Constraining electrons to move along thin wires has two consequences: 1.The average electron density is reduced because only part of space is filled by metal 元r2 neff a2 n, 2.The thin wires have a large self-inductance and it is not easy to change the currents flowing in them.So it appears as if the electrons had acquired a tremendously large mass H=品（日。） The vector potential associated with the field H(p)=67×A aoi=[nn] a yp< a-p =0 p 2 I=πr2nev r<a Approximation in the mean field limit A(p)≈lonr2neu 2π \p】Constraining electrons to move along thin wires has two consequences: 1. The average electron density is reduced because only part of space is filled by metal 2. The thin wires have a large self-inductance and it is not easy to change the currents flowing in them. So it appears as if the electrons had acquired a tremendously large mass  a   I 1 0 ( )    H A   The vector potential associated with the field Approximation in the mean field limit 0 