We are going to be working with $$current densities$$ for the rest of the term. Let$$s practice writing down some current densities. These are important for understanding books and papers where folks often use these forms as shorthand to describe what they are talking about. $1.$ A sphere $($radius R$,$ total charge Q uniformly distributed throughout the volume$)$ is spinning at angular velocity z$$ about its center, which is at the origin. What is the volume current density J$($r$,$ $,)$ at any point $($r$,$ $,)$ in the sphere? $($Don$$t forget direction too!$)2.$ A very thin DVD has been rubbed so that it has a fixed, constant, uniform surface electric charge density everywhere on its top surface. It is spinning at angular velocity about its center $($which is at the origin$).$ What is the magnitude of surface current density K at a distance r from the center? What is the volume current density J in cylindrical coordinates? $($This may be a little tricky, since the disk is $$very thin,$$ there will be a function. Hint: write down a formula for $($s$,,$ z$)$ first. And, remember that J should be a vector!$)3.$ A very thin plastic ring $($radius R$)$ has a constant linear charge density, and total charge Q$.$ The ring spins at angular velocity about its center, which is the origin. What is the current I, in terms of given quantities? What is the volume current density J in cylindrical coordinates? $($This may be a little tricky, since the ring is $$very thin,$$ there will be some functions. Hint: write down a formula for $($s$,,$ z$)$ first. And, remember that J should be a vector!$)$