Electricity & Magnetism Equation Sheet
Think about how to set up the problem first, then apply the needed principles and formulas.
Electric Field & Force
Circuits
Induction
F = kqr20 q
0
E = Fq = kq
r2
kQx
Ering = (x2 +a
2 )3/2
Eline = 2πλ0 r
I = dQ
dt = nqvd A
J = AI
ρ= E
J
σ = ρ−1
ε = − dΦ
dt
ε = vBL
H
~
~ · dl
ε = (~v × B)
H
~ = − dΦB
~ · dl
E
ρ(T ) = ρ0 [1 + α(T − T0 )]
E
iD = ε0 dΦ
dt
V = IR
H
Epara. plates = σ0
Vterm. = ε − Ir
p = qd (dipole moment)
~
~τdipole = p~ × E
P = IV = I 2 R = VR
τdipole = pE sin φ
1
1
1
R = R1 + R2 + · · · (parallel)
Peq
Ijunction = 0
P
Vclosed loop = 0
N1 ΦB1
i2
ε1 = −M didt2
L = N Φi B
di
ε = −L dt
U = 12 LI 2
B2
u0 = 2µ
0
B2
u = 2µ
L
τ=R
i = I0 e−t/τ
h
z
Edisk = 2σ0 1 − R2 +z
2
Esheet = 2σ0
i
U = −pE cos φ
ΦE = EA cos φ
R
~
~ · dA
ΦE = E
H
~ = Qenc
~ · dA
E
dt
M=
2
Req = R1 + R2 + · · · (series)
τ = RC
Q(t) = Q(1 − e−t/τ ) (charging)
0
Q(t) = Qe−t/τ (discharging)
I(t) = I0 e−t/τ (charging)
Electric Potential
R
~ = −∆U
W = F~ · dl
I(t) = −I0 e−t/τ (discharging)
U = kqr0 q
I0 = − Qτ0
V = Uq = kqr 0
R
~
~ · dl
∆V = − E
λ
Vcyl = 2π
ln
0
di
εi = i2 R + Li dt
q
1
ω = LC
q
R2
1
ω = LC
− 4L
2
Magnetism
~
F~ = q~v × B
R
r
Vring = x2kQ
+a2
~ = −∇V
~
E
Capacitance
C = 0 Ad = VQ
E = σ0 = 0QA
V = Ed = Qd
0A
Q2
1
U = 2C = 2 CV 2 = 12 QV
u = 12 0 E 2
AC Circuits
i = I cos(ωt)
ΦB = BA cos φ
~
~ · dA
ΦB = B
H
~ =0
~ · dA
B
~
F~ = I~l × B
Irms = √I2
~
~τmag. dipole = µ
~ ×B
~
µ
~ = IA
VC = IXC
vrms = √v2
1
XC = ωC
XL = ωL
J B
C
tan φ = XL −X
R
nq = − zEz y
~ = µ0 q~v×r̂
B
2
Pav = 12 IV cos φ
4π
ε = κ0
Ceq = C1 + C2 + · · · (parallel)
Bsolenoid = µ0 nI
1
1
1
Ceq = C1 + C2 + · · · (series)
0N I
Btoroid = µ2πr
H
~ = µ0 Ienc
~ · dl
B
Enew = Eκold
VL = IXL
p
Z = R2 + (XL − XC )2
U = −µB cos φ
r
0I
Bwire = µ2πr
I1 I2 L
F = µ02πr
2
0 Ia
Bloop = 2(xµ2 +a
2 )3/2
Cnew = κCold
~ = µ0 (I + 0 dΦE )
~ · dl
B
dt
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ω0 = √LC
V2
N2
V1 = N 1
I1 V1 = I2 V2
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EM Waves
Constants
Miscellaneous
E = cB
0 = 8.854 × 10−12 NC·m2
2
~·B
~ = AB cos θ
A
9 N ·m2
C2
B = 0 µ0 cE
1
k = 4π
= 8.99 × 10
0
~·B
~ = (Ay Bz − Az By )î
A
c = √10 µ0
~
E(x,
t) = Emax cos(kx ± ωt) ĵ
mp = 1.67 × 10−27 kg
+ (Az Bx − Ax Bz )ĵ
me
= 9.11 × 10−31 kg
+ (Ax By − Ay Bx )k̂
~
B(x,
t) = Bmax cos(kx ± ωt) k̂
e = 1.602 × 10−19 C
c
v = √1εµ = √κκ
m
~= 1E
~ ×B
~
S
1eV = 1.602 × 10−19 J
Asphere = 4πr2
Wb
µ0 = 4π × 10−7 A·m
Vsphere = 43 πr3
2
I = Sav = 12 0 cEmax
c = 2.998 × 108 m
s
Circum. of circle = 2πr
1 dp
S
EB
A dt = c = µ0 c
1u = 1.66 × 10−27 kg
Acircle = πr2
µ0
Scientific Notation Prefixes
Factor Prefix
Symbol
−12
10
picop
−9
10
nanon
−6
10
microµ
−3
10
millim
−2
10
centic
3
10
kilok
6
10
megaM
9
10
gigaG
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MC 1.401
972-883-5480
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0