# Magnetic Force on a current carrying conductor

Why does a current carrying conductor parallel to the magnetic field not experience a force?

The Lorentz force law says that the force $$\mathbf{F}$$ due to a magnetic field $$\mathbf{B}$$ on a particle with charge $$q$$ moving with velocity $$\mathbf{v}$$ is $$\mathbf{F} = q\,\mathbf{v}\times\mathbf{B}. \tag{1}$$ If $$\mathbf{v}$$ is parallel to $$\mathbf{B}$$, then $$\mathbf{v}\times\mathbf{B} \propto \mathbf{B}\times \mathbf{B}= 0$$ (because the cross-product of any vector with itself is zero), so the force is zero.
In a wire carrying a current in the direction $$\mathbf{u}$$, the charge carriers are moving with velocity $$\mathbf{v}\propto\mathbf{u}$$, so we again have $$\mathbf{v}\times\mathbf{B}=0$$ if $$\mathbf{u}$$ is parallel to $$\mathbf{B}$$.