Derivation of $F=πBsin θ$?

Question

I was searching for a formula for the magnetic force on a current-carrying conductor, and though I am accustomed to the formula $$F=IlBsin θ$$ where $I=$ current, $l=$ length of conductor, $B=$ magnetic field strength and $θ$ is the angle between the conductor and the magnetic field lines).
I found another one in the following link. I read through the derivation of $F=πBsin θ$, but I am still unsure how it was possible to conclude this.

Farcher · Accepted Answer

$pi$ is a "badly chosen" label given it is not formally defined and it is not equal to $3.142....$ but rather equal to $Il$ where $I$ is the current and $l$ is the length of the conductor.
It might well be a typo where Il was mistaken for $pi$?
Look at the text below Figure 22.8.2 where both versions of the equation for the force occur.

Derivation of $F=πBsin θ$?

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