**Magnetic flux** through any surface area is defined as the total number of magnetic lines of force passing through that surface.

Let us consider a uniform magnetic field of strength $B$ acting on a small surface area $A$ making an angle $\theta$ with the normal on the surface. Then, magnetic flux $(\phi)$ is measured by the dot product of magnetic field $(\overrightarrow{B})$ and area vector $(\overrightarrow{A})$.

\[\therefore\phi=\overrightarrow{B}\cdot\overrightarrow{A}\]

\[\phi=BA\cos\theta\]

Magnetic flux $(\phi)$ is a scalar quantity because it is a scalar product of vector $(\overrightarrow{B})$ and area vector $(\overrightarrow{A})$.

- If magnetic field $(B)$ is parallel to the surface (i.e. angle between $B$ and the normal $(\theta)$ is $90°$) then \[\phi=BA\cos 90°=0\text{ [minimum value]}\]
- If magnetic field $(B)$ is perpendicular to the surface (i.e. angle between $B$ and the normal $(\theta)$ is $0°$) then \[\phi=BA\cos 0°=BA\text{ [maximum value]}\]

In SI unit, magnetic flux is measured in Weber $(\text{Wb})$.

If $B=1\text{ T}$, $A=1\text{ m}^2$ and $\cos\theta=1$, then we have

\[\phi=BA\cos\theta=1\text{ Wb}\]

Hence, magnetic flux is said to be of $1\text{ Wb}$ if a uniform magnetic field of $1\text{ T}$ acts normal to the area of $1\text{ m}^2$.

## Magnetic Flux Density

The number of magnetic lines of force per unit normal area is called magnetic flux density. It is also known as **magnetic field strength** or **magnetic field induction**.

Mathematically, \[\text{Magnetic Flux Density}=\frac{\text{Magnetic Flux}}{\text{Normal Area}}\]

\[B=\frac{\phi}{A}\]

Its SI unit is $\text{Wb m}^{-2}$ which is called Tesla $\text{T}$. \[\therefore 1\text{ T}=1\text{ Wb m}^{-2}\]

Another non SI unit commonly in use is Gauss $\text{(G)}$ which is related to Tesla as $1\text{ T}=10^4\text{ G}$.

[**Learn more about Magnetic Flux Density:** Magnetic Flux Density (Magnetic Vectors)]

## Flux Linkage

Consider a coil of $N$ number of turns having cross sectional area of each turn $=A$. Let the coil be placed in a magnetic field of strength $B$ which makes an angle $\theta$ with the normal to the plane of the coil. Then, the total magnetic flux passing through the coil is called **flux linkage**.

\[\therefore\text{Flux Linkage }(\phi)=NBA\cos\theta\]