Question

nmateral wth magnetre suseptiblity, Xm current) T a As shoun n Fy. the shb n paralel to the χ fiane, between z -a, and Zia'2 Above χ lane, the current r, out of the page, below h+7x arto the pageOuhside the slab is vacuum z<-a) three different, eines. (2)a)-arka, Fund in and B

Answer 1

Given that J(z) = J_0(z/a) x i) for z > a The total current enclosed is I_f = integral J. doubleheadarrow = integral^a_- a J_0(z/a) l dz = 0 then contour integral pi. dl = I_free = I_f = 0 so H = 0 for z > a Now B = mu H = 0 and m = mu_0 x_m B = 0 for z > a: h = 0: B = 0 and mu_0 H B = 0 ii) similarly for z < - a also contourintegral H. dl = I_free = 0 Rightarrow H = 0: B = 0 and m = 0 iii) for - a < z < a we have taking on square amplifier loop of length we have the current enclosed by the loop area is I_f = integral J. doubleheadarrow Rightarrow I_ene = integral^2_- a J_0(2/a) l dz = J_0 l/2a [z^2 - a^2] and iron Ampere's law contourintegral H. dl = J_0l/2a [z^2 - a^2]