Feuille de formule – Électricité et magnétisme

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Feuille de formule – Électricité et magnétisme
Constantes :
g = 9,8 m s 2
e = 1,6 × 10 −19 C
ε 0 = 8,85 × 10 −12 C 2 / (N ⋅ m 2 )
k = 9 × 10 9 N ⋅ m 2 / C 2
µ0 = 4π × 10 −7 kg ⋅ m/C 2
c = 3 × 10 8 m s
Électron :
me = 9,11 × 10
Proton :
−31
mp = 1,67 × 10
kg
Neutron :
−27
mn = 1,67 ×10
kg
mµ = 1,88 × 10 −28 kg
kg
qn = 0
q p = +e
q e = −e
Muon :
−27
q µ = −e
Formules :
d x(t )
dt
d v x (t )
a x (t ) =
dt
v x (t ) =
v
2
v
v
Fg = mg
v
d θ z (t )
dt
d ω z (t )
α z (t ) =
dt
v2
r
ω z (t ) =
2
v x = v x 0 + 2a x ( x − x 0 )
g =G
M
r2
f =µ n
Fr = ke
v
v
Fe = qE
v
qQ
Fe = k 2 rˆ
r
v
Q
E = k 2 rˆ
r
v
dQ
E = ∫ k 2 rˆ
r
v
v v
Fm = q v × B
v
v v
Fm = I l × B
v
v v
dFm = I d l × B
v
v
µ0 I d l × rˆ
B=∫
4π
r2
2k λ
E=
R
B=
aC =
v x (t ) = v x 0 + a x t
∑ F = ma
E=
1
axt 2
2
x (t ) = x 0 + v x 0 t +
µ0 I
2π R
σ
2ε 0
E=
B=
kQ
D (D + L )
E=
2k λ
R
µ0 I
sin (α 2 ) − sin (α 1 )
4π R
sin (α )
B=N
kλ
E⊥ =
R
µ0 I
2R
sin (α A ) − sin (α B )
B=N
E f = E i + Wa
v v
W = ∫ F ⋅ ds
v v
W = F ⋅s
E = K +U
v
v
v
p f = pi + J
v
v
J = ∫ F dt
v v
J = F ∆t
v
v
p = mv
v v
P = F ⋅v
E = ∫ P dt
P=
dE
dt
Wc = −∆U
U e = qV
C=
q
∆V
qQ
r
Q
V =k
r
ε0A
C vide =
d
Ue = k
Ue = ∑k
qi q j
ri j
v v
∆ V = − ∫ E ⋅ ds
i< j
Cvide =
R
k
Ur =
1 2
ke
2
1 kq 2
2 r
v v
∆V = − E ⋅ s
µ0 I
2R
E // =
sin 3 (α )
B=
kλ
R
µ0 n I
2
cos(α A ) − cos(α B )
cos(α 2 ) − cos(α 1 )
1
mv 2
2
v d pv
F=
dt
K=
U g = mgy
U g = −G
mM
r
Ue =
Ue =
1
C ∆V 2
2
Ex = −
E=
dV
dx
E ext
K
C = KC vide
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Feuille de formule – Électricité et magnétisme
∆V =
∆U e
q
I=
∆q
∆t
L
A
∆V = R I
R=ρ
P = I ∆V
P = RI 2
∑I
I = n A e vd
i
(∆V )2
R
=0
i
Q = m C ∆T
i
−1
q = q 0 e −t / RC
ε eff =
T1 / 2 = RC ln 2
ε0
2
v v
Φ m = ∫ B ⋅ dA
v v
Φm = B⋅A
ε ind = vBl sin θ
∑ ∆V
=0

1
Réq = ∑ 
R
 i i
2
1 ε0
P=
2 R
Réq = ∑ Ri
P=
i
i
ε ind =
dΦ m
dt
Mathématique :
v
v
v
v
A = (Ax , Ay , Az ) = Ax i + Ay j + Az k
v
A = A = Ax2 + Ay2 + Az2
ax 2 + bx + c = 0
⇒
x=
v v v v
A ⋅ B = A B cos (θ ) = Ax B x + A y B y + Az B z
v
v v v v
v
v
A × B = A B sin (θ ) nˆ = ( Ay B z − Az B y )i − ( Ax B z − Az B x ) j + ( Ax B y − Ay B x )k
− b ± b 2 − 4ac
2a
C = 2π r ,
A =π r2,
A = 4π r 2 , V = 4π r 3 / 3
sin 2 (θ ) + cos 2 (θ ) = 1
2 cos θ sin θ = sin (2θ )
ln ( A) + ln (B ) = ln ( AB )
 A
ln ( A) − ln (B ) = ln 
B
Table de dérivée et d’intégrale :
d ln x 1
=
dx
x
d cos x
= − sin x
dx
d sin x
= cos x
dx
d tan x
= sec 2 x
dx
∫ x dx = ln x + C
∫ cos (x )dx = sin (x ) + C
∫ sin (x )dx = − cos (x ) + C
∫ tan (x ) dx = ln sec(x ) + C
d xn
= nx n −1
dx
n
∫ x dx =
∫A
2
x n +1
+C
n +1
1
1
1
x
dx = arctan  + C
+ x2
A
 A
∫ (A
x
2
+x
)
2 3/ 2
dx =
−1
2
A +x
2
+C
∫ (A
1
2
+x
)
2 3/ 2
x
dx =
A
2
A2 + x 2
+C
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