Field and Wave Electromagnetics质疑英语
Field and Wave Electromagnetics
interchangeLecture 12
李融林
R.L. Li
4.5Magnetic Fields in Materials and Magnetic
Circuits
Behavior of Magnetic Materials
Nonmagnetic if
(Vacuum)
Diamagnetic,if
(Silver,Lead,Copper,Water)
全外教
Paramagnetic, if
(Air, Aluminum)龙舌兰英文
Ferromagnetic, if
(Cobalt, Nickel, Iron, Silicon iron, Mumetal)
好奇心英文The orbiting electrons cau circulating currents and form microscopic magnetic dipoles.In the abnce of an external magnetic field the magnetic dipoles of the atoms of most materials have random orientations,resulting in no net magnetic moment.The application of an external magnetic field caus both an alignment of the magnetic moments of the spinning electrons and an induced magnetic moment due to a change in the orbital motion of electrons.4.5.1 Magnetization and Equivalent Current Densities
We define a magnetization vector,M ,as
becomeswhich is the volume density of magnetic dipole moment. The magnetic dipole moment d m = M dv’
will produce a vector magnetic potential
(Note that
for a magnetic dipole of moment .)
Using
we can rewrite d A as
where V’is the volume of the magnetized material. We now u the vector identity
to rewrite
The following vector identity enables us to change the volume integral of the curl of a vector into a surface integral:
where F is any vector with continuous first derivatives.暮光之城3剧情
Proof: Applying divergence theorem to (F x C), where C is a constant vector, we have
Since小学数学概念教学
soo
and
we havezhenghong
