Explain the concept of magnetic flux.

Explanation

Magnetic flux through a plane of area A placed in a uniform magnetic field B as shown in figure can be written as `Phi_B=vecB.vecA=BA cos theta`…(1)
Where `theta` is angle between `vecB` and `vecA`. Equation (1) can be extended to curved surfaces and nonuniform fields as shown in below figure.

If the magnetic field has different magnitudes and directions at various parts of a surface as shown in figure, then the magnetic flux through the surface is given by
`Phi_B=vecB_1.d vecA_1 +vecB_2 . dvecA_2 `+....= `Sigma_"all" vecB_i. d vecA_i`...(2)
where .all. stands for summation over all the area elements `dvecA_i` comprising the surface and `B_i` is the magnetic field at the area element `dA_i`.
Equation (2) can be written as below.
`Phi=lim Sigma vecB_i. dvecA_i` where i=1,2,3,.., n `|Delta veca_i| to 0` all
This summation can be written in the form of integration as follow.
`Phi=int_S vecB. dvecA`
Magnetic flux is a scalar quantity. It.s SI unit is weber (Wb) or tesla meter square `(Tm^2)` or volt x second (VS). Its dimensional formula is `[M^1 L^2 T^(-2) A^(-1)]`.
Definition of 1 Wb : “If 1 T magnetic field is applied perpendicularly to `1m^2` surface, then magnetic flux linkes with surface is called 1Wb".
`therefore` 1 weber = 1 tesla x `1 m^2`
`therefore` 1 Wb = `1Tm^2`
CGS unit of magnetic flux : CGS unit of magnetic flux is Maxwell.
1 Maxwell. `(M_x)`=1 Gauss x `1 cm^2`
`1 M_x= 1 G cm^2` [ `because` G is unit of Gauss]
thus 1 Wb = 1 T x `1m^2= 10^4 G xx 10^4 cm^2`
1Wb=`10^8 M_x`
When `vecA` and `vecB` are in same direction flux is positive and when they are in opposite direction flux is negative and when `vecA` and `vecB` are perpendicular then magnetic flux is zero.