Maxwell’s Equations (so far…) *Not complete

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.

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.

Where there is a time-varying magnetic field, there is also a curly electric field.

Curly electric field (both inside and outside solenoid)

No curly electric field

We call the curly electric fields Non-Coulomb electric fields E NC They are related to magnetic fields that are changing in time:

Which direction does the electric field curl?

Right thumb along Fingers curl in direction of

Which direction does the electric field curl?

What if we put a conducting wire around the solenoid? A current is induced in the wire.

Solenoid B increasing Metal wire How big is the current i 2 ?

EMF (ElectroMotive Force) EMF is actually not a force. It is the energy per unit charge added to a circuit during a single round trip. EMF = Units: Volts

Metal wire EMF = Solenoid B increasing

Metal wire (Ohm’s Law) 电阻 Solenoid B increasing

We can measure E NC by measuring the induced current.

Experiments: i 2 is only present when i 1 is changing. EMF

Experiments: i 2 is proportional to the area of the solenoid. EMF

Faraday’s Law This is the magnetic flux through the loop. EMF

Faraday’s Law The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path. EMF

Faraday’s Law The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path.