Can anybody help? "Current density" (without any other adjectives) means "charge passing a plane per unit time, per unit area of the plane". "Surface current density" means "amount of charge in a thin sheet of current passing a given place, per unit time, per unit length across the wide dimension of the sheet of current".
Electric surface current density is defined as the amount of electric current per area. SI unit of electric surface current density is ampere per square meter. Other common units are ampere per square centimeter and ampere per square inch.
If the surface current density is uniform, the total current I in any width b is I = Kb where we assume that the width b is measured perpendicularly to the direction in which the current is flowing. The geometry is illustrated by Figure 7.2.