Physics 200: Fundamental Equations Formulas Cheat Sheet
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1Physics 200: Fundamental Equations
Maxwell’s Equations
Q
Gauss’s Law for Electric Field:
E d A =
inside
= 4πkQ
inside
ε
0
Gauss’s Law for Magnetic Field:
B d A = 0
dΦ
Amp` e re/Maxwell:
B d = µ
I
+ µ
where Φ
= E d A
0
encl
0 0
E
dt
dΦ
Faraday’s Law:
= E d =
where Φ
= B d A
induced
B
dt
Fields, Forces, and Energy
kQ
Q
1
elec
9
2
2
Electric Force: F
=
1
2
ˆ r
; where k =
= 9
10
(N m
/C
)
12
1 on 2
2
r
4πε
0
12
k dQ
elec
dV
Electric field: d E =
ˆ r ;
F
= q E
; E
=
at q
x
on q
2
r
dx
A
k dQ
Electric potential: V
V
=
E d ;
dV =
A
B
B
r
Electrostatic energy: ∆U
= q∆V
of q
Dielectrics: E
= E
/κ
;
= κ
; C = κ
C
in
E
E 0
E
0
applied
in
mag
Magnetic Force: d F = Id
B;
F
= qv
B
on q
µ
Id
ˆ
7
Magnetic field: d B =
0
;
µ
= 4π
10
(T m/A);
0
2
4πr
Magnetic dipole: µ = N I ˆ n A;
T orque : τ = µ
B;
U
=
µ B
dipole
Circuits
1
2
Capacitors: C = Q/∆V ; U
=
C(∆V )
E
2
Power: P = I∆V ;
dQ
ρ dL
∆V
Resistors: I =
=
; dR =
dt
R
A
1
1
1
1
Series/Parallel: C
=
C
; C
=
C
; R
=
R
; R
=
R
i
parallel
i
series
i
series
i
i
i
i
parallel
Kirchhoff ’s Laws:
∆V
= 0;
I
=
I
i
in
out
Closed loop
t/RC
t/RC
RC: Q(t) = Q
1
e
; Q(t) = Q
e
final
initial
Φ
dI
1
2
dI
Inductors:
=
L
; L = N
; U
=
LI
; M
= Φ
/I
;
=
M
2
B
12
in 2
in 1
1
12
ind
dt
I
2
dt
t/(L/R)
t/(L/R)
LR: I(t) = I
1
e
; I(t) = I
e
;
final
initial
Electromagnetic Waves and Field Energy Density
1
1
2
2
Field Energy Density: u
=
ε
E
;
u
=
B
;
Momentum: p = U/c
E
0
B
2
2µ
0
1
8
Waves: c =
= 3
10
m/s;
c = λf ;
k = 2π/λ;
ω = 2πf
µ
ε
0
0
1
1
2
P
Poynting vector: S =
E
B ; Intensity: I = S
= c
ε
E
=
; cB = E
av
avg
0
m
µ
2
A
0
Optics
Reflection/Refraction: c
= c/n
;
θ
= θ
;
n
sin (θ
) = n
sin (θ
)
1
1
1
1
2
2
inc
ref
Interference: Constructive: δ = 2πm; Destructive: δ = 2π(m + 1/2)
o
o
Phase shift of reflected wave: n
n
, 180
if n
< n
; 0
otherwise
1
2
1
2
Additional Information
σ
σ
ε
A
Electric fields: E
=
; E
= 2kλ/r;
E
=
; C
=
0
infinite sheet
infinite line
conducting plate
parallel plate
2ε
ε
d
0
0
2
µ
I
µ
N Ia
2
Magnetic fields: B
=
0
; B
= µ
nI; L
= µ
n
Al; B
=
0
0
0
infinite wire
solenoid
solenoid
current loop
2
2
3 2
2πr
2(x
+a
)
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