I am a high school student and I would like to know why in a magnetic field the Force, $F$, is equal to $BIL\sin(\theta)$, where $\theta$ represents the angle between the magnetic field and the current.
I understand that $F$ is proportional to $B$, $I$ and $L$, but I do not understand the inclusion of $\sin (\theta)$. In other words, I would like to see a simple proof or explanation of why the effective length of the wire is $L \sin(\theta)$