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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).
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.
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?
NCE
dt
Bd
Right thumb along
Fingers curl in direction of
dt
Bd
NCE
increasing i
What if we put a conducting wire around the solenoid?
NCE
NCE
A current is induced in the wire.
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
in wire resistance
EMF2 i
1r 2r
(Ohm’s Law)电阻
SolenoidB increasing
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