Biot-Savart Law.

A dusty record of radius has accumulated a uniform static surface charge density [C/m2 ]. When played, the record spins with angular speed [s-1 ]. Assume the record spins counter-clockwise when viewed from above.

a. Take the divergence of the surface current to show that it is steady.

b. Calculate the , , and components of the incremental magnetic field (d) at height above the center of the disk produced by an element of current at a distance from the center of the disk.

c. Use the results of part to set up integral expressions for the magnetic field at height above the center of the disk. Mathematically inspect the resulting integrals. Are there any components that are equal to zero?

d. Use symmetry arguments based on the geometry of the problem to support your findings from part c.