  It has been shown that the electron system with ODLRO in the reduced density
matrix $\rho _2$ can not support a uniform magnetic field, i.e., ODLRO\ in $%
\rho _2$ implies the Meissner effect \cite{2}\cite{3}, furthermore, the
magnetic field trapped in the system is quantized\cite{3}. This note extends
above results in two cases. We show that (1) the system with ODLRO in $\rho _2$
can not support a non uniform, cylindrically symmetric magnetic field; (2) the
system with ODLRO in $\rho _2$ can not support a magnetic field slowly varying
in space, and the magnetic flux trapped in it is quantized.
