# Magnetic Force exerted by a current carrying wire

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.

$$I$$ 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.