An equation in Laughlin Argument paper (1981)

In his paper Quantized Hall conductivity in two dimensions, Laughlin considers a ribbon of two-dimensional metal bent into a loop of
circumference $L$, and pierced everywhere by a magnetic
field $H_o$ normal to its surface. He says that the current through the loop is equal to the adiabatic derivative of the electronic energy $U$ of the system wrt the magnetic flux $phi$ through the loop:
$$I=cfrac{partial U}{partial phi}=frac{c}{L}frac{partial U}{partial A}$$

My question is what is the origin of this equation and why is the current equal to the adiabatic derivative of the electronic energy $U$?