Question

Only need help on B

1. [Total: 20 pts a) 112 pts) A long coaxial cable carries a uniform volum e charge density ρ throughout an inner cylinder (radius a) and a uniform surface charge density σ on the outer cylinder (radius b). The cable is overall electrically neutral. Find E everywhere in space, and sketch it b) [8 pts We typically consider cases in class where charge is distributed completely uniformly, but it's not always that way - let's consider a sphere (radius R) with surface charge density σ σ0 sin2(0) cos2(d). Describe briefly in word and/or pictures what this charge distribution "looks like". Can you use Gauss's Law to calculate the electric field in this case? Why/why not? Briefly, but clearly, explain. If you can use Gauss's Law t calculate the E-field, do so. If vou cannot use Gauss's Law briefly describe the procedure to calculate the E-field. (There is no need to perform any integral in this part of the problem.) ate the E-field, do so. If you cain

Answer 1

We always use Gauss law to find Electric fields whether distribution is symmetric otherwise Anti symmetric but Gauss law is used for symmetrical geometry (i.e.,) geometry may be spherical, cylindrical or planner. Gauss law, contourintegral E vector middot n^^ds = q_in/t_0 q_in = doubleintegral sigma_0 (theta, phi) dA dA = R^2 sin theta d theta d phi rightarrow surface Area element in (r, theta, phi) q_in = integral^2 pi_0 integral^pi_0 sin^2 theta cos^2 phi d theta d phi R^2 sin theta q_in = sigma_0 R^2 integral^2 pi_0 cos^2 phi d phi integral^pi_0 sin^3 theta d theta q_in = sigma_0 R^2 [integral^2 pi_0 cos^2 phi d phi integral^pi_0 sin^3 theta d theta] {for sphere of Radius R phi rightarrow 0, 2 pi theta rightarrow 0, pi r rightarrow 0 to R} Because integral^2 pi_0 cos^2 phi d phi cos 2 phi = 2 cos^2 d - 1 Now integral^2 pi_0 (cos^2 phi + 1)/2 d phi 1/2