Phys math help.pdf

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Physique math´ematique : r´esum´e
1
Magnetostatics
Biot and Savart law
~
~ = k. I dl × ~x
dB
|x|3
(1)
~ = I dl
~ ×B
~
dF
(2)
Z
~ =µ
~ dl
B.
∂S
Z
~
~ dS
J.
(3)
S
~ =∇
~ × A(~
~ x)
B
(4)
~ = −µ0 J~
∆A
(5)
Coulomb gauge
Magnetic moment
m
~ =
1
2
Z
~ x0 ))
d3 x0 (~x0 × J(~
(6)
Density of magnetic moment
1
~
~
M(x)
= (~x × J(x))
2
(7)
µ0 3~x(m~
~ x) − m.~
~ x2
~
B(x)
=
4π
x5
(8)
Torque in classical mechanics
T~ =
X
~ri × F~i
(9)
i
Torque in magnetostatics
~
T~ ' m
~ ×B
(10)
Faraday induction law
E =−
with φ =
R
S
~ and E =
~ dS
B.
R
∂S
~
~ dl
E.
1
dφ
dt
(11)