Magnetic fields (6.3.1)

A magnetic field is an area where a magnet or magnetically susceptible material will experience a non-contact force.

Magnetic field lines represent the size, shape and strength of a magnetic field.

It is important to note that magnetic field lines originate from the north pole of a magnet and enter into the south pole.

The direction of the flux lines shows the direction of the force that would be experienced by a free magnetic north pole at that point in the field. Another north pole would be:

• attracted towards the south pole, and
• repelled away from the north pole.

Bar magnets and neodymium magnets, found in a typical school laboratory, are examples of permanent magnets. They are called permanent magnets because, unlike temporary magnets produced by moving charges, their magnetic fields will not dissipate.

Materials become magnetic due to their electrons. Each electron acts as a miniature magnet, possessing both a north and a south pole.

In most materials, electrons are paired and spin in opposite directions, effectively neutralising their individual magnetic fields. However, in substances like neodymium, some electrons remain unpaired. These unpaired electrons spin in the same direction, leading to a cumulative magnetic field and thus, magnetic properties in the material.

A current passing through a wire creates a temporary magnetic field around it due to the moving charges. The moment the current stops flowing, the magnetic field dissipates.

The diagram above shows a solenoid. A current is passed through a coil of wire, creating a temporary magnetic field around it. This field can be strengthened or weakened by altering the current.

The shape, size and strength of a magnetic field can be represented by magnetic field lines. The technical term for magnetic field lines is flux lines:

• Flux lines that are closer together represent a stronger field (a greater magnetic flux density).
• Flux lines further apart represent a weaker field (a lower magnetic flux density).
• Magnetic flux lines do not cross.

You can visually show a magnetic field’s shape and size by scattering iron filings around a magnet. The filings will align with the magnetic field lines. Alternatively, you could place small plotting compasses around the magnet. The needles will also align with the field lines.

It is important to note that the flux lines originate from the north pole of a magnet and enter into the south pole.

The direction of the flux lines shows the direction of the force that would be experienced by a free magnetic north pole at that point in the field. Another north pole would be:

• attracted towards the south pole, and
• repelled away from the north pole.

A uniform magnetic field arises where the field lines are equally spaced and parallel. This represents an area where the magnetic field strength (the magnetic flux density) is the same everywhere in the region.

In the above diagram, the region directly between the north and south poles contains a uniform field, whereas the outside area (shown by the curved field lines) does not.

Two opposing magnetic poles are attracted to each other. A strong magnetic field between the two poles pulls them towards each other.

The diagram below shows that this is due to the flow from north to south being diverted from the magnet’s own south pole to the other magnet’s south pole.

The magnetic field is considered a uniform field where the lines are equally spaced and parallel. This represents an area where the magnetic field strength (the magnetic flux density) is the same everywhere.

Two like poles (north-north or south-south) will repel each other. Between the magnets, there is a null area where no force is experienced. This is because magnetic flux lines cannot cross.

Magnetic field lines (flux lines) are observed around permanent magnets and current-carrying wires. The shape of the magnetic field depends on the arrangement of the wire.

Some examples of this include a long straight wire and a coil of wire, referred to as a solenoid.

A straight current-carrying wire will produce a circular magnetic field around it at 90 degrees to the direction of the current.

The field is strongest and closest to the wire, but it gets weaker with distance. This is shown by the field lines being denser closer to the wire and becoming increasingly spaced as the distance from the wire increases.

The direction of the magnetic field can be determined by using Maxwell’s right-hand rule.

To apply Maxwell’s right-hand rule:

• The thumb should point in the direction of the conventional current flowing through the wire. In an electrical circuit with a cell, the conventional current flows from the positive end of the cell to the negative end of the cell.
• The fingers curl in the direction of rotation of the circular magnetic field.

Current flowing through a coil of wire will produce a magnetic field similar to that found around a permanent bar magnet. This arrangement is known as a solenoid. It will form a north pole at one end (where the field lines originate from) and a south pole at the other (where the lines return to).

The right-hand rule can be used to determine which end is the north pole and which is the south pole.

• Grab the coil so that the fingers follow the direction of the conventional current
• The thumb will point towards the north pole.

The strength of the magnetic field can be increased by using more turns in the coil or by adding a ferrous core, such as an iron nail.

In a flat coil of wire carrying a current, the magnetic field lines will leave from one side of the coil (the north pole) and enter the other side of the coil (the south pole).

The direction of the field lines can be found using the right-hand rule. The thumb points in the direction of the conventional current. The fingers curl in the direction of rotation of the circular magnetic field.

Fleming’s left-hand rule can be used to determine the direction of the force on moving charged particles in a magnetic field.

• The middle finger points in the direction of conventional current, so it is important to note that this is the direction in which positive charges are travelling.
• The index finger represents the direction of the magnetic field.
• The thumb points in the direction of the force felt by the moving charge.

A common memory tool to remember the order is FBI. Where:

• F represents force,
• B represents magnetic field, and
• I represents current.

The direction of the magnetic field can be represented in three different ways depending on the observer’s viewpoint. If the magnetic field is:

• at right angles to the observer, it is represented by arrows pointing in the direction of the field.
• pointed towards the observer, or out of the page, it is represented by circles or dots.
• pointed away from the observer, or into the page, it is represented by crosses.

A common memory tool is to picture an archery arrow. If the arrow travels away from you, you see the cross shape of the feathers on the back, whereas if it travels towards you, you will see the round shape of the arrowhead.

When a charged particle enters a uniform magnetic field, it will experience a force. Using Fleming’s left-hand rule, you can determine the direction of that force.

In the diagram above, the magnetic field is acting into the page. The conventional current is the direction in which positive charges are travelling. This causes the positive charge to experience an upward force. The negative charge will experience a force in the opposite direction.

The strength of a magnetic field (magnetic flux) can be investigated using a current-carrying wire and a digital balance. The experiment is set up as in the diagram below, with a magnet resting on a digital balance. The balance should be zeroed.

1. A taught wire should be passed between the two poles of the magnets and clamped in place so it cannot move. Ensure the wire is perpendicular to the magnetic field, as this will generate the largest forces and help reduce uncertainty in the measurements.
2. The length of the wire within the field should be measured.
3. The wire is connected to a series circuit that includes a way to alter the current, such as a variable resistor or a variable power supply, and a way to measure the current, such as an ammeter.
4. Slowly increase the current in equal increments and measure the force detected by the balance. The balance will typically be set to read in grams, which can be converted into newtons by first dividing by 1000 and then multiplying by 9.81.
5. This should be done at least seven times, and each result should be repeated thrice.
6. Then, a graph should be plotted, with force on the –axis and current multiplied by length on the -axis. The gradient will equal the strength of the magnetic field.

The strength of a magnetic field is referred to as the magnetic flux density and is measured in Teslas (T). It can be thought of as the density of magnetic flux lines within a area.

A standard magnet found in a school laboratory will have a magnetic flux density of approximately . The magnets in MRI machines are much stronger, reaching or more. When activated, the electromagnets in the Large Hadron Collider can reach up to .