Superconductivity Current

Section 54

A simply connected body can have no steady surface current in the absence of an external magnetic field.

In spherical coordinates, DY = 0 has solutions that are powers of r: ra, where a can be positive or negative. If dY/dr is zero at both r = a and r = infinity, the only possible value of a is zero. Then dY/dr = 0 at all r, or Y = constant, giving H = 0.

An H-field of this kind cannot exist -> there can be no steady current on a simply connected body.

For a simply-connected body in an external H-field, a magnetic moment M appears

Multiply connected superconductor

f is many valued

Zero, since H=B outside and divB = 0.