Explain the concept of magnetic flux.

(N/A) Magnetic flux through a plane of area $A$ placed in a uniform magnetic field $B$ as shown in the figure can be written as $\Phi_{B} = \vec{B} \cdot \vec{A} = BA \cos \theta$.
Where $\theta$ is the angle between the magnetic field vector $\vec{B}$ and the area vector $\vec{A}$. The equation can be extended to curved surfaces and non-uniform fields.
If the magnetic field has different magnitudes and directions at various parts of a surface,then the magnetic flux through the surface is given by the summation of flux through small area elements $d\vec{A}_i$:
$\Phi_{B} = \sum_{i} \vec{B}_{i} \cdot d \vec{A}_{i}$
In the limit where the area elements become infinitesimally small,this summation becomes an integral:
$\Phi_{B} = \int_{S} \vec{B} \cdot d\vec{A}$
Magnetic flux is a scalar quantity. Its $SI$ unit is weber $(Wb)$,which is equivalent to tesla meter squared $(T \cdot m^2)$ or volt-second $(V \cdot s)$. Its dimensional formula is $[M^1 L^2 T^{-2} A^{-1}]$.
Definition of $1 \ Wb$: If a magnetic field of $1 \ T$ is applied perpendicularly to a surface of area $1 \ m^2$,then the magnetic flux linked with the surface is $1 \ Wb$. Thus,$1 \ Wb = 1 \ T \cdot m^2$.