Question

what is the direction of current in a infinite current carrying sheet

Answer 1

The current in an infinite current-carrying sheet flows uniformly in a specific direction within the plane of the sheet.

Answer 2

The current in an infinite current-carrying sheet flows uniformly in a specific direction within the plane of the sheet. This direction is usually defined when the problem is set up, for example, along the x-axis if the sheet lies in the x-y plane. It is characterized by a surface current density vector, $\vec{K}$, whose direction indicates the direction of current flow.

The current cannot flow perpendicular to the sheet, as it is current in the sheet, meaning charge carriers are moving within the material of the sheet.