D.4.1 (HL)—Magnetic flux

Define magnetic flux

Magnetic flux measures the magnetic field passing through an area. Here $\theta$ is the angle between the field and the normal to the surface, not the surface itself. Flux has unit weber, $\mathrm{Wb}=\mathrm{T\,m^2}$.

Worked example — square loop

For side $6.2\,\mathrm{cm}=6.2\times10^{-2}\,\mathrm{m}$, $A=(6.2\times10^{-2})^2\,\mathrm{m^2}$. In $B=4.3\times10^{-4}\,\mathrm{T}$ with $\theta=45^\circ$, $\Phi=BA\cos\theta=1.2\times10^{-6}\,\mathrm{Wb}$. For $N$ identical turns, flux linkage is $N\Phi$.

Use flux linkage

For a coil with $N$ turns, the linked flux is $N\Phi$. A change can result from changing $B$, $A$, $\theta$, or the number of turns. Keep the angle convention explicit: it is not generally the angle between B and the plane itself.

Check the geometry

At $\theta=0$, field and area normal align and $\Phi=BA$. At $\theta=90^\circ$, the field is parallel to the surface and $\Phi=0$. Convert area to square metres before substitution.

Common trap

Do not use the angle between B and the plane when the formula expects the angle to the normal. Do not confuse flux $\Phi$ with flux linkage $N\Phi$.