An arbitrary-shaped tangle of wire is connected such that it carries a current \(I_{0}\) from position \(\vec{r}_{1}\) to position \(\vec{r}_{2}\) in a region where there is an external uniform magnetic field \(\vec{B}_{0}\). Show that the magnetic force exerted by the external field on the wire is given by \(\vec{F}_{\mathrm{w}}^{B}=I_{0}\left(\vec{r}_{2}-\vec{r}_{1}\right) \times \vec{B}_{0}\).