Magnetic Field
Electricity and Magnetism

## Magnetic field

Glossary Definition for 16-19 #### Description

A magnetic field exists in any region where a charged particle is subject to a force that depends only on the particle’s charge, velocity and position. The force acts at right angles to both the magnetic field and the particle’s velocity.

The magnetic field at a point is a vector quantity, usually represented by the symbol B.

The magnitude of the magnetic force,F, acting on a positive charge q moving at velocity v in a magnetic field B is

F = qvBsinθ

where θ is the angle between the direction of travel of the particle and the direction of the magnetic field (i.e. the angle between v and B), and v and B are, respectively, the magnitudes of v and B. The force is therefore zero if the particle is moving parallel to the field direction ( θ = 0, sinθ = 0) and greatest when motion is at right angles to the field (sinθ = 1, F = Bqv). Figure 1: The magnitude of the force exerted by a magnetic field upon a moving positively charged particle depends upon the angle, θ , between the particle’s velocity, v, and the magnetic field B. This magnitude is shown by the length of the blue arrow in each diagram. Figure 2: A particle of positive charge q moving with velocity v in a magnetic field which is directed into the page.

When a current exists in a wire within a magnetic field, a force acts on the wire that is the total of all the individual forces on each of the charged particles. When the magnetic field is uniform over a straight section of wire with length L, then that section of the wire is subjected to a force whose magnitude is given by

F = ILBsinθ

where I is the current and θ is the angle between the directions of the wire and the magnetic field.

#### Discussion

Representing magnetic fields Magnetic fields can be represented graphically by magnetic field lines, also called lines of flux. The direction of a field line at any point indicates the field direction at that point. A small dipole test magnet (e.g. a compass needle) placed at a point in the field would align along the field line passing through that point.

A strong field is represented by field lines drawn close together; the more closely spaced, the stronger the field. The magnitude of a magnetic field is proportional to the number of lines of flux passing at right angles through unit area, so that the term ‘magnetic flux density’ is often used as an alternative name for B. The term ‘magnetic field strength’ is also occasionally (incorrectly) used for B itself, and this glossary avoids that term because it might cause confusion between B and B, and also with another quantity introduced in university level physics.

Magnetic fields due to currents in wires At a distance r from a long straight wire, surrounded by air and carrying a current I: B = μ0Ir
where μ0 is the permeability of free space (of a vacuum). Figure 3: The magnitude, B of the magnetic field around a straight current-carrying wire, can be represented by the spacing of field lines, shown in red (a), or in a graph (b).

The field lines are circular and centred on the wire. The field direction is given by the ‘right-hand grip rule’ as shown in figure 3a.

Inside a long straight solenoid with N turns in a length L, with an air core and carrying a current I:

B = μ0INL

The field direction is parallel to the axis of the solenoid.

If the solenoid is wound onto a magnetic material such as iron, the field is much stronger:

B = μrINL

where μr is the relative permeability of the core material. Non-magnetic materials have μr ~ 1. Materials that can be highly magnetised, such as iron, have high relative permeabilities, depending on their purity. Alloys can be manufactured with relative permeabilities of many thousand.

tesla, T

kg s-2 A-1

#### Other commonly used unit(s)

N m-1 A-1, guass, G (1 G=1 × 10-4 T); weber per square meter, Wb m-2

#### Mathematical expressions

• F = sILBsinθ

where F is the magnitude of the force exerted on a straight wire of length L, carrying a current I at an angle θ to the field direction.
• F = qvBsinθ

where F is the magnitude of the force exerted on a positive charge q moving at speed v at an angle of θ to the field direction. This is illustrated in figure 2 for the case θ = 90 °.
• At a distance r from a long straight wire, surrounded by air and carrying a current I, the magnetic field magnitude in very nearly

B = μ0Ir

where the approximation is due to the fact that the magnetic permeabilities of air and of a vacuum are very nearly equal.
• Inside a long straight solenoid with N turns in a length L, with an air core, carrying a current I the magnetic field magnitude is very nearly

B = μ0INL

where μ0 is the permeability of free space (vacuum). The field direction is parallel to the axis of the solenoid.

#### Related entries

• Charge
• Current, electric
• Emf
• Magnetic flux

#### In context

A magnetic field with magnitude B = 1 T is a strong field. The USA National Magnetic Field Laboratory (MagLab) currently hold the record of 45 T for the world’s strongest magnet with a continuous field.

The Earth’s magnetic field resembles that of a large bar magnet titled at about 10 ° to Earth’s rotation axis. Close to Earth’s magnetic poles, the field is vertical and has a magnitude of about 65 μT (6.5 × 10-5 T), and near the equator it is horizontal with a magnitude of about 25 μT. The magnetic fields inside most MRI scanners have a magnitude around 1.5 T. Other naturally occurring magnetic fields range from about ~ 10-14 T (in a magnetically shielded room) to about ~ 1010 T (at the surface of a pulsar).

#### Reference

• https://nationalmaglab.org/news-events/news/national-maglab-racks-up-another-record
###### Magnetic Field
is used in analyses relating to Solenoid Magnet MRI Scanner Particle Accelerator
can be represented by Field Line
can be determined for a Star