PHYSICS 208 EXAM II
Formula/Information Sheet
• Basic constants:
Gravitational acceleration on Earth’s surface
Permittivity of free space
Permeability of free space
Elementary charge
Unit of energy: electron volt
Unit of energy: kilowatt-hour
• Properties of some particles:
• Some indefinite integrals:
g
0
µ0
e
1 eV
1 kWh
Particle
Proton
Electron
Neutron
R
R
R
dx
x
dx
(x2 +a2 )3/2
√ dx
x2 ±a2
=
=
ln x
√x
=
ln (x +
a2
=
=
=
=
=
=
9.8 m/sec2
8.8542 × 10−12 C2 /N·m2 [ k = 1/4π0 = 8.9875 × 109 N·m2 /C2 ]
4π × 10−7 T·m/A [ km = µ0 /4π = 10−7 Wb/A·m]
1.60 × 10−19 C
1.60 × 10−19 J
3.6 × 106 J
Mass [kg]
1.67 × 10−27
9.11 × 10−31
1.67 × 10−27
Charge [C]
+1.60 × 10−19
−1.60 × 10−19
0
R
R
2
x2 +a
√
x2 ± a2 )
R
dx
a+bx
x dx
(x2 +a2 )3/2
√x dx
1
b
=
=
ln (a + bx)
− √ 21 2
√ x +a
x2 ± a2
=
x2 ±a2
|q1 q2 |
|~r2 − ~r1 |2
q
k 2 R̂
R
X
X kqi
~i =
E
R̂i
2
Z
Z Ri
kdq
~i =
R̂
dE
R2
Coulomb’s law
(q at ~r1 , q0 at ~r2 )
|F~ |
=
Electric field [N/C = V/m]
~ ≡ ~r0 − ~r)
(q at ~r0 , observer at ~r, R
~ r)
E(~
=
(group of charges)
~
E
=
(continuous charge distribution)
~
E
=
~
(on q subject to E)
~
|E|
~
|E|
F~
= 2k|λ|
r
= 2πk|σ|
=
line charge λ
sheet charge σ
Electric force [N]
Electric flux
Gauss’ law
(small area ∆Ai , outward normal n̂i )
∆ΦE
=
(through an entire surface area)
ΦE
=
(through a closed surface area)
ΦE
≡
~ · n̂)out
(E
=
Conductor
Electric potential [Volt = J/C]
Electric potential energy [J]
(definition, step-length ds along ŝ)
∆V
~
qE
~ i · n̂i ∆Ai = Ei ∆Ai cos θi
E
Z
Z
X
~ · n̂dA
E
lim
∆ΦE =
dΦE =
∆A→0
I
I
dΦE =
~ · n̂dA = 4πkQenc
E
4πkσS
=
Z
Z
B
VB − VA =
∆V
V (~r)
=
=
~ i ≡ ~r − ~ri )
(group of charges, R
V (~r)
=
(continuous charge distribution)
V (~r)
=
∆U
=
Z
~ i |) =
Vi (|R
Z
dV =
X kqi
kdq
~
|R|
~ i|
|R
~
E
U12
=
=
=
(V (∞) = 0)
(V (∞) = 0)
Z
B
~ · ŝds
E
UB − UA = −q0
A
~ from V
E
Electric potential energy of two-charge system
~ · ŝds
E
A
~ · (~rB − ~rA )
−E
q
k
(V (∞) = 0)
~
|R|
X
B
dV = −
A
~ = constant)
(E
(point charge q at ~r0 )
(definition)
k
q0 (VB − VA )
~
~ = gradient operator)
−∇V
(∇
q1 q2
k
|~r1 − ~r2 |
Capacitance [Farad = C/V]
Sphere of radius R
Parallel plates of area A and separation d
Effect of dielectric on electric field
(definition)
Electrostatic potential energy [J] stored in capacitance
Electric energy per unit volume
Electric dipole moment (2a = separation between two charges)
Torque on electric dipole moment
Potential energy of an electric dipole moment
Current [A]
(definition)
with motion of charges
Current density [A/m2 ]
Resistivity [Ω·m]
Resistance [Ω]
Current provided by Emf E [V]
Power provided by emf E [J/s]
Energy loss rate by R [J/s]
Time constant in RC circuit [s]
(definition)
for uniform cross-sectional area A
internal resistance r
Magnetic force [N]
Magnetic field [N]
Magnetic moment [A·m2 or J/T]
Torque [N·m]
Energy [N·m]
sheet charge σm = qm /A
Q
= ∆V
= R
k
A
= 4πkd
= E0 /κ
1 Q(t)2
UE (t) =
2 C
uelectric = 0 E 2 /2 = E 2 /8πk
|~
p| = 2aq
~
~τ = ~
p×E
~
U = −~
p·E
C
C
C
E
I
I
J
ρ
R
R
I
P
P
τRC
on pole qm
due to pole Qm
poles ±qm separated by l
on a magnet
of a magnet
≡
=
=
=
≡
=
=
=
=
=
F~
~
|B|
|~
µ|
~τ
U
~
|B|
d Q(t)
dt
nqvd A
R
I
(where I = J~ · n̂ dA)
A
~|
|E
~
|J|
∆V
I
ρ A`
(E − ∆V )/r
EI
I 2 R = (∆V )2 /R = I(∆V )
RC
~
= qm B
= kmR|Q2 m |
= qm l
~
=~
µ×B
~
= −~
µ·B
= 2πkm |σm |