# Episode 411: Describing magnetic fields

Lesson for 16-19

- Activity time 110 minutes
- Level Advanced

The field around a permanent magnet should be familiar to your students. In practice, where we want a controllable field, we use electromagnets. In this episode, students learn about these fields and the factors that determine their strength and direction.

Lesson Summary

- Demonstration and discussion: The field around a permanent magnet (20 minutes)
- Student experiment: Field plotting (20 minutes)
- Student questions: Revision questions on magnetic fields (20 minutes)
- Student experiments: Measuring flux densities (30 minutes)
- Discussion: Mathematical formulae (10 minutes)
- Student questions: Calculating flux density (10 minutes)

## Discussion and demonstrations: The field around a permanent magnet

Your specification may require the study of the magnetic field due to a permanent magnet but even if this is not the case, such work forms a good introduction to magnetic fields.

The use of two permanent magnets will remind students that there is a magnetic field around each magnet. (This can be done quickly with an OHP or by allowing the students to experiment with a pair of magnets.)

Like other fields, the magnetic field is a way of describing a region of space where other magnets will experience a force. It can be represented by field lines that show both the size and direction of the force.

Teacher: How is the field strength represented?

Student: By the spacing of lines.

Teacher: How is its direction shown?

Student: By arrows showing the direction a compass points or free north pole

moves.

Teacher: Can we find a unit

or free

pole?

Student: No

A discussion of why not will introduce/remind students of magnetic domains.

If there is no unit pole

, then in any definition of the magnetic field, it is not possible to simply extend the idea of unit charge/mass found in electric and gravitational fields.

How can we show up magnetic fields? This gives the opportunity to do some field plotting with iron filings or plotting compasses. There may be a computer program available to extend this further.

If your specification requires it, then this is a good time to define neutral points as places where two or more fields cancel out.

**Iron filings and a horseshoe magnet (Advancing Physics)**

## Student experiment: Field plotting

Having covered magnetic fields for permanent magnets, you can move on quickly to revise the basic magnetic field patterns due to the electric current in a long straight wire, small flat coil and solenoid. Again, this revision is a reminder of pre-16 ideas and demonstrations.

Students can look at some field patterns. If you use the worksheet, you will have to explain that flux is a new term that, for the moment, is simply being used as another word for the field pattern. Its significance will become much clearer quite quickly and it would probably confuse students if a more formal approach were used at this stage. The work is useful because it introduces alternating fields from an alternating current and shows how a search coil can be used to investigate these.

Episode 411-1: Magnetic field shapes seen as flux patterns (Word, 174 KB)

For some specifications, this will serve as a good revision of the basic pre-16 ideas used to describe magnetic fields and it will be possible to move quickly on to the idea of flux density and the force on a conductor.

## Student questions: Revision questions on magnetic fields

The ideas covered above can be reinforced with an activity based on using magnets in automatic train protection. One section suggests that students check that

but this could be made into a written exercise before a couple of questions are attempted.

Episode 411-2: Brush up on magnetism (Word, 43 KB)

Some more questions, revising basic ideas about magnetic fields.

Episode 411-3: Magnetism reminders (Word, 39 KB)

## Student experiments: Measuring flux densities

Some specifications require a more detailed investigation of the magnetic fields due to currents.

Your students should be able to measure the fields due to a long straight wire (sometimes a difficult experiment in which to get good results), a small flat coil and a solenoid. There are many possible approaches and the choice of apparatus will depend on what you have available. A calibrated Hall probe is useful, but the nature of the relationships can be deduced with ac and a search coil. (If you use a calibrated probe then you will need to explain that the unit for field /flux density is the tesla (T) and that this will be defined very soon.)

Whichever flux measurement technique is available, you need only set your students the task of establishing how the flux density depends on the current flowing and the distance (radial distance from a long wire, and along the axis of a flat coil or solenoid).

Episode 411-4: Fields near electric currents (Word, 198 KB)

## Discussion: Mathematical formulae

For a long, straight, current-carrying wire, students will probably find that the field is proportional to the current but the 1r relationship for distance is not always easy to confirm.

Offer them the equation

*B* = μ_{0}*I*2 π *r*

where
μ_{0} = 4 π × 10^{-7} N A^{-2}
is a constant known as the permeability of free space, and ask if their results are compatible with this.

For a solenoid, students should be able to check the relationship of field to both current and the number of turns per unit length.

Hence

*B* = N *I*μ_{0}*L*

The mathematical formula for the field for a small flat coil is not required.

For a coil wound around iron field is given
*B* = N*I*μ*L* where μ depends on the type of iron or other magnetic core material.

## Student questions: Calculating flux density

Episode 411-5: Flux and flux density (Word, 96 KB)