If you had a infinite current sheet in the xy plane at z = 0 with K = Kk where k is the unit vector in the y direction. i) Find the expression for the magnetic field strength. ii) Compare this with the electric field for an infinite sheet of charge. iii) Obtain the expression for the vector magnetic potential. I need some help with (iii) because I think I have the first two. This is how I did it. i) I applied Ampere's Circuital law around a closed rectangular contour. The rectangle was constructed such that it was perpendicular to the infinite sheet of charge. The rectangle had a length of L and it protruded a distance d from each side of the sheet. Now since only the top and the bottom edges of the contour contribute to the calculation and their sum is 2BL. The total current enclosed in the rectangle is IL. Hence ∫ B · ds = μ_0 I 2BL = μ_0 I B = μ_0 I / 2 Since H (the magnetic field strength) equals 1/μ B we have H = ( μ_0 / μ )( I / 2 ) Is the correct? ii) The electric field around an infinite sheet of charge is easily obtained from Gauss's Law which gives you E = (1 / ε_0 )( ρ / 2 ) Notice the constants of permittivity and permeability are common and the current become charge density. Any reasons why these should be so similar? iii) Okay, I have not much of an idea on this one. Any help would be appreciated. !?!?
