Download Useful Equations and Constants in Physics and Electromagnetism - Prof. Edward J. Brash and more Study notes Physics in PDF only on Docsity!
Potentially Useful Equations and Constants
Quadratic Formula
T he roots of ax
2
x =
−b ±
b
2
− 4 ac
2 a
Physical Constants
Speed of Light c 3.00 × 10
8
m/s
Acceleration due to Gravity g 9.8 m/s
2
Speed of Sound in Air at 20
◦
C v s
343 m/s
Coulomb’s Law Constant k=
1
4 π 0
8.99 × 10
9
Nm
2
/C
2
Electron Charge -e -1.602 × 10
− 19
C
Proton Charge +e 1.602 × 10
− 19
C
Permittivity of Free Space 0
8.854 × 10
− 12
C
2
/Nm
2
Permeability of Free Space μ 0 4 π × 10
− 7
Tm/A
Electron Mass m e
9.11 × 10
− 31
kg
Proton Mass m p
1.67 × 10
− 27
kg
Waves, Oscillations, and Sound
f =
T
v = λf
T
spring
= 2 π
√
m
k
T
pendulum = 2 π
√
L
g
v string
√
T
μ
μ =
m
L
I =
P
4 πr
2
β = 10 log(
I
I
0
y(x, t) = Acos(
2 π
λ
x −
2 π
T
t)
Electric Field
F
E
= q ~E
Point Charges
|F
E | = k
|q 1 ||q 2
r
2
|E| = k
|q|
r
2
V = k
q
r
U = k
qq 0
r
Gauss’ Law
Q
enclosed
0
E ·
A = EAcos(θ)
Electric Potential and Electric Potential Energy
V = Ed
E = −
∆V
∆s
U = q 0
V
∆U = q 0
∆V
W = −∆U
mv
2
A
+ U
A
mv
2
B
+ U
B
Capacitance
C =
Q
V
C =
0
A
d
= κ 0
U =
CV
2
U
volume
0
E
2
Magnetic Torque on a Current Loop
τ = N IABsin(θ)
Ampere’s Law
∫
B ·
dl = μ 0
I
enclosed
ΣB
||
∆L = μ 0
I
enclosed
Magnetic Field from a Straight Current-Carrying Wire
B =
μ 0
I
2 πr
Forces Between Current-Carrying Wires
F =
μ 0
I
1
I
2
2 πd
L
Magnetic Field at the Center of a Current Loop of N Turns
B =
N μ 0
I
2 R
Magnetic Field of a Solenoid
B = μ 0
N
L
I
Magnetic Flux and Faraday’s Law
M
B ·
A = BAcos(θ)
V
induced
= −N
M
∆t
= −N
dΦ M
dt
Electric Generators
V
induced = N ABωsin(ωt)
Inductance
|V
induced
| = L
∣
∣
∣
∣
∆I
∆t
∣
∣
∣
∣
= L
∣
∣
∣
∣
dI
dt
∣
∣
∣
∣
L =
μ 0
N
2
A
L
U =
LI
2
U
volume
B
2
μ 0
Transformers
V
p
V
s
N
p
N
s
P
p
= P
s
I
p
V
p
= I
s
V
s
AC Circuits
V
rms
V
max
I
rms
I
max
ω =
2 π
T
= 2πf
X
C
ωC
X
L
= ωL
Z
RLC
√
R
2
− X
C
2
