Current in an infinite current sheet

[chipotleaway]

Suppose we have a infinite current sheet of surface density $\sigma$ and apply Ampere’s law to find the magnetic field. Using a rectangular loop of side lengths L, why would the enclosed current be $I=\sigma L$? Doesn't this imply the RHS has units of $\frac{Q}{m}$?

Shouldn't we be looking at this: $I=\frac{dQ}{dt}=\sigma \frac{dA}{dt}$?

 

[Dale]

A surface current density has units of A/m in the SI system. Multiplying that by length (units of m) gives current (units of A).