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.

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