1) A shperical sheel has inner radius R_in and outer radius R_out. The shell contains total charge Q, uniformly distributed. The interior of the shell is empty of matter and charge. Find the electric field for (a)r>R_out, (b)r<R_in, and (c)R_in<r<R_out respectively. Then sketch a graph of E versus r. [E=electric field] These are the answers I get: a) E=KQ/r^2 [radially outward] where K=9.0x10^9 b) E=0 c) [KQ(r^3-R_in^3)]/[r^2(R_out^3-R_in^3)] where K=9.0x10^9 My problem is for the sketching part on the interval R_in<r<R_out. How can I know the shape of [KQ(r^3-R_in^3)]/[r^2(R_out^3-R_in^3)]. Can I just do some cancellation like r^3/r^2 = r? Would it just be a straight line? But the expression seems like it's a rational function, so would it still be linear? However, to sketch rational functions would require 3 full pages of analysis using calculus...is there any way to do a quick sketch for this part while getting the correct shape? Does anyone have any idea? Thanks for helping!