Question

A coaxial cable consists of a fixed inner conductor with radius R1, which is surrounded by a concentric cylindrical tube with inner radius R2 and outer radius R3 (Figure 1). The conductors carry oppositely directed currents I0 of equal size, which are homogeneously distributed over their cross sections. Determine the magnetic field at a distance r from the axis for a) <R1, b) R1 <r <R2, c) R2 <r <R3 and d) R3 <r.
(Show the appropriate ampere loop for each area.)

10 R2 Abbildung 1

Answer 1

holution: To Cumend рє0 cylinder of unit area gadiub RL 2 IR = Aup/m² AR, 2 outer cylinder and outer corth inner radius R2 radius R2 1. FR₂-R 3 = Amp / m² * (R3 - R2² ) Ampere's circultal law on & Bode = Mo I enclosed B magnetic field de a ampesian loop length I enclosed total enclosed loop. cument in am perian

cylindrical coordinate system $8-ti = Ho I enclosed I enclosed so AR? B! 210) Motor? R2 B Но Іо у 27 R² Ho Ior 20R? ANS BiCYCRz AR3 this case tenclosed То TIO V Bar = Ho Io Io B Ho Io Qar B = Moto 0 ANS

R2 <r<R3 In this Case Ienclosed To - Ion 26R) * (R² R2) H 3 Tenclosed Toll 2 2 -R2 R3²-R2²) bo B. 2ar = Holo (1-6² R4 (R3² R23) B Mo Io 63 82 -3 R2 enr R 3 - R? = B = Ho To Rze - 2² 0 2tr R3² - R₂² d>8> R3 R Here a Tanclosed -To-To 1 1 B I, 1