Question

Please provide a clear solution with all steps using clear hand writing. Sketches are necessary. Note: I know that this question has been solved online but I couldn't get it. So, provide your own solution that is more easy to understand. If you can be available after you provide your answer for counter questions, that will be appreciated.

Calculate the magnetic field due to (i) a very thin current sheet in the xy-plane (infinitely sized in x, y) with a current density JJ., for z=0 everywhere else (Jy is a surface current density with units A/m). (ii) a current density in a slab of height d centred along the xy-plane Juâ, for 2] <d/2 10, everywhere else (Jy is a volume current density with units A/m²). (1) (ii) current sheet volume current

Answer 1

18 infinite eussent sheet fast for 250 1o, everywhere else Take cross section of the infinite sheet. cosment out of page Is Alm Boots a line current - - - All of If in I of dots are infinite we put out ward then magnetic representing length our thumb direction curling of field. of sight hand in meana (h) Sdirection of fingures gives direction Taking central point P, and P2 At of point field. direction p Z B B

Now from consider centers line at equidistant tho in infinite ŷ and ĝ ܟ 8 ܕ - 4 ви 01 = 02 B sing, =B sin 02 (2 components » cancelled By symmetry I of So - ² component will be the sheets. Net direction of ý for zoo and field t would be for zxo. I Ampesian circuital law. B.de - Ho Tenclosed. such that it is Take a ampesian loop crossing the Sheets & Bode = (B. de + B co R 1 o* 3 4 - 08.02 = (@r(-99.13 (9) + Bilett)) + Si el  [de] + Brdice)

bode = als de let length of the paret CY ampesian loop a bel De 1 then in loop cument enclosed Tenclosed ISIL & 2B (de = loist QB2Y - MISH B = Mous I Tesla And B = S Moss (9) ; z>0. ANS I HO IS ( 9 ) ; ZLO SJv å for 12/24 Volume coment O, everywhere else. field would be Direction found of B (magnetic same as i

Taking cross section view to thickness of loop (width) ta 77 @ @ = thichness . Id/2 A ... Id/2" TILL. I. T B Tase 1 trd Take a ampesian thickness. 3 loop crossing the sheet Rode = 2B (de § some as procedure previous . I enclosed = Jy * d*(21) Mo Jvd (24) دو د (2) فہوما - - Solvd Tesla 2 o = Mo Jud (-} }; 270 2 Mold (6) ; 240 /

Case 2 Ald 2 often fol di = 12B (de 7 - bias . I enclosed - Jugut 9 8 3 - 414 B = Malvt JVE To Testa B = Haut (8) Z7o Hlobrt () 20 ANS