2.0 Magnetic Flux

Magnetic flux is the number of magnetic field lines passing through a closed surface. It is denoted by ${\Phi _m}$ . Magnetic flux is given by the product of magnetic field and the area perpendicular to the magnetic lines.IMG

${\Phi _m}$ = $BA\cos \left( \theta \right)$

$ = B \bullet A$ (dot product)

The SI unit of magnetic flux is Weber or volt –second.

Magnetic flux through an arbitrary surface which has different magnitudes and directions of magnetic field and different area of passing magnetic field can be given by the sum of the magnetic flux of all components.

= $\sum\limits_{}^{} {{B_i}} \bullet {A_i}$

Example: What is the value of magnetic flux passing through a hemisphere of radius $R$? Magnetic field is perpendicular to the surface at each point (shown in figure).

Solution: For a small area $dA$ magnetic flux is

$d{\Phi _m} = B \bullet dA$

$d{\Phi _m} = BdA\cos (\theta )$

For $\theta = 90^\circ $

$d{\Phi _m} = BdA$

${\Phi _m} = B\sum {dA} $

${\Phi _m} = BA$

${\Phi _m} = 2B\pi {r^2}$ Weber