SP212 Spring 2014 Equation Sheet, page 1
103 kilo k ,
Prefixes:
10−3 milli m ,
106 mega M ,
10−6 micro µ ,
10−9 nano n ,
me = 9.109 × 10−31 kg ,
mp = 1.673 × 10−27 kg ,
Coulomb’s Law and Electric Charge:
dq = λds ,
~
~ = FE ,
E
q0
dq = σdA ,
ΦE =
Gauss’ Law:
Electric Potential:
V =
1
4π0
~ · dA
~,
E
Es = −
q = CV ,
Capacitance:
U=
R
q2
1
= CV 2 ,
2C
2
L
,
A
Circuits:
dW
,
dq
q = CE 1 − e−t/RC ,
q = q0 e−t/RC ,
e = 1.602 × 10−19 C
µ0 = 4π × 10−7 T·m/A ≈ 1.26 × 10−6 T·m/A
H
i=
q = ne, n = 0, ±1, ±2, ±3, ....
~ r) =
dE(~
1 dq
r̂
4π0 r2
p~ = q d~ ,
~ ,
F~E = q E
~ · dA
~ = qenc ,
E
0
E=
σ
,
0
Z f
~ · d~s ,
Vf − Vi = − E
∆U
,
q
∂V
,
∂s
1 |q1 ||q2 |
,
4π0 r2
1 q
r̂ ,
4π0 r2
~ ,
~τ = p~ × E
E=
V =
i
Ex = −
κ0 A
C=
,
d
dq
i=
,
dt
ρ − ρ0 = ρ0 α(T − T0 ) ,
E =
10−15 femto f
∂V
,
∂x
λ
,
2π0 r
n
X
n
X
∂V
,
∂y
Ez = −
σ
20
E=
Vi =
i=1
Ey = −
Ceq =
~
U = −~
p·E
n
1 X qi
4π0
ri
i=1
∂V
,
∂z
U=
1 q1 q2
4π0 r
n
Cj (parallel) ,
j=1
X 1
1
=
(series)
Ceq
Cj
j=1
1
u = 0 E 2
2
Current and Resistance:
R=ρ
~ =
E
FE =
dq = ρdV ,
∆V =
dq
,
r
10−12 pico p ,
1015 peta P
1 eV = 1.602 × 10−19 J
c = 3.00 × 108 m/s ,
Electric Fields:
1012 tera T ,
1
= k = 8.99 × 109 N·m2 /C2 ,
4π0
0 = 8.85 × 10−12 C2 /N·m2 ,
Constants:
Z
109 giga G ,
Pemf = iE ,
Z
i=
~,
J~ · dA
P = iV = i2 R =
Req =
n
X
j=1
CE = q0 ,
i = nAevd ,
RC = τC ,
q dq
0
=−
e−t/RC
dt
RC
J~ = (ne)~vd ,
R=
V
,
i
~ = ρJ~
E
V2
R
n
Rj (series) ,
X 1
1
=
(parallel)
Req
Rj
j=1
dq
E
i=
=
e−t/RC ,
dt
R
VC = E 1 − e−t/RC
SP212 Spring 2014 Equation Sheet, page 2
Magnetic Fields:
~ ×B
~ ,
F~B = iL
~ ,
F~B = q~v × B
~ ×B
~ ,
dF~B = idL
~ · d~s = µ0 ienc ,
B
B = µ0 in ,
Electromagnetic Oscillations:
I
Maxwell’s Equations:
I
Savg = I =
θc = sin−1
Interference:
λ
λn = ,
n
n2
,
n1
,
m=−
pr =
θB = tan−1
2L = m
a sin(θ) = mλ, m = 1, 2, 3, ... ,
µ0 Lia ib
2πd
µ0 iR2
2(R2 + z 2 )3/2
I
dΦB
~ · d~s
, E = BLv , E = E
dt
E
1 − e−Rt/L , τL = L/R
i=
R
E = −N
di
,
dt
1
, i = −ωQ sin(ωt + φ)
LC
I
I
,
c
~ · d~s = − dΦB
E
dt
pr =
|m| =
c=
2I
,
c
E
1
=√
,
B
µ 0 0
1
I = I0 ,
2
~ ×B
~
~= 1E
S
µ0
I = I0 cos2 θ
n2
n1
n1 n2
n2 − n1
+
=
p
i
r
1 1
1
2
+ = = ,
p
i
f
r
i
,
p
Fba =
~ · d~s = µ0 id,enc + µ0 ienc
B
h0
h
1
d sin θ = m +
λ, m = 0, 1, 2, ...
2
d sin θ = mλ, m = 0, 1, 2, ... ,
1 λ
2L = m +
, m = 0, 1, 2, ... ,
2 n2
Diffraction:
ω=√
µ0 iφ
,
4πR
Bloop (z) =
B = Bm sin(kx−ωt) ,
PS
,
4πr2
i = −p,
Images (Mirrors and Lenses):
1
1
−
r1 r2
I=
dΦB
,
dt
EL = −L
I
B=
µ0 iN 1
,
2π r
~ · dA
~=0,
B
dΦE
i d = 0
,
dt
E = Em sin(kx−ωt) ,
n2 sin(θ2 ) = n1 sin(θ1 ) ,
I
~ · dA
~ = qenc ,
E
0
Em
Erms = √ ,
2
1 2
,
E
cµ0 rms
1 1
1
+ = = (n − 1)
p
i
f
L
= µ 0 n2 A ,
l
B2
=
2µ0
q = Q cos(ωt + φ) ,
~ · d~s = µ0 0 dΦE + µ0 ienc ,
B
dt
Electromagnetic Waves:
E =−
~
U = −~
µ·B
µ0 i
,
2πR
B=
Btoroid =
~ · dA
~,
B
2π
|q|B
= 2πf =
T
m
~ ,
~τ = µ
~ ×B
µ0 id~s × r̂
,
4π r2
n = N/L ,
Z
Induction and Inductance: ΦB =
I
~ · d~s = − dΦB , L = N ΦB ,
E
dt
i
1
i = i0 e−Rt/L ,
UB = Li2 ,
uB
2
ω=
~,
µ
~ = N iA
~ =
dB
Magnetic Fields Due to Currents:
I
mv 2
,
r
|q|vB =
λ
, m = 0, 1, 2, ..
n2
sin θ = 1.22
λ
,
d
θR = 1.22
λ
,
d
d sin θ = mλ, m = 0, 1, 2, ...