Consider an infinite sheet of parallel wires. The sheet lies in the xy plane. A
ID: 1261813 • 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)
Part A
Write an expression for B? (d), the magnetic field a distance d above the xy plane of the sheet.
Use ?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, ?0, and the unit vectors i^, j^, and/or k^.
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) Part A Write an expression for B? (d), the magnetic field a distance d above the xy plane of the sheet. Use ?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, ?0, and the unit vectors i^, j^, and/or k^.Explanation / Answer
We can do a loop that is a rectangle of length a that encloses a part of the plane.
By symmetry, the magnetic field is of constant magnitude everywhere along the length of the loop.
Thus, as there is a positive line integral for the upper and lower lengths,
Integral [B dl] = uo Ienc
As I enclosed is N*I,
2Ba = uo N I
Thus,
B = - [uo N I / (2a)] i^ [by right hand rule] [ANSWER]