Phys math help.pdf


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3

Electric and magnetic fields in media

Polarization

Ptot
=σ≡P
V

(19)

~ P~ (x)
ρP (x) = −∇.

(20)

σP (x) = ~n.P~ (x)

(21)

~ D
~
ρext = ∇.

(22)

~
P~ ' 0 χe .E

(23)

~ ' E
~
D

(24)

~ E
~ 'ρ
∇.


(25)

~2 − E
~ 1) = 0
~n21 × (E

(26)

~2 −D
~ 1 ) = σext
~n21 .(D

(27)

~ = 0 E
~ + P~
with D

with = 0 (1 + χe )

Continuity

Energy
1
2

Z

~ D)
~
d3 x(E.

(28)

~ ×M
~ (x)
J~M (x) = ∇

(29)

~ ×H
~ = J~ext


(30)

~ = µH
~
B

(31)

W =
Magnetostatics in media

~ =
with H

1 ~
µ0 B

~
−M

Relation between B and H

for isotropic diamagnetic and paramagnetic substances
~ = F (H)
~
B
for ferromagnetic substances
3

(32)