Question

7 5.10 An infinitely long, thin conducting sheet defined over the space 0 < x < w and - < y < oo is carrying a current with a uniform surface current density JS = 95 (A/m). Obtain an expression for the magnetic field at point P = (0, 0, z) in Cartesian coordinates.

is there any way I can do this problem using the following formula? if yes, how?

Answer 1

z 5.10 The sheet can be considered to be a large number of infinitely long but nastow wires each doe corde lying Plooght R lR l = 38722 next to each other, with each carrying ronella-----> a current In Is die The wire at a distance ac from origin as at a distance vector Ŕ - from point P, with R =-ê xe + 2z' The magnetic field due to an infinitely long wire cassying a cursent BØ I We now need to adapt this expressian to the present situation by xeplacing I with Inc = f, dx, replacing & with R=(8c² + 225/2 as shown in figure above and by assigning the proper direction for the magnetic field. from the Biot - Savast law, the direction of Ħ is governed by ī XR , where Ī is the direction of current flow. In the present case I is in the 9 direction. Hence the direction of the field is O IRR - ŷ x - ff x + ² z ĉz+ in TIKR) iġx réx+ż z) = (a + Z2)/2 Ĉz+ ²x Ix Therefore, the field dit due to the current Ix is dH = + 1/2 = (êz+ & x) Is d xc za (x²+22) and the total field is Fi(0,0,2) = j(&z=2x) while e fez+ 2xset 0 [22[ztortes+ 2(41,42+7)] - CE zatan 1695 + 2 [[n(ww7+2) – An (22)]] fox zło - Lê za tan (%) +2:46. (Wizycoms for Z+0 An alternative approach is to employ I = I am STS XR as directly, which is equal to equation o