Consider an infinite sheet of parallel wires. The sheet lies in the xy plane. A
ID: 2207943 • Letter: C
Question
Consider an infinite sheet of parallel wires. The sheet lies in the xy plane. A current I runs in the -y direction through each wire. There are N/a wires per unit length in the x direction. (Figure 1) Write an expression for B_vec(d), the magnetic field a distance d above the xy plane of the sheet. Use mu_0 for the permeability of free space. Express the magnetic field as a vector in terms of any or all of the following: d, I, N, a, mu_0, and the unit vectors x_unit, y_unit, and/or z_unit. B_vec(d) =
Explanation / Answer
Apply Ampere's Law: use a rectangular circulation loop around the current sheet. Applying Flemings rule "right/or left" shows that all Bz components cancel along "w sides", leaving only Bx components which are parallel to the two "L sides" ---->x 2 *?s B . dL = uo Ie --->enclosed current 2BL = uo Ie Solving for B B = uo * Ie / 2*L Since the enclosed current is: Ie = I*N*L where N is the number of wires per unit length B = uo * I*N*L / 2*L B = uo * I*N / 2 By your given N ---> N/a: B = uo * I*N / 2*a Answer: Bx = uo * I*N / 2*a i OR: Bx = - uo * I*N / 2*a i Depending on the coordinate system and/or Flemings rule.