Formulário Física II UFRGS

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~F =
1
4pi�0
q1q2
r2
rˆ
�0 = 8,85× 10−12 C
2
N m2
k =
1
4pi�0
= 9× 109 N m
2
C2
e = 1,6× 10−19 C
~F = q ~E
~E =
1
4pi�0
q
r2
rˆ
p = qd
~τ = ~p× ~E
∆U = −~p · ~E
∮
~E · d ~A = qint
�0
ΦE =
∫
~E · d ~A
∆V = Vf − Vi = −
∫ f
i
~E · d~l
= −Wif
q
=
∆U
q
V =
1
4pi�0
q
r
Es = −∂V
∂s
Uij =
1
4pi�0
qiqj
rij
q = CV
C =
�0A
d
Ceq =
n∑
i=1
Ci (paralelo)
1
Ceq
=
n∑
i=1
1
Ci
(série)
U =
q2
2C
=
1
2
qV =
1
2
CV 2
u =
1
2
�0E
2
q′ = q(1− 1/κ)
�0
∮
κ~E · d ~A = q
i =
∫
~J · d ~A
J =
i
A
~J = (ne)~vd =
ne2τ ~E
me
τ =
mevd
eE
R =
V
i
~E = ρ ~J
R =
ρL
A
ρ− ρ0 = ρ0α(T − T0)
P = i∆V = i2R =
∆V 2
R
Req =
n∑
i=1
Ri (série)
1
Req
=
n∑
i=1
1
Ri
(paralelo)
q(t) = CE
(
1− e−t/τC
)
q(t) = CEe−t/τC
τC = RC
~FB = q~v × ~B
~F = q ~E + q~v × ~B
d~FB = i d~l × ~B
~τ = ~µ× ~B
µ = NiA
∆U = −~µ · ~B
d ~B =
µ0
4pi
i d~l × rˆ
r2
µ0 = 4pi × 10−7 T m
A
∮
~B · d~l = µ0i
ΦB =
∫
~B · d ~A
E= −N dΦB
dt
∮
~E · d~l = −dΦB
dt
L = N
ΦB
i
EL = −Ldi
dt
i(t) =
E
R
(
1− e−t/τL
)
i(t) =
E
R
e−t/τL
τL =
L
R
UB =
1
2
Li2
uB =
B2
2µ0
P =
dU
dt
q(t) = Q cos(ω0t+ φ)
i(t) = −ω0Q sen(ω0t+ φ)
ω0 =
1√
LC
q(t) = Qe−
tR
2L cos(ωt+ φ)
ω =
√
ω20 −
(
R
2L
)2
E(t) = Em sen(ωt)
i(t) = I sen(ωt− φ)
VR = IR;VL = IXL;VC = IXC
XL = ωL;XC =
1
ωC
Em =
√
V 2R + (VL − VC)2
Z =
√
R2 + (XL −XC)2
I =
Em
Z
tan(φ) =
VL − VC
VR
=
XL −XC
R
cos(φ) =
R
Z
P
méd
= I2rmsR = ErmsIrms cos(φ)
Erms =
Em√
2
;Vrms =
Vm√
2
Irms =
I√
2
Vs = Vp
Ns
Np
IpVp = IsVs
∮
~B · d ~A = 0
∮
~B · d~l = µ0
(
ic + �0
dΦE
dt
)
id = �0
dΦE
dt
∫
x
(x2 + a2)3/2
dx = − 1√
x2 + a2
∫
1
(x2 + a2)3/2
dx =
x
a2
√
x2 + a2
K =
1
2
mv2
|FC | = mv
2
R
P = ~F · ~v
ω = 2pif
Esfera
V =
4
3
piR3
A = 4piR2
dV = R2 dR sen(θ) dθ dφ
dV = 4piR2dR
Cilindro
V = piR2L
A = 2piRL
dV = RdRdθ dz
Circunferência
A = piR2
dA = 2pi RdR
p = 2piR