Explain your reasoning in detail. state where the formulas are coming from, and why they are applicable here. (the goal is, after all, so that we can check and if necessary, you improve your approach and way of thinking about such problems.) write legibly, and draw large and clearly labeled sketches 1. a washer made of nonconducting material lies in the x - y plane, with the center at the coordinate origin. the washer has an inner radius a and an outer radius b (so it looks like a disk of radius b with a concentric circular cut-out of radius a). the surface of the washer is uniformly charged with a surface charge density σ. (a) what is the electric field (as a vector) at a distance z along the z-axis (which coincides with the axis of symmetry of the ring)? note: this part requires integration.] (b) what happens when you let a -> 0? (this corresponds to a charged disk of radius (c) what happens to the answer from part (b) when you let z become very large, i. e., when z »> b? how does this compare to the electric field of a single charge q tv2σ at a distance r-z? note: in this part, you may find the following approximation useful where x is a variable which is very small (i. e., x < 1) and is a real number.! (this formula comes from a taylor expansion, after ignoring terms of order x and higher.) this kind of tool is employed in problems where you have two expressions which nearly cancel, and are trying to tease out the leftover (d) what happens to the answer from part (b) when you next let b -> +oo? (this limit corresponds to an infinite uniformly charged plane. its field can also be calculated using gauss's law, so the answer to this part is hiding in the prelecture for unit 4.)