## Magnetic flux

Glossary Definition for 16-19

#### Description

For a uniform magnetic field, **B**, with direction normal to a plane area of size *A*, the magnetic flux φ
through the area is

φ = *B**A*

In the more general case, as shown in **figure 1**, the magnetic flux is defined as
φ = *B**A*cosθ

*Figure 1: A flat loop of area A is in a region where the magnetic field is B (shown with red field lines in (a)). The component of B directed normally through the area is shown by the vertical dotted line in (b).*

where θ is the angle between the field direction and a line normal to the plane of the area. *B*cosθ is the component of *B* passing at right-angles through the area.

When the field is non-uniform, the flux is calculated using the value of *B* (or *B*cosθ) averaged over the area.

#### Discussion

Magnetic flux is an important quantity that allows us to calculate the emf generated in a coil of wire when the flux through the coil changes, as happens in a dynamo or certain types of microphone. The mechanism for the former typically involves the rotation of a magnet around a stationary coil of wire; the moving magnet creates a time-varying magnetic flux through the coil and hence generates an emf. The size of the emf generated this way is proportional to the rate of change of flux (Faraday’s Law) and its direction is such as to oppose the change in flux that caused it (Lenz’s Law).

#### SI unit

weber, Wb (1 Wb = 1 T m^{2})

#### Expressed in SI base units

kg m^{2} s^{-2} A^{-1}

#### Mathematical expressions

- For a uniform magnetic field of magnitude
*B*, directed normally to the area*A*, the magnetic flux though the area is

φ =*B**A* - In the more general case, as shown in
**figure 1**, the magentic flux is defined as

φ =*B**A*cosθ - When there is a time-varying magnetic flux through a coil of wire with
*N*turns, an emf ε is generated given by a combination of Faraday's Law and Lenz's Law as

ε = − d(*N*θ)d*t*

#### Related entries

- Emf
- Magnetic field

#### In context

The main coil of a typical MRI scanner has an internal cross-sectional area around π × 30 cm^{2} = 0.28 m^{2} and a magnetic field of magnitude 1.5 T. Hence the magnetic flux through this coil is around 0.42 Wb.

#### Reference

- www.healthcare.siemens.co.uk/magnetic-resonance-imaging/0-35-to-1-5t-mri-scanner/magnetom-avanto/technical-details