Post on 04-Apr-2018
7/30/2019 Key concept in Magnetic Flux
1/25
Electromagnetic Induction
Key Concept is Magnetic Flux
7/30/2019 Key concept in Magnetic Flux
2/25
7/30/2019 Key concept in Magnetic Flux
3/25
7/30/2019 Key concept in Magnetic Flux
4/25
Faradays Law
Key Concept is CHANGE in Magnetic Flux
A CHANGING
B through any closed loopinduces an EMF around the loop.
The induced EMF equals the negative of
the time rate of change of the total magnetic
flux through the loop
dt
d B =
7/30/2019 Key concept in Magnetic Flux
5/25
Faradays Law
It doesnt matter why the flux changes
dt
d B =
1) Constant B, Changing Area:
2) Constant Area, Changing B:
3) Constant Area, Constant B, Changing Cos :
==surface surface
B cosBdAAdB rr
where
7/30/2019 Key concept in Magnetic Flux
6/25
7/30/2019 Key concept in Magnetic Flux
7/25
7/30/2019 Key concept in Magnetic Flux
8/25
Direction of the Induced EMFs and Currents
In the previous problem, we found the directionof the induced current by noting that the forceresulting from the induced current had tooppose the applied force. This obbservation canbe generalized into:
Lenzs Law
The direction of any magnetic induction effect
is such as to oppose the cause of the effect
7/30/2019 Key concept in Magnetic Flux
9/25
The Alternator(see Y&F example 30-4)
The magnetic field ,and the angular frequency , are constant
tcosBAcosBAB ==
By Faradays Law:
r
tcosABdt
d B
==
7/30/2019 Key concept in Magnetic Flux
10/25
The Generator(see Y&F example 30-5)
The magnetic field ,and the angular frequency , are constant
tcosBAcosBAB ==
The split-ring commutator rectifies the EMF:
r
tcosABtcosAB ==
7/30/2019 Key concept in Magnetic Flux
11/25
7/30/2019 Key concept in Magnetic Flux
12/25
Direction of the Induced EMFs and Currents
In the previous problem, we found the directionof the induced current by noting that the forceresulting from the induced current had tooppose the applied force. This obbservation canbe generalized into:
Lenzs Law
The direction of any magnetic induction effect
is such as to oppose the cause of the effect
7/30/2019 Key concept in Magnetic Flux
13/25
Induced Electric Fields
nIABA 0B ==
dt
dInA
dt
d0
B
==
This seems very mysterious because there isNO magnetic field outside the solenoid and
therefore there can be NO force on the chargesinside the conducting loop!
The EMF will induce a current that will be
indicated by the Galvanometer.
7/30/2019 Key concept in Magnetic Flux
14/25
Induced Electric Fields
Faradays Law hold even if there is
no Motion and no Magnetic Field
nIABA 0B ==
dt
dInA
dt
d0
B
==
Faradays Law implies that there is an
Induced Electric Field
= ldErr
=dt
dldE B
rr
This Induced Electric Field is a
non-electrostatic field that arises,
not from static charges, but from a
changing B field alone.
7/30/2019 Key concept in Magnetic Flux
15/25
Maxwells Equations
The equations below summarize all of the
underlying physics of Electricity and Magnetism
=0
enclosedQAdE
rr
= 0AdBrr
+= dt
dildB E0C0
rr
= dtd
ldE Brr
Gausss Law
Gausss Law for
magnetism
Amperes Law
Faradays Law
( )BvEqFr
v
vv
+= Lorentz Force Law
AND
7/30/2019 Key concept in Magnetic Flux
16/25
Maxwells Equations in Free Space
If there are no charges and no currents,
Maxwells Equations have a very simple andvery symmetric form:
= 0AdErr
= 0AdBrr
dt
dldB E00
=
rr
= dtd
ldE Brr
Note that a changing B will induce an E and
a changing E will induce a B. This B can in turn induce
an E, which will induce a B, and so on
It can be shown that these equations predict the
existence of a self-sustaining wave that propagates
with a velocity of:
00
1v=
Experimentally this velocity is found to be exactlyequal to the speed of light.
All visible light, as well as radio wave,
microwaves, x-rays, gamma rays, ultraviolet andinfrared radiation are all electromagnetic in origin!
7/30/2019 Key concept in Magnetic Flux
17/25
7/30/2019 Key concept in Magnetic Flux
18/25
7/30/2019 Key concept in Magnetic Flux
19/25
7/30/2019 Key concept in Magnetic Flux
20/25
Inductance
Mutual
Inductance
7/30/2019 Key concept in Magnetic Flux
21/25
Inductance
7/30/2019 Key concept in Magnetic Flux
22/25
Inductance
7/30/2019 Key concept in Magnetic Flux
23/25
How Big is a Henry
7/30/2019 Key concept in Magnetic Flux
24/25
SELF-INDUCTANCE
7/30/2019 Key concept in Magnetic Flux
25/25
Circuit Elements