1. Determine the force on a current loop due to a set of N current loops carrying current I situated atpositions r using the concept of the magnetic field \mathbf{B}(\mathbf{r})=\frac{\mu_{0}}{4 \pi} \sum_{k=1}^{N} \oint I_{k} \mathrm{~d} \ell_{k} \times \frac{\mathbf{r}-\mathbf{r}_{k}}{\left|\mathbf{r}-\mathbf{r}_{k}\right|^{3}} and the fact that \mathbf{F}=\oint I d \ell \times \mathbf{B}(\mathrm{r}) Also show that the given expression for the magnetic field satisfies \text { provided } \nabla \cdot \mathbf{j}=\mathbf{0} \text {. }

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7