Define magnetic flux. State its S.I. unit and write its dimensional formula
Defination of Magnetic Flux :
It is defined as the number of magnetic field lines passing through a surface. It is denoted by .
Consider a surface S in a uniform magnetic field $\vec{B}$. Let the surface is made up of small elements each of area vector $\vec{dS}$ . If the magnetic field makes an angle with the area vector $\vec{dS}=(ds) \hat{n}$ then the magnetic flux linked with the small element is given by
$d\phi_B = \vec{B} \cdot d\vec{S} \quad ...(1)$
The magnetic flux through the surface S is equal to the sum of magnetic flux linked with all elements each of area vector $\vec{dS}$ of the surface.
That is,
$\phi_B = \sum \vec{B} \cdot d\vec{S} \quad ...(2)$
If the elements are very small in area and extremely large in number, then the magnetic flux linked with the closed surface is written as
$\phi_B = \oint_S \vec{B} \cdot d\vec{S} \quad ...(3)$
S.I Unit of Magnetic Flux :
S.I. unit of magnetic flux is weber (Wb).
$1 \text{ Wb} = 1 \text{ tesla metre}^2 \; (1 \text{ T m}^2)$
Dimensional formula of magnetic flux:
$\phi_B = B \times ds$
$= \text{magnetic field} \times \text{area}$
$= M^1 L^0 T^{-2} A^{-1} \times L^2$
$= [M L^2 T^{-2} A^{-1}]$