Question

2c. A insulating cylindrical shell with length L and inner radius a, outer radius b, has uniform charge density p. Find the E, not near the ends, for three regions, ra, arb, r>b. * Note, a linear density A could also be given cross section 3c. An insulating shell has inner radius a and outer radius b and a uniform charge density p. Find E at all r (ra; arb; r> b)

Answer 1

R < a Gaussian surface will be cylinder integral E vector ds vector = q_in/epsilon_0 {q_in = 0} E(2 pi r L) = 0 E = 0 a < r < b: Gaussian surface cylinder of radius r. q_in = integral^r_0 Pdv = P integral^r_a 2 pi r L dr = P pi L(r^2 - a^2) integral E vector ds vector = E(2pi rL) = P pi L(r^2 - a^2) E = P(r^2 - a^2)/2r b > r: similarly Gaussian surface is cylinder q_in = PL pi(b^2 - a^2) integral E vector ds vector = E(2pi rL) = P pi L(b^2 - a^2) E = P(b^2 - a^2)/2r