lectures 16-17 (ch. 29) electromagnetic induction 1.the law of em induction 2.the lenz’s rule 3....
Post on 29-Dec-2015
233 Views
Preview:
TRANSCRIPT
Lectures 16-17 (Ch. 29)
Electromagnetic Induction1. The law of EM induction2. The Lenz’s rule3. Motional emf: slide wire generator, Faraday’s disc dynamo, Ac and dc current generators
Electromagnetic Induction, 1830-1832
Joseph Henry (1797-1878) Michael Faraday (1791-1867)
Change of magnetic flux through the loop of wire induces current (i.e. emf) in the loop.
Law of EM Induction (Faraday’s law)
)(111][
cos
2 weberWbmT
dABdABAdB
B
AAA
B
dt
d B
dt
dl B
0
Flux can be changed by change of B or A or angle between B and dA.In order to find the direction of the induced current it is convenient to write the faraday’s law in the form
It is convenient to choose in such direction that
0l
Ad
where is the unite vector of a circulation in the loop which direction is connected with by a RHR:
0 AdB
Ad
0l
Ad
Wilhelm Weber (1804 – 1891)
Examples. Find direction of the induced current.
0l
0l
00 l00 l
Induced current is in the direction of
0l
Induced current is in the direction opposite to
0l
dt
dl B
0
Lenz’s law
Heinrich Lenz (1804 –1865)
Magnetic field produced by induced current opposes change of magnetic flux
Motional emfSlide-wire generator
Blvl
lvdtdAdt
dAB
dt
dl B
0
0
Origin of this emf is in separation of charges in a rod caused by its motion in B.
vBl
ldBv
q
ldF
BvqF
a
b
a
b
m
m
)(
Motional emf exists in the conductor moving in B. It does not require the existence of the closed circuit.
The secondary magnetic force
lBIFm
'
lBIFF mext
'
External force is required to keep constant velocity of the rod
R
vBlBlv
RIBlv
dt
dxF
dt
dWP
R
vBl
RRIP
extmech
el
2
222
)(
)(
m’
Example. Find motional emf in the rod.
IL
d
Example. Find induced current in the loop with resistance R.
I
V
V
ExampleA single rectangular loop of wire with the dimensions inside a region of B=0.5 T and part is outside the
field. The total resistance of the loop is 0.2Ω . The loop is pulled from the field with a constant velocity of 5m/s.
1)What is the magnitude and direction of the induced current?2) In which part of the loop an induced emf is developed?3) Find the force required to pull the loop at a constant velocity.4) Explain why such force is required.
xB v0.1m
0.5m
0.75m
Example
30cm
40cmv=2cm/s
xB=1T
Find emf in each side of the loop and the net emf when the loop is the region:a)all inside the region of Bb)partly outside of this regionc)all outside of this region
AC –current generator (alternator)
R
tABtIABB
R
tBA
RI
tBAdt
d
tBA
tBA
222 sinsin
sin
sin
cos
,cos
Induced current results in torque which slows down a rotation. External torque is required to maintain the rotation with a constant frequency.
2007 Nobel Prize in Physics
Peter Grünberg Albert Fert
For the discovery of the giant magnetic resistance
Tiny magnetic field triggers large change in electrical resistance.
Better read-out heads for pocket-size devices: miniaturization of PC, ipods, etc.
Big RB
Small RB
Resistance strongly depends on the direction of the spin in the first ferromagnetic layer. When it is the same as in the next ferromagnetic layer R is small, when it’s opposite to it R is big.
I
Eddy currents responsible for levitation and Meisner effect in superconductors
Meisner’s effect
Bind
B0
vN
S
Induced nonelectrostatic electric field
dt
d B
Origin of emf? No motion, moreover no B outside solenoid, i.e. in the region of a wire loop. Then it should be E which results in induced current.
0
0,
ldE
dt
dldE
ldFEqF
dt
d
q
ldF
B
elel
Bel
Nonconcervative force
Nonelectrostatic field
0dt
dI
0dt
dI
B(t) should induce E by independently on the presence of the loop of the wire!Let’s find E(r).
dt
dldE B
r
R
dt
dinE
dt
dBRrE
Rr
rdt
dinE
KniBdt
dBrrE
Rr
m
2
2
0
2
2
2
)22
,
2
.1
E
R
r
R
Displacement current
1
2
dB/dt produces E. Let’s show that dE/dt produces B!Consider the process of charging the capacitor.Calculate B in front of the plate of capacitor at r>R.
encl
line
IldB 0
Using the plane surface 1 we get cirB 02 Using the bulging surface 2 we get 02 rB
We come to contradiction! What is wrong ?
)(
,
,,,
0
000
00
dc
ddd
Ec
iildB
dt
dE
A
iji
dt
d
dt
dEA
dt
dqi
AEqEdVd
ACCVq
1.Now we get the same answer for both surfaces 1 and 2!2. B≠0 between the plates!
)(dt
dildB E
General form of Amper’s law
Let’s find B between the plates.
r
iB
irB
RrR
riB
R
i
A
ij
R
rirjrB
Rr
c
d
c
cdd
cd
2
2
.22
2
.1
0
0
20
2
2
2
02
0
B
rR
μ= Kmμ0, ε=Kε0,
In free space K=1, Km =1
Maxwell’s equations
James Clerk Maxwell (1831 –1879)
)(dt
dildB Eencl
dt
dldE B
enclq
AdE
0 AdB
Two Gauss’s laws + Faraday’s law +Amper’s law
Maxwell introduced displacement current, wrote these four equations together, predicted the electromagnetic waves propagating in vacuum with velocity of light and shown that light itself is e.m. wave.
1865 Maxwell’s theory 1887 Hertz’s experiment1890 Marconi radio (wireless communication)
top related