Magnetic Flux and Gauss Law
Another important vector is magnetic flux density B. It is related to H via:
The flux associated with a magnetic field is therefore a measure of the number of magnetic field lines penetrating some surface.
The above picture shows the special case of a plane area S and a uniform flux density B. The normal to the field is at an angle with the field. In this case, the flux is given by:
if B is the value of the flux density.
Generally, if an element of area dS on an arbitrarely shaped surface,
has a magnetic field running through it, the magnetic flux through this area
is BdS, if B is the value of the field at this element.
The total magnetic flux is:
In the applet below, you see a the cross-section of a plane in a magnetic field. Change the angle it has with the field, and notice when it is at maximum and minimum.
Magnetic field are continous and form loops. This is illustrated in the solenoid in the figure below.
For any closed surface the number of lines entering that
surface is equal to the number leaving it, as shown above in red.
That means that the net flux is zero. This is called Gauss' Law.
It is expressed thus:
Therefore at any point: