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I think this is a misunderstanding on my part, but I want to clear this up.

If I have a current carrying wire, it exerts a magnetic force of $F_B=IlB\sin(\theta).$ My teacher said that this means that $F_B$ scales linearly with $I.$

However we also know that the magnetic field $B$ scales with $I,$ since in this case $B=\frac{\mu_0I}{2\pi r}.$

So $F_B=IlB\sin(\theta)=\frac{\mu_0I^2l}{2\pi r} \sin(\theta),$ which means $F_B$ scales with $I^2$?

I feel like the substitution is wrong, but I don't see why.

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$I$ is the current in the wire on which we are measuring the force. $B$ is the magnetic field produced by some other wire or by some other magnetic device, not the magnetic field produced by the wire in question. Therefore the $B$ in this equation has no dependence on $I$ at all.

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  • $\begingroup$ ahh so the magnetic field is not the same magnetic field being produced by the wire. that makes sense, thanks! $\endgroup$
    – MandelBroccoli
    Commented May 1, 2021 at 3:39

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