Magnetic Flux

Magnetic flux is identical to Electric Flux in that it measures how much of a Magnetic Field travels through an area. However, because magnetic fields always exist as closed loops, it presents some complications, such as Gauss’ Law always equalling zero.

However, magnetic flux is essential in understanding Electromagnetic Induction, and is used in deriving Faraday’s Law of Induction.

Definition §

Formula §

Magnetic Flux on an Area

$${\Phi }_B=\vec{B}\cdot \vec{A}=BA\cos (\theta )$$

Terms §

• ${\Phi }_B$ = Magnetic Flux (in Webers, $\text{Wb}$ or (rarely) volt-seconds ($\text{Vs}$))
• $\vec{B}$ = Magnetic Field (in $\text{T}$)
• $\vec{A}$ = Area Vector (in ${\text{m}}^2$)
• $\theta$ = Angle between $\vec{B}$ and $\vec{A}$ (from Dot Product)

Magnetic Flux on a Surface is always zero

See below for derivation, but basically because of the dipole nature of magnets, the net flux is always zero

Through Surfaces §

Recall how the Electric Flux of a closed surface can be obtained when there is an internal electric field:

Due to the lack of magnetic monopoles, all magnetic fields exist as loops, resulting in the magnetic flux of a closed surface always being zero, whether the source of the fields is internal (inside) or external:

This means Gauss’ Law does not apply, or at least, isn’t useful.

However, Ampère’s Law does work