Study Guide
PY 208 Equation Sheet
F el =
1 q1 q2
ˆ
4π 0 r2 r
E · dA =
E ring =
q encl
0
qz
1
4π 0 (z 2 +R2 )3/2
F = Eq
E point =
1 q
ˆ
4π 0 r2 r
E dip, axis =
∆V = −
q = CV
C=
C = κC
I=
P = IV
1
C eq, ser
τ = RC
I= t ρ=
q
V
µ0 N I
L
0A
E line =
1 q
4π 0 r
V point =
σ
2 0
1 2λ
4π 0 r
=
1
C1
1
C2
R=
ΣI in = ΣI out
+
uE =
V = IR
dq dt 1
K = 2 mv 2
1
Req, par
t ε −τ
Re
=
1
R1
+
1
R2
t
V disch = εe− τ
1
2
2 0E ρL A
C eq, par = C 1 + C 2 t V charg = ε 1 − e− τ
t
q
A
B point =
λ= µ0 qv׈ r 4π r2
q
L
B wire =
µ0 2I
4π r
B loop, axis =
F = qv × B
F wire = I l × B
V = −L dI dt Ns
V s = V p Np
I s = I p Np s C circle = 2πr
Acircle = πr2
Asphere = 4πr2
Acyl = 2πrL
V sphere = 4 πr3
3
V cyl = πr2 L
1
V cone = 3 πr2 h
v = λf
E = cB
S=
µ0 I
2r
µ = IA
B solenoid =
εinduced = −
I=
P
4πr2
dΦB dt n=
c v 1 µ0 E
×B
n1 sin θ1 = n2 sin θ2
1
√ z z 2 +R2
∆U = q∆V
U cap = 1 CV 2
2
d
1−
q charg = εC 1 − e− τ σ= B · dl = µ0 I thru
· dl
E disk =
1 p
4π 0 z 3
E dip, ⊥ =
∆V loop = 0
Req, ser = R1 + R2
σ
2 0
E plate =
1 2p
4π 0 z 3
b aE p = qd
q disch = εCe− τ
W = F · dl
F net = ma
N
S=
1 µ0 EB
n1 sin θcrit = n2
Lenses and Mirrors
1
p
+
1 i =
1 f i m = −p
f=
rc
2
lens power =
1 f Special Relativity β= v c γ=√
1
1−β 2
∆t = γ∆t0
L=
L0 γ Quantum Mechanics – Note: E here is energy, not electric field
E photon = hf
E 2 = (pc)2 + mc2
E bind = ∆mc2
2
N = N0 e−λt
h=
h
2π
Constants e = 1.6×10-19 C
∆x ∆px ≥
1
4π 0
λdB =
∆y ∆py ≥
Nm2
C2
0
h
2
= 8.85×10-12
C2
Nm2
mp = 1.6726×10-27 kg
mn = 1.6749×10-27 kg
c = 3×108 m/s
c =
F el =
1 q1 q2
ˆ
4π 0 r2 r
E · dA =
E ring =
q encl
0
qz
1
4π 0 (z 2 +R2 )3/2
F = Eq
E point =
1 q
ˆ
4π 0 r2 r
E dip, axis =
∆V = −
q = CV
C=
C = κC
I=
P = IV
1
C eq, ser
τ = RC
I= t ρ=
q
V
µ0 N I
L
0A
E line =
1 q
4π 0 r
V point =
σ
2 0
1 2λ
4π 0 r
=
1
C1
1
C2
R=
ΣI in = ΣI out
+
uE =
V = IR
dq dt 1
K = 2 mv 2
1
Req, par
t ε −τ
Re
=
1
R1
+
1
R2
t
V disch = εe− τ
1
2
2 0E ρL A
C eq, par = C 1 + C 2 t V charg = ε 1 − e− τ
t
q
A
B point =
λ= µ0 qv׈ r 4π r2
q
L
B wire =
µ0 2I
4π r
B loop, axis =
F = qv × B
F wire = I l × B
V = −L dI dt Ns
V s = V p Np
I s = I p Np s C circle = 2πr
Acircle = πr2
Asphere = 4πr2
Acyl = 2πrL
V sphere = 4 πr3
3
V cyl = πr2 L
1
V cone = 3 πr2 h
v = λf
E = cB
S=
µ0 I
2r
µ = IA
B solenoid =
εinduced = −
I=
P
4πr2
dΦB dt n=
c v 1 µ0 E
×B
n1 sin θ1 = n2 sin θ2
1
√ z z 2 +R2
∆U = q∆V
U cap = 1 CV 2
2
d
1−
q charg = εC 1 − e− τ σ= B · dl = µ0 I thru
· dl
E disk =
1 p
4π 0 z 3
E dip, ⊥ =
∆V loop = 0
Req, ser = R1 + R2
σ
2 0
E plate =
1 2p
4π 0 z 3
b aE p = qd
q disch = εCe− τ
W = F · dl
F net = ma
N
S=
1 µ0 EB
n1 sin θcrit = n2
Lenses and Mirrors
1
p
+
1 i =
1 f i m = −p
f=
rc
2
lens power =
1 f Special Relativity β= v c γ=√
1
1−β 2
∆t = γ∆t0
L=
L0 γ Quantum Mechanics – Note: E here is energy, not electric field
E photon = hf
E 2 = (pc)2 + mc2
E bind = ∆mc2
2
N = N0 e−λt
h=
h
2π
Constants e = 1.6×10-19 C
∆x ∆px ≥
1
4π 0
λdB =
∆y ∆py ≥
Nm2
C2
0
h
2
= 8.85×10-12
C2
Nm2
mp = 1.6726×10-27 kg
mn = 1.6749×10-27 kg
c = 3×108 m/s
c =