Solenoids and Magnetic Fields

This lecture is based on Serway, Sections 30.4 to 30.8.

A solenoid is a long coil of wire wrapped in many turns. When a current passes through it, it creates a nearly uniform magnetic field inside.
Solenoids can convert electric current to mechanical action, and so are very commonly used as switches.
The magnetic field within a solenoid depends upon the current and density of turns.

In order to estimate roughly the force with which a solenoid pulls on ferromagnetic rods placed near it, one can use the change in magnetic field energy as the rod is inserted into the solenoid. The force is roughly

              
                                 change in magnetic field energy
              force on rod   =   --------------------------------
                                distance rod moves into solenoid

The energy density of the magnetic field depends on the strength of the field, squared, and also upon the magnetic permeability of the material it fills. Iron has a much, much larger permeability than a vacuum.
Even small solenoids can exert forces of a few newtons.
Magnetic flux is defined just as electric flux is: the amount of magnetic field passing perpendicularly through some area. The units of magnetic flux are webers: 1 Wb = 1 T / 1 meter-squared
Gauss' Law for magnetism states that the integral of magnetic flux over some closed surface is equal to zero.
"Displacement Current" is the name given by physicists to an imaginary current which is really just a time-varying electric flux through some area.
With "displacement current" included, Ampere's Law is always true.
Note that a time-varying electric field can act like a current and create a magnetic field -- one more piece of evidence that magnetic and electric phenomena are closely related.

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