V- Magnétisme

P
q M ~v
~
B=µ0
4π
q ~v ×~ur
r2
r M P ~ur
~
MP
~
B=µ0
4π
q ~v ×~ MP
k~ MP k3

q
P
~
E=1
4π0
q ~ur
r2
~
B(P) = µ00(~v ×~ E(P)) P
0µ0
µ00c2= 1 c
µ0= 4π·10−7kg m A−1s−1(H.m−1)
~
B
1T= 104Gauss
E
d e m
a=e E/m
v
v2= 2 a d = 2e E d/m
r
Be=µ0
4πr2e E d m
e
r2
E= 105V/m d = 10 cm r = 1 mm e =
1,6·10−19 C m = 9,11 ·10−31kg Be= 0,95 ·10−12 T
Ee= 1,44 ·
10−3V/m

n
A
~vM
dl (n e A dl)
d~ B=µ0
4π
(n e A dl) ( ~vM×~ur)
r2
~vMd~ l
d~ B=µ0
4π
(n e A vM) (d~ l×~ur)
r2=µ0 4π
i(d~ l×~ur)
r2
i d~ l~
B
~
B=µ0
4πZi d~
l×~ur
r2
~
B~ B

dB =µ0
4π
i dl sin θ
l2B=µ0i 4πZ+∞
−∞
dy sin θ
l2
sin θ= cos φ
y=rtgφ dy =r
cos2φdφ
l=rcos φ
B=µ0i
4π r Z+π/2
−π/2
cos φ dφ =µ0i
2π r
B=µ0i
4π r Zφ2
φ1
cos φ dφ =µ0i
4π r (sin φ2−sin φ1)
Ox

~uri d~ l~
B Ox
~
B=~ı ZdBx=~ı ZdB sin θ=~ı Zµ0
4π
i dl sin θ
r2
=~ı µ0
4π
isin θ
r2Zdl =~ı µ0 4π
isin θ
r2(2πa) = µ0 2
i a2
(a2+b2)3/2~ı
~
B=µ0
2π
i S
(a2+b2)3/2~ı =µ0
2π
M
(a2+b2)3/2~ı
S=πa2
M=i S
b= 0
~
B=µ0
2
i
a~ı
ba
~
B=µ0
2
i a2
b3~ı
~
B