# What is the definition of magnetic flux?

Magnetic flux defined as “No of field lines intercepting perpendicularly to the plane (or) surface”.

Mathematically interprected by

$phi =overrightarrow{B}centerdot overrightarrow{A}$ $overrightarrow{B}$ – Magnetic induction

$overrightarrow{A}$ – Area vector

Here,

Area is a vector quantity, direction of the Area vector $(overrightarrow{A})$ is perpendicular to the plane (or) surface.

vFor open surface,

We can taken any one direction as Area vector $(overrightarrow{A})$ but we stick to that till the end of problem

vFor closed surface:

Area vector is outward normal.

Case I: [$overrightarrow{B}$ is uniform] and [given surface is plane]

Look at the given plane, Area vector $(overrightarrow{A})$

Of the plane is making angle (Ɵ) with direction of the magnetic induction $left( overrightarrow{B} right)$ the magnetic flux for the plane can be

written as

φ = BAcosƟ

Here, we have resolved the $overrightarrow{B}$ into its components BcosƟ and BsinƟ. Here BcosƟ is perpendicularly intercepting the given plane.

Case: II [$overrightarrow{B}$ is uniform and given surface is arbitrary shape]

For any arbitrary surface, flux can be defined as by dividing the surface into small differential element area (dA) and flux linking the elemental area is (dφ)

dφ = B . dA

Sum of flux through all the elemental area gives rise to flux through the arbitrary surface.

$int{dphi }=int{B.dA}$

If area vector is making angle $overrightarrow{B}$ then $int{dphi }=int{B.dA}$ cos Ɵ

Special cases:

Magnitude of flux is the function of three parameters they are strength of the magnetic induction$(overrightarrow{B})$, magnitude of area and angle (Ɵ) between the $overrightarrow{B}$ and $overrightarrow{A}$ with respect to this flux can be

φ = +ve and -ve

φ = 0 (can be zero also)

(i) Ɵ = 0° [Ɵ – Angle between $overrightarrow{B}$ and$overrightarrow{A}$] $begin{matrix} phi =B.cos theta ,,,,,,,,,,,,,,,,,,,,,, \ phi =BA,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, \ phi =max imum(theta =0{}^circ ) \ end{matrix}$

(ii) Ɵ = 90°

φ = BAcos Ɵ

Magnetic flux density

Magnetic flux is the measure of intensity (or) strength field in the given area.

Magnetic flux is measured in unit is tesla – m2 = Weber

1Wb = Tm2

$frac{Wb}{{{m}^{2}}}=1T$

Wb/m2 is the unit of magnetic induction $(overrightarrow{B})$ some time which is referred as magnetic flux density.

Magnetic flux density = is nothing strength of the magnetic induction.