Question

2) A coaxial cable (along 2) consists of a thick uniform cylindrical metallic wire of radius Rį and a thin metallic shell of radius Rg > Ri. The current density ji =jo (+2) is uniformly distributed within the volume of the inner wire and the current density j2 = jo (-2) flows through the outer shell. The region Ri <r< R2 contains a dielectric with A = 20- a) Calculate the B-field everywhere in terms of the net current I. b) Calculate the total magnetic energy per unit length in (J/m) (the energy density is up = B - B/24 (J/m3)). c) Calculate the self-inductance L of the cable (use U = LIP/2, where I is the current).

Answer 1

Answell! Given that A solid Cylindrical of Radius R and this metallic Shell of Radius R₂ Q>R, The I = Joltel corent density Now, Let the length of the Cylinder is d' the innerCylinder The total current enclosed in Ir, a JAR? lal curent enco enclosed in the outer cyclinder curent The total аТе, - Je, cal Elery where in terms of calculate the ô - field the net cuwent ?'

let, for a region VR2 total current enclosed by an amperian loop =) IRI = JARI : IRL =JAR? Therefore, le a JK (Rq2_Rq?) so, Applying Ampere's lawan ja la Mole ) BAZÃY = Mole والد o now the substituting Ie vawes Ba Mo JŲ (R2?_R,2) 27v 13.- Mo5 (821 - 16 to calculate the total magnetic Energy per unit length Ie = IR, I BX 22Y = Mo I RI I B= Mo IR, KY 29R12

MotJ ARAXN 2 TX BAY Twhere IRI=JARI? (c) to calculate the self inductance 1 of the table NOW, Total curent enclosed by the amperiar loop is Те = TAR, * from, the above we can get an equation go og Mole Therefore, Bx car = Mole @ NOU, @ we get substituting the Ie in BY B = MIRI? Here Mo al so, В. Але, 2Y Magnetic flon through the small area do = Bildir