3. Scalar potential in magnetostatics. In magnetostatics, it is in general not possible to dene a scalar potential function U such that B = VU and that U is continuous and has a uniquely dened value everywhere. This is unlike electrostatics. This is because we would have ya J = VxB E VXVU = 0, which would clearly cause a contradiction wherever the current density J is nonzero. However, in many cases, it is still possible to introduce such a scalar potential U in restricted regions of space where current is absent. Below you will explore this idea. (a) Apart from the J = 0 requirement, the topology of the restricted region of space also matters. Consider the following two cases: [Hint The line integral of B gives the difference of U between two points. This difference has to be path independent] (1) (1 point) Currents are conned on a sphere surface. Is it possible to separately introduce two magnetostatic scalar potentials Uh, and Um, one inside the sphere and one outside the sphere, respectively? (2) (1 point) Currents are conned on a torus surface. Is it possible to separately introduce two magnetostatic scalar potentials Uh, and Um, one inside the torus and one outside the torus, respectively