Charged Sphere with a Hole -- Check my work? 1. The problem statement, all variables and given/known data You have a spherical shell of radius a and charge Q. Your sphere is uniformly charged except for the region where θ<= 1° (which has σ = 0). Imagine that your field point is somewhere on the positive z-axis (so z could be larger or smaller than a). Determine E as a function of z. I believe I can represent this as a uniformly charged sphere without a hole and a thin disk with a charge density of -σ. Then the law of superposition lets me add the two together. I think I did it right, but before I go on to the computer program portion of the assignment, I'd love if somebody would double-check my logic and work. If you see an error, please let me know. If you think it's correct, let me know that, too. 2. Relevant equations sin(1°) = r/a Where r is the radius of the disk. r = sin(1°)a = 0.017a E field of a sphere: E(r) = Q/(4∏r2ε0) = σa2/(r2ε0) E field of a disk: E(z) = q/(2∏ε0(0.017a2)*(1-z2/(√z2+(0.017a)2)) 3. The attempt at a solution Along the z-axis, the E field of the sphere can be written as E(z) = σa2/(z2ε0) Therefore, Etotal = σa2/(z2ε0) + q/(2∏ε0(0.017a2)*(1-z2/(√z2+(0.017a)2)) or Etotal = σ/ε0*(a2/z2 - 1/2 + z/√(z2 + (0.017a)2) Is this correct? I'm sorry if it's messy and thank you, thank you in advance.