Magnetic Fields Tutorial 4 - Magnetic Flux Density, Flux, and Flux Linkage

We have seen how B is called the magnetic field strength, or the flux density, and is measured in Tesla, T.  The magnetic flux density can be thought of as the concentration of field lines.  We can increase the force by increasing any of the terms within the equation.  If we coil up the wire, we increase its length within the magnetic field.


If we look at the magnetic field of a solenoid, we know that it is like a bar magnet:



We can see that the magnetic field strength is uniform within the solenoid.  However the flux density becomes less at the ends, as the field lines get spread out.

We need a term that tells us the number of field lines, and it is called the magnetic flux.  It is given the physics code F (‘Phi’, a Greek capital letter ‘Ph’, or 'F'), and has the units Weber (Wb).  The formal definition is:

The product between the magnetic flux density and the area when the field is at right angles to the area.

In code we write:

F = BA

Remember that flux density is the number of field line per unit area, not unit volume!

The flux linkage is the flux multiplied by the number of turns of wire.  If each turn cuts (or links) flux F, the total flux linkage for N turns must be NF.  We can also write this as NBA.  In other words:

Flux linkage = number of turns of wire ´ magnetic field strength ´ area


The diagram shows the situation when the flux linkage is the greatest.


Question 1

How much flux links a 200 turn coil of area 0.1 m2 when it is placed at 90o to a magnetic field of strength 2.5 ´ 10-3 T?


Now we turn the coil through an angle q.

We now have to change our formula to take the angle into account:

NF = BAN cos q

Where the flux linkage is the greatest, q = 0, hence cos q = 1.  If the coil were parallel to the field, q = 90o therefore cos q = 0.

The flux linkage can be changed in two ways:

We give the change in flux linkage the physics code DF.

Question 2

The coil in question 4 is now turned so that it makes an angle of 60 o with the magnetic field lines.  What is the change in flux linkage?