Question

Why φ (phi) = x and r = y ?

Answer 1

See below

Explanation:

They are saying that `bb hat Phi = bb hat x`, ie the direction of the B field is into the y-z plane.

Current is flowing up the z-axis so this is what you would expect from, say, the right hand thumb rule: magnetic field lines will be concentric with the z-axis and will flow orthogonally into the y-z plane

From the Formula: `B = k / r`. In this case, distance from the z axis means that `B = k / y`, as that is the distance from centre of wire, ie the z-axis, to any point on the y-z plane