Flux, Flux Linkage and How do you Induce an Electromagnetic Force?

Flux, Flux Linkage and How do you Induce an Electromagnetic Force?

Method 1:

Pick up a metal rod and swing it about in a magnetic field - for example, the Earth's magnetic field. Although you won't realise it, you have just induced an emf across the ends of the rod.

A simple version would be this:

Inducing Magnetic Fields

As you swipe the metal bar to the left (as shown above) you sweep through the area of field shown by the crosses.

It's this movement through a field that induces (produces) an emf across the bar ends.

Any of the following would mean that you induced more emf:

  • A longer bar would 'sweep' out more area of field.
  • A stronger field would mean you swept through more field lines when moving the same distance.
  • A faster swipe would mean you swept out more area of the field per second.

So the induced emf depends on the length of the conductor, the strength of the magnetic field and the speed at which the conductor cuts the field.

Method 2:

Method 1 shows that moving a conductor through a magnetic field induces an emf, however, it is possible to induce an emf in a stationary conductor, by changing the magnetic field around it. There is more about this in 'Faraday's Law' - the next Learn-it.

The magnetic field strength, B, multiplied by the area swept out by a conductor, A, is called the magnetic flux, φ.

φ = BA

Units of flux: weber, Wb.

You can think of flux as being the amount of magnetic field that you've swept through (not just the area you swept through, but area x field strength.)

The more magnetic flux you sweep through per second, the more emf you induce. Remember the area must be perpendicular to the field!

Note: Don't confuse magnetic flux, φ, with magnetic flux density, which is another name for magnetic field strength, B.

The magnetic flux density or magnetic field strength can be defined as the magnetic flux perpendicular to unit area.

When we are dealing with stationary conductors in changing magnetic fields, we often work with loops and coils of wires.

The area, A, that you use for a single loop of wire is obviously πr2, but what if you have a coil with a number of loops?

Simply treat each loop of the coil as if it was on its own. Hence, if you have 'n' loops in the coil you have 'n' times the area and therefore 'n' times the flux.

This is called flux linkage, Φ.

Magnetic Flux Linkage


What is the flux linkage in a coil of 15 turns and area 25cm2 in a field of strength 5T?


Φ = nφ = nBA = 15 x 5 x 25 x 10-4 = 0.1875 Wb.

Note: Area must be in m2 and the conversion factor is 10,000cm2 to 1m2.