## What is magnetic flux?

Magnetic flux is a measurement of the total magnetic field which passes through a given area. It is a useful tool for helping describe the effects of the magnetic force on something occupying a given area. The measurement of magnetic flux is tied to the particular area chosen. We can choose to make the area any size we want and orient it in any way relative to the magnetic field.If we use the field-line picture of a magnetic field then every field line passing through the given area contributes some magnetic flux. The angle at which the field line intersects the area is also important. A field line passing through at a glancing angle will only contribute a small component of the field to the magnetic flux. When calculating the magnetic flux we include only the component of the magnetic field vector which is normal to our test area.

- If we choose a simple flat surface with area A as our test area and there is an angle θ between the normal to the surface and a magnetic field vector (magnitude B) then the magnetic flux is,

Φ=BAcosθ.

In the case that the surface is perpendicular to the field then the angle is zero and the magnetic flux is simply BA A. Figure 1 shows an example of a flat test area at two different angles to a magnetic field and the resulting magnetic flux.

Exercise 1:

If the blue surfaces shown in Figure 1 both have equal area and the angle θ degree, how much smaller is the flux through the area in Figure 1-left vs Figure 1-right?

## How do we measure magnetic flux?

The SI unit of magnetic flux is the Weber (named after German physicist and co-inventor of the telegraphWilhelm Weber) and the unit has the symbol Wb\mathrm{Wb}Wb.

Because the magnetic flux is just a way of expressing the magnetic field in a given area, it can be measured with a magnetometer in the same way as the magnetic field. For example, suppose a small magnetometer probe is moved around (without rotating) inside a0.5 m20.5~\mathrm{m^2}0.5 m2 area near a large sheet of magnetic material and indicates a constant reading of 5 mT5~\mathrm{mT}5 mT. The magnetic flux through the area is then(5⋅10−3 T)⋅(0.5 m2)=0.0025 Wb(5\cdot 10^{-3}~\mathrm{T})\cdot(0.5~\mathrm{m^2}) = 0.0025~\mathrm{Wb}(5⋅10−3 T)⋅(0.5 m2)=0.0025 Wb. In the event that the magnetic field reading changes with position, it would be necessary to find the average reading.

A related term that you may come across is themagnetic flux density. This is measured in Wb/m2\mathrm{Wb/m^2}Wb/m2. Because we are dividing flux by area we could also directly state the units of flux density in Tesla. In fact, the term magnetic flux density is often used anonymously with the magnitude of the magnetic field.

caused by the changing magnetic field.

- While the magnetic flux through a closed surface is always zero, the magnetic flux through an open surface need not be zero and is an important quantity in electromagnetism.[citation needed]

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