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Maxwell’s Equations (so far…). *Not complete. *Not complete. Can a distribution of static charges make this field?. Electrostatic forces are conservative . The change in potential around a loop must be zero. for fields made by charges at rest. means: - PowerPoint PPT Presentation
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Maxwell’s Equations (so far…)
0
inside
q
AdE
0 AdB
enclosed0isdB
0 sdE
*Not complete
*Not complete
sd
E
rEsdE 2
0 sdE
for fields made by charges at rest.
Can a distribution of static charges make this field?
Electrostatic forces are conservative.
The change in potential around a loop must be zero.
0 sdE
means:
No curly electric fields.
BUT: This is only true for “Coulomb” fields (fields caused by stationary charges).
There is another way to make electric fields.
increasing B
E
E
E
E
E
E
E
E
Where there is a time-varying magnetic field, there is also a curly electric field.
increasing i
Curly electric field (both inside and outside solenoid)
E
increasing B
steady i
No curly electric field
changingnot B
We call the curly electric fields Non-Coulomb electric fields ENC
They are related to magnetic fields that are changing in time:
dt
BdENC
increasing i
Which direction does the electric field curl?
dt
Bd
NCE
increasing i
Which direction does the electric field curl?
NCE
dt
Bd
Right thumb along
Fingers curl in direction of
dt
Bd
NCE
increasingB out,
Which direction does the electric field curl?
page into dt
Bd
NCE
B
decreasingB out,
Which direction does the electric field curl?
page ofout dt
Bd
NCE
B
increasingB in,
Which direction does the electric field curl?
page ofout dt
Bd
NCE
B
decreasingB in,
Which direction does the electric field curl?
page into dt
Bd
NCE
B
increasing i
What if we put a conducting wire around the solenoid?
NCE
NCE
A current is induced in the wire.
B
SolenoidB increasing
Metal wire
1i2i
NCE
NCE
NCE
NCE
1r 2r
How big is the current i2?
EMF (ElectroMotive Force)
EMF is actually not a force.
It is the energy per unit charge added to a circuit during a singleround trip.
EMF = sdENC
Units: Volts
B
Metal wire
1i2i
NCE
NCE
NCE
NCE
22 rEsdE NCNC
EMF =
1r 2r
SolenoidB increasing
B
Metal wire
1i2i
NCE
NCE
NCE
NCE
in wire resistance
EMF2 i
1r 2r
(Ohm’s Law)电阻
SolenoidB increasing
1i
We can measure ENC by measuring the induced current.
2i
B
1i2i
1r 2r
Experiments: i2 is only present when i1 is changing.
i
t
1i
2i
EMF dt
dB
B
1i2i
1r 2r
Experiments: i2 is proportional to the area of the solenoid.
B
1i2i1r
2r
21rEMF
Faraday’s Law
21rBdt
d
This is the magnetic flux through the loop.
B
B
1i2i
1r 2rEMF
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
AdBdt
dsdE
The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path.
