dNemf
dt
demf
N
![Page 51: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/51.jpg)
From before
geometry.on only depends also
asjust geometry, on theonly Depends
)(
0
20
00
0
0
d
AC
AlnL
nAl
NlnAN
i
NL
niANBANN
so
niB
![Page 52: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/52.jpg)
THE BIG INDUCTION
As we begin to increase the current in the coil The current in the first coil produces a
magnetic field in the second coil Which tries to create a current which will
reduce the field it is experiences And so resists the increase in current.
![Page 53: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/53.jpg)
Trying to make an equation out of this…..
dt
diLemf
or
Lidt
d
dt
demf
Li
total
)(
: thatknow also We
L) ofn (definitio N
had We
B
![Page 54: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/54.jpg)
Back to the real world…
i
0
equationcapacitor
theas form same
0
:0 drops voltageof sum
dt
dqR
C
qE
dt
diLiRE
Switch to “a”
![Page 55: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/55.jpg)
Solution
R
L
eR
Ei LRt
constant time
)1( /
![Page 56: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/56.jpg)
Switch position “b”
/
0
0
teR
Ei
iRdt
diL
E
![Page 57: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/57.jpg)
Max Current Rate ofincrease = max emf
![Page 58: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/58.jpg)
constant) (time
)1( /
R
L
eR
Ei LRt
Solve the lo
op equation.
![Page 59: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/59.jpg)
IMPORTANT QUESTION
Switch closes. No emf Current flows for a
while It flows through R Energy is conserved
(i2R)
WHERE DOES THE ENERGY COME FROM??
![Page 60: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/60.jpg)
For an answerReturn to the Big C
We move a charge dq from the (-) plate to the (+) one.
The (-) plate becomes more (-)
The (+) plate becomes more (+).
dW=Fd=dq x E x d+q -q
E=0A/d
+dq
![Page 61: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/61.jpg)
The calc
2
0
2
020
2
00
22
0
2
00
00
2
1
eunit volum
energy
2
1
2
1
2
1)(
2
2
)()()(
E
E
u
AdAdAd
AA
dW
or
q
A
dqdq
A
dW
dA
qdqddqEddqdW
The energy is inthe FIELD !!!
![Page 62: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/62.jpg)
What about POWER??
Ridt
diLiiE
i
iRdt
diLE
2
:
powerto
circuit
powerdissipatedby resistor
Must be dWL/dt
![Page 63: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/63.jpg)
So
2
2
2
12
1
CVW
LiidiLW
dt
diLi
dt
dW
C
L
L
Energystoredin the
Capacitor
![Page 64: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/64.jpg)
WHERE is the energy??
l
Al
NiBA
l
Ni
niB
nilBll
id enclosed
0
0
0
0
0
B
or
0
sB
![Page 65: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/65.jpg)
Remember the Inductor??
turn.onegh flux throu MagneticΦ
current.
inductorin turnsofNumber
i
Ni
NL
?????????????
![Page 66: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/66.jpg)
So …
l
AiN
l
NiANiW
l
NiA
iNi
NiLiW
L
Ni
i
NL
2220
0
0
0
22
2
1
2
1
2
1
2
1
2
1
![Page 67: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/67.jpg)
2
0
2
0
22
0
0
2220
0
2
1
or
(volume) 2
1
2
1
B
:before From
2
1
BV
Wu
VBl
AlBW
l
Ni
l
AiNW
ENERGY IN THEFIELD TOO!
![Page 68: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/68.jpg)
IMPORTANT CONCLUSION
A region of space that contains either a magnetic or an electric field contains electromagnetic energy.
The energy density of either is proportional to the square of the field strength.
![Page 69: Magnetic Induction April 1, 2005 Happenings Short Quiz Today New Topic: Magnetic Induction (Chapter 30) Quiz NEXT Friday Exam #3 – April 15 th. Should](https://reader036.vdocuments.us/reader036/viewer/2022062408/56649eb05503460f94bb5824/html5/thumbnails/69.jpg)