Faraday’s Law dt d B The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path. EMF
Faraday’s Law EMF The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path.
Jan 06, 2018
Example The magnetic field in the solenoid increases from 0.1 T to 0.7 T in 0.2 seconds. What current will the ammeter measure? Ammeter 电表 Wire Solenoid
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Faraday’s Law
dtd B
The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path.
EMF
Solenoid
Wire
Ammeter 电表The magnetic field in the solenoid increases from 0.1 T to 0.7 T in 0.2 seconds.
What current will the ammeter measure?
2solenoid cm 3A
B
Example
solenoidBAB
tBA
dtd B
solenoidEMF
5.0R
A 108.1EMF 3R
i
Solenoid
Wire
Ammeter 电表The magnetic field in the solenoid increases from 0.1 T to 0.7 T in 0.2 seconds.
What current will the ammeter measure?
2solenoid cm 3A
B
Example
0B
0EMF
dtd B
5.0R
0EMF
Ri
EMF in a coil with many turnsNCE
NCE
NCE
NCE
B
B increasing
turnone around distance
EMF turns
NC
N NC
EN
sdE
EMF in a coil with many turnsNCE
NCE
NCE
NCE
B
B increasing
turnoneEMFEMF N
EMF in a coil with many turnsNCE
NCE
NCE
NCE
B
B increasing
dtdN B
EMF
Solenoid
Wire
Ammeter 电表The ammeter measures a current of 10 A.
Now, we replace the single wire with a coil containing N = 20 turns.
What is the current now?
2solenoid cm 3A
B
Example
5.0R
A 106.3
EMF
EMF
2
turnone turnone
NiR
N
Ri
Another way to make currents with magnetic fields:
Motional EMF动生电动势
v
A conductor moves through a magnetic field. What happens to the charges in the conductor?
B
Magnetic forces polarize the conductor.
v
A conductor moves through a magnetic field. What happens to the charges in the conductor?
B
Connect it to a circuit – it acts like a battery.
i i
v
Magnetic forces acting on the moving rod create EMF in the circuit.
B
sdBvsdqFB
EMF
L i i
vB
L
BLvEMF
i i
Magnetic forces acting on the moving rod create EMF in the circuit.
v
We can also calculate the EMF using the change in magnetic flux.
B
i iL
tLvA
tv
tLvBABB
vB
i iL
tv
BLvtB
But we know this is
the same as the EMF!
We can also calculate the EMF using the change in magnetic flux.
vB
i iL
tv
dtd B
EMF
We can also calculate the EMF using the change in magnetic flux.
dtd B
EMF
This equation works, no matter if
• the magnetic field is changing (Faraday’s Law),
• the area of the circuit is changing (motional EMF),
• or both!
Magnitude of EMF = rate of change of magnetic flux
dtdAB
dtdBA
dtABd
EMF
In a uniform magnetic field:
caused by changing magnetic field
caused by motion in magnetic field
B
B
A
n̂
Example
0.20 m
0.10 m
v
What EMF is induced in the loop, as it moves to the right?
Magnetic flux is not changing, so no EMF.
0EMF
ABdtd
dtd B
30
B
T 3B
B
30
Example
0.20 m
0.10 m
n̂
2initial m 020.0m 10.0m 20.0 A
What EMF is induced in the loop, if it is stretched (被拉大了 )?
T 3B
B
30
Example
0.22 m
0.12 m
What EMF is induced in the loop, if it is stretched (被拉大了 )?
n̂
2initial m 020.0m 10.0m 20.0 A
2final m 026.0m 12.0m 22.0 A
T 3B
Stretching is done in a time of 0.1 s.
23 m 106 A
B
30
Example
0.22 m
0.12 m
What EMF is induced in the loop, if it is stretched (被拉大了 )?
n̂
dtdABAB
dtd
dtd B
EMF
T 3B
s 1.0t
23 m 106 A
B
30
Example
0.22 m
0.12 m
There will be an induced current in the loop while it is being stretched.
n̂
V 2.0s 1.0m 10630cosT 3EMF
23
T 3B
s 1.0t
23 m 106 Aii
ii
Maxwell’s Equations (so far…)
0
inside
qAdE
0 AdB
enclosed0isdB
0 sdE *Not complete
*Not complete
Maxwell’s Equations (so far…)
0
inside
qAdE
0 AdB
enclosed0isdB
AdBdtdsdE
*Not complete
Gauss’ Law for electric fields
Gauss’ Law for magnetic fields
Faraday’s Law
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