What is the magnetic flux density field of two parallel infinity long conductors with current I and distance a?

Question

Wikipedia gives the magnetic flux densities of current loops. The magnetic flux density of two infinitly long conductors look the same, but I am not sure about the numeric accuracy of the value of the field. What is the equation for the field, given the current I and the distance of the conductors a?

Zalnd · Accepted Answer

As Puk already answered you, the resultant magnetic flux density is the superposition of the magnetic flux densities generated by each wire. I'm submitting a new answer because I think that the equation in the Cartesian coordinate system will help the summation.
The magnetic field due to a infinite single wire located at $(x_0,y_0,z)$ is
$$vec{B}(x,y,z)=frac{mu I}{2 pi [(x-x_0)^2+(y-y_0)^2]} [-(y-y_0)hat{x}+(x-x_0)hat{y}+(0)hat{z}]$$
Considering that the wires are crossed by the $y$-axis and the origin has an equal distance from both wires, you may have $+I$ flowing along the wire at $(-a/2,0,z)$ and $-I$ flowing along the wire at $(+a/2,0,z)$.

Puk · Answer

The magnetic field due to a single infinite straight wire has magnitude
$$ B(r) = frac{mu I}{2pi r} $$
where $I$ is the current and $r$ is the distance from the wire. The direction is perpendicular to the axis of the wire and the radial direction, as indicated by the right hand rule. Just add the fields due to the two wires.

What is the magnetic flux density field of two parallel infinity long conductors with current I and distance a?

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