IV- Electrocinétique

S
i(t) = lim
∆t→0
q(t+ ∆t)−q(t)
∆t=dq(t) dt
~
i(t) = ZS ~ ·~ndS
S

i(t)
~
N
e e =−1,6.10−19 C
~vM
S
∆t
∆q S ∆t
∆q= (N e) (S vM∆t)
i(t) = lim
∆t→0
∆q
∆t=N e vMS
~ =Ne ~vM
~
E
~
E

~
E
m~ E
γ=eE
m
2τ
vi= 0 vf= (2τ)γ= (2τ)eE
m
vM=(vi+vf)
2=e E τ m
i(t) = N e vMS=N e2E
mS τ
j=N e2τ
mE=σE
σ=N e2τ
m
ρ= 1/σ
τ N
ρ(T) = ρ0(1 + α(T−T0))
α

j=σ E
L S
∆V
∆V=E L
i(t) = j S = (σ E)S=σS∆V
L
∆V=R i(t)R=1
σ
L
S=ρL S
R
L S
∆V
i
h
σ

i=Z~ ·d~ S=Zj dS =jZdS = (σE) (2πrh)
~
E E =−dV
dr i=−(2πσrh)dV dr
ZVb
Va
dV =−Zb
a
dr
r
i
2πσh Vb−Va=−i 2πσh ln b a
R=Va−Vb
i=1 2πσh ln b a
VA−VB= (VA−VC)+(VC−VD)+(VD−VB)
=R1i+R2i+R3i
=Req i
Req =R1+R2+R3
n
Req
Req =
n
X
i=1
Ri
i=i1+i2+i3=∆V
R1
+∆V
R2
+∆V
R3
=∆V
Req