Long, straight conductors with square cross sections and each carrying current I are laid side-by-side to form an infinite current sheet as shown in Fig. The conductor lies in the x-y plane, are parallel to the y-axis and carry current in the +y direction. There are n conductors per unit length measured along x-axis.

what are the magnitude and direction of the magnetic field for distance a below the current sheet?

Explanation

(a) Below the sheet, all the magnetic field contributions from
different wires add up to produce a magnetic field that points
in the positive x-direction. (Components in the z-direction
cancel.) Using Ampere's law, where we use the fact that the field is antisymmetrical above and below the current sheet, and
that the legs of the path perpendicular provide nothing to the
integral. So, at a distance beneath the sheet the magnetic field is
`I_(encl)=nLI implies ointvecB.dvecl=B2L=m_0nLI`
`B=(mu_0nI)/2`,
in the positive x direction. (Note that there is no depe-dence
on a.)