Magnetic Flux Density

# Magnetic Field Density

Let's take a round permanent magnet from the stepper motor of an old printer. A magnet has several magnetic poles that create a magnetic field in its surroundings - a space with magnetic forces. The course of magnetic forces (the shape of the field) can be observed with the help of iron filings, which are sprinkled around the magnet. The filings are arranged in the magnetic field in the direction of the magnetic force lines, as they are attracted by the magnetic force along the force lines.

Round permanent magnet. is the north pole and is the south pole of the magnet

The filings are most concentrated near the poles of the magnet. In the picture above, we can see that the magnet has four pairs of magnetic poles. Magnetic poles always appear in pairs, which is why they are also called magnetic dipoles. Since the filings are most concentrated near the poles, we conclude that the magnetic field is strongest there. We say that the magnetic field density is greatest there. The magnetic field density is therefore a physical quantity. Let's denote it with the letter and we can measure it.

Around a permanent magnet, it is measured with the help of:

In the sketch, a greater or lesser density of the magnetic field can be illustrated by a greater or lesser distance between the lines of force. At the poles of the magnet, where the density of the magnetic field is greater, we draw lines close together. Around the magnet, we draw them at a greater distance from each other.

In addition to a permanent magnet, a magnetic field can also be created with the help of an electric current. It is caused by a straight wire or several parallel wires through which an electric current flows. In this case, a magnetic field is created around the wire. If the wire is wound on a cylinder, we get a coil (see below). The magnetic field of the coil is similar to the magnetic field of a bar magnet.

The density of the magnetic field created by the current is directly related to the magnitude of the current flowing through the wire. In this material, we will learn how to calculate the magnetic field density caused by:

• a straight conductor through which an electric current flows or

• current loops - winding or coil.

## Magnetic field density around a conductor and coil

Using the magnetic field strength , we can calculate the magnetic field density . The strength and density of the magnetic field in a vacuum are connected by the formula:

where the is called the permeability of free space and is given as:

Let us now write the magnetic field density at a distance from a current-carrying conductor which is given as:

and inside a narrow air coil with turns and length , the magnetic field density is given as:

Example

The example is available to registered users free of charge.

### Permeability of free space

Although we have already stated the value of the permeability of free space above, it can also be calculated. The definition of current 1 A helps us to achieve this:

• If a current of 1 A flows in the same direction through each of two infinitely long, parallel conductors spaced 1 m apart,

• then the force between the conductors is equal to .

Example

The example is available to registered users free of charge.

The magnetic field density around a long, straight conductor is:

The magnetic field density inside a long and narrow coil is:

The permeability of free space is:

material editor: OpenProf website