Question

Two long, straight wires, one above the other, are separated by a distance 2a and are parallel to the x-axis. Let the be in the plane of the wires in the direction from the lower wire to the upper wire. Each wire carries current I in the What are the magnitude and direction of the net magnetic field of the two wires at a point in the plane of the wires (a) midway between them; (b) at a distance a above the upper wire; (c) at a distance a below the lower wire?

Answer 1

Answer:

field B = µ₀c I / 2πr

The field in the xy plane due to the fact that the two wires are perpendicular to the plane Bx and By are everywhere 0 on the plane.

a) Midway between, the Bz components cancel, so <0, 0, 0> T

b) Bz = µ₀ x I / 2πa + µ₀ x I / 2π(3a) = (µ₀ x I / 2π)(1/a + 1/3a)

Bz = (µ₀ x I / 2πr)(3/3a + 1/3a) = (µ₀x I / 2πr)(4 / 3a) = 2µ₀ x I / 3πa

c) By symmetry, Bz = -2µ₀ x I / 3πa (that is, down into the plane)