Magnetic Flux is defined as;

**“a total number of lines of magnetic force passing through any surface placed perpendicular to the magnetic field. It is denoted by φ (Greek Letters Phi).**

**Magnetic Flux Formula**

The magnetic flux is also defined as the dot product of magnetic field B and vector Area A, as shown in the following figure.

$\text{Magnetic }\!\!~\!\!\text{ Flux}=\text{ }\!\!\varphi\!\!\text{ }=B.A~~~\text{ }\cdots \text{ }~~~~~\left( 1 \right)$

Where θ is the angle between B and vector area A or the outward normal drawn to the surface area as shown in above figure. A is a vector area whose magnitude is the area of the element and its direction is along the normal to the surface of the element.

**Maximum Flux**

If the magnetic field is directed along the normal to the area, so θ is 0 as shown in the following figure.

Now by equation (1), we get

$\varphi =BAcos~\left( {{0}^{}} \right)$

Hence

$\varphi =BA~~~~\cdots \text{ }~~~~\left( 2 \right)$

Equation (2) shows that the magnetic flux is maximum when the angle between a magnetic field and normal to an area is zero.

**Minimum Flux**

If the magnetic field is parallel to the plane of area and angle between the field and normal to an area is 90^{° }as shown in the figure.

Then

$\varphi =BAcos~\left( {{90}^{o}} \right)$

$\varphi =0$

It means that flux through an area in this position is zero or minimum.

**Magnetic Flux Unit**

SI unit of magnetic flux is Weber, as explained below,

$\varphi =BAcos\theta $

$\varphi =BA~~~~\text{ }~~\therefore ~~surface~area~perpendicular~to~B,~so~Cos\theta =1~~$

$\varphi =\frac{Newton}{Ampere-meter}*~mete{{r}^{2}}$

$\varphi =\frac{N}{A-m}*~{{m}^{2}}$

$\varphi =\frac{Nm}{A}$

$\varphi =Weber$

Hence magnetic flux unit is NmA^{-1}^{ }or weber. Whereas

\[1\text{ }Weber={{10}^{8}}lines\text{ }of\text{ }force\]

**Example**

A certain magnet has a flux φ = 1.5 Weber. How many lines of force does flux represent?

Solution:

By definition,

\[1\text{ }Weber={{10}^{8}}lines\text{ }of\text{ }force\]

So,

\[1.5\text{ }Weber\text{ }=\text{ }1.5\text{ }*\text{ }{{10}^{8}}lines\]

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