High Temperature Superconducting Magnetic Levitation

7.2 Maxwell’s equations Ë 219

In the absence of a free surface current density, the tangential component of the
magnetic field intensity will be continuous in passing through the surface from Region
1 (H 1 )to Region 2(H 2 ), as expressed by

n 12 ×(H 2 −H 1 )= 0. (7.3)

7.2.2Faraday’s law

This equation describes how a time-varying magnetic field generates an electric field
in a stationary object. It can be expressed in either the differential form

∇×E= −휕B

휕t

, (7.4)

or the integral form

[

C

E⋅dI= −X

S

휕B

휕t

⋅ds. (7.5)

The tangential component of the electric fieldEis always continuous in passing
through the surface from Region 1(E 1 )to Region 2(E 2 ), i.e.

n 12 ×(E 2 −E 1 )= 0. (7.6)

7.2.3Gauss’s law

This equation presents the relationship between the electric field and the electric
charge that generates the electric field. It can be expressed in either the differential
form

∇ ⋅D=휌, (7.7)

or the integral form

X

S

D⋅ds=X

V

휌dv. (7.8)

In the absence of a free surface charge density, the normal component of the electric
displacement will be continuous in passing through the surface from Region 1(D 1 )to
Region 2(D 2 ), as expressed by

n 12 ⋅ (D 2 −D 1 )= 0. (7.9)