Question

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Q.6 30 Along coaxial cable consists of two concentric condu shown in the Figure. There are equal and opposite com with radius a has a non-uniform current density J cable has uniform current density ntric conductors with the dimensions opposite currents I in the conductors rent density J = ar and the outer ara Find the magnetic field B at r within the inner conductor (r<a). Find B between the two conductors (a<r<b). Find B with in the outer conductors (b<r<c). Find B outside the cable (r>c). (c) (d)

Answer 1

thee Its simplified figure will look this : Inner cable is uniform Current 9;=xoi Alm2 non- den pity Outes current it is cable has uniform density, suppose To. n 1 c2 - 6 1 (al we take an Ampere loob with radius eka. Novo apsolying Ampere low along Joob with radiusza 6 Bol - o l'enclosed Be Constant due to symmetsy.. .: 8 pel = lo x J; (192) = lo xa dixit 1² Moltes B x 204 = Noaties Lenclosed means Current ' inside the Ampere loob.y B= Mox 9² 'Tesla (b) again we take an Ambeie loop with liadius & a<r<b, as shown in the figure . I enclosed = J; x PT Geizao yata2 . r goes manimum for innes Coductor is - Perlosed a gaxaxtia? = Qara z I Now, apply Ampere's Jano; $8.de e lo I enclosed e lo xxia in inner Bx 21 M = MORTGB B = Moxas Tecla Mo I Tesla 20 total - Current conductor (c) Again we take on Ampue loole with radios & ber<c. e enclosed = 1002_6²) ALTO Dinnes Conductor outer Conductor Current total current Bubtracted because as both are are apposite. there a directions '. I enclosed = 2 x T (9126²) - 2003 T (362) = 1 1 026²) - ana3 & Bidla Mo I enclosed a Mo ?/ 1262) - Laos (e262) By 2TH = Mo ana3 , 42-62) -ana x=x563) - 1 c2_6²) B= llo ratas ei-b² -1 = MoxaB Tech श्रा 91 L. e²-62 29 I c2 (d we take an Ampere's loop with exc I enclosed = 1 due to outer conductor) - Il duel . to innen conductor) B.di Mo I enclosed - loxo=0 .. B=0 Tesla