Question

The - a magnetic field intensity in the - region xxo, assumed to be free space, is given Ai = 4 årt sây+ 328 Alm. In the region xco, assumed to be occupied by material with relative permeability M, the magnetic field intensity is Ar= 2ax +3ây +4 az Alm. Determine My and the surface current density at the boundary between the two regions.

Answer 1

DO 2 <o If magnetic field intensities x 7o Griven : Medium 1 A 48x + 5ay + 3 62 Alm. free space Medium 2 M2 22ut záy +Yaz Alm. Medium with Mr. ah both we represent will look like. mediums with boundary, they will Ah Now x=0 that means y z plane is the boundary : aģ and ai of each # will be tangential component is and will be normal component. K к Hit o Ha Fan yo That Z medium ag component a Verti Bound Layo medium ary Hi Hit + Hin -> Hit ر - 42x + 5ây Alm 3 å.2 Alm Hin H2+ 42 Similarly + Han Hat 2 åx + 3ay Alm На こ 4âz Alm Mit AW thin II an 2 そこ。 Z 1 d currat + 2 width ow and Ampene's Low at Applying of Boundary any height oh I & Hide k.aw ht where 'k' is surface density. it it on thin sh K.AW = rn sh - Mataw . As sho =Fit - H2+) AW + (Hint Han).0 (Hit H2E) AW Mit Hat K Hit & hat from eq cis and eq cii) - (4âr +5ây)-(22x+3ây) = k k = (2 âx +2 ây) Alm K. AN : k.ow .. Putting values of we can also white from Boundary equations- Hra =rkhan Bin of fabile AS B Ish My Magnetic flux density Apply Morwell's Equation imaginary pill box- 87.43 = 0 Bio © urr billbox B Bin AS Banaso Bin Brn We know that Hin BE = Mo Mo # sou Moter, Fin = Mother han Mri Putting valeres from eq is of equins 32 Mra yaz Tan Mrr 0.75