3.(adapted from Prob. 4, p. 128, Brown's Introductory Physics II) (a)Find the potential due to a thin disk of charge with radius R and uniform surface charge density \sigma_{0}=\frac{Q}{\pi R^{2}}

at a point on the z axis, a distance z from the center of the disk. Do this one of two ways: (i) Use the definition of potential as the negative integral of the electric field and integrate the form in assignment 3A #2. Be careful evaluating at infinity: do the integral as a single function (don't evaluate the pieces separately) and take the limit of that result to find the value at infinity. (ii) Use the result that we derived in class for the potential due to a ring of charge Q with radius a,and integrate rings of charge dq and radius r to build a disk of radius R. Follow the same process that we used in chapter 2 to find the electric field due to a disk by changing Q and a for the ring into dq and r, rewriting dq in terms of o, and r, and integrating with respect to r. (b)Expand the result to leading order in the two limits R>>z: and R<