Question

This is a easy, HA5.5 Magnetostatic field of on infinite, quasi filiform colinder with longitudinal cavity off axis. [30 points mathematically lout nortrivial conceptual problem. [Hint: Use the superposition principle for B] Consider an infinite, quasi filiform colindric conductor with radius a. O stationary current I lower along the longitudinal axis of the conductor, the current, which ar directed upward, is uniformly distributed through the conductor cron - section. As shown in Gring HA5.9, a colindrical cavity with radiur a!2 ir open longitudinally, throughout the entire lenght of the conductor. The cavity is off as is such that its center is the mid point of a radius of the original conductor, aftene opening the lengetudinal cavity, the initial current density asociated with I ir maintained constant. Calculate magnitude (including pigu land direction of the magnetostátic field B at point ó Center of the conductor), at point © Center of the cavity), 141 and at norint p cat distance d Aron O), B8) 733 [10 pointa 1, Bcc) Cdo pointer 1, and peopriate fo 21 d Ligure 145.9.

Answer 1

calculation of Br inside & out side of a long Eylinder hausting zinī form current density J. Amperian loop Since I is uniform. J TR² According to Ampere cirevital law & Bode = Malene. Boat ane in same 2 56 dl cos on Molene direction. => B lae = Mofone => Baar Molene . > Ba Morene glur for inside. Jene - Sf-as --J Sis -] cr? Mo Jar Bina Mour Mo Ir 9.16 26. 2 TR² for out side Iene - JTR2: Bout lo JR? 2 ur 20 = Mo JAR? Mol 200r 2)

let come to problery 0 OI 0 a d z - Magnetic field at o ! Bor Bienter Bpercipheri Moi QAR. - MoIn GAR? Molxo 210 (22) Mo Il 2T (2/2) Mo Il са Here so 1 ta2 Mo да — до І Iurrent is uniforery I' a(2/2)2 I': 1/4 Boro x 2 - 4 40a i magnitude of B at ! Mol. 4.ta using right hand thumb rule ie thum represents dirn of current cuald finger represents B int ir dirn of B at o is en og ý. S

Beenter Magnetic field at e in B B, Moir Mohr 20R² 20R? Mol (2/2) Mo (1/4)xo 2lt az 200(0/22 lol (magnitude) 4 na direction of B at ć is 9 Magnetic field at point p', out out BI By UOI! 272 Mol1/4) gad 2 tt (d-a/2) Mol Mol व 8a (0~9/2). direction of B at ' depends upon the strong ith of field of cylinder (1) & cavity (2) at Poie . a Llore - Mol depends on a Generally, direction of B at p due to cylinder is 9 And cavity is a 11