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)
=

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


dt

(11)