Formula Sheet
Electromagnetic Waves
Electric field and Magnetic field form sinusoidial relationships expressed such as
sin (kx+ωt)
E (t )=Emax¿ ; B (t )=Bmax(sin (kx+ωt ))
Where k is the wave number, and ω is the a
...
Formula Sheet
Electromagnetic Waves
Electric field and Magnetic field form sinusoidial relationships expressed such as
sin (kx+ωt)
E (t )=Emax¿ ; B (t )=Bmax(sin (kx+ωt ))
Where k is the wave number, and ω is the angular frequency
Maxwell’s Equations tells us that
E=cB
;
B=ϵ
0 μ0CE
;
c=
1
√ϵ0 μ0
c being the speed of light, μ0 being the permitivvity of free space (4pi * 10^-7
These waves have a wavelength λ , velocity v, and frequency, which are expressed in the fluid
relationship;
f = ω
2 π ; v=(2 2ωkπ π)=λf = 2kπ2∗πϖ ;
We should also know the following potential energy densities produced by both fields, as well as the
totals
U
E=
12
ϵ
0 E2
; U
B=
12
B2
μ0
;
U
tot=U E+U B
;
U
tot=2U E=2UB
AS well as the relationships of the average energy densities, and the root-mean-squares.
U
Eave=
12
ϵ
0(√E20)2 ; UBave=21μ0(√B20)2 ; Erms=√E20 ; Brms=√B20 ;
And the peculiar Poyntig, S, which is known as the intensity of the wave.
S=
E0 B0
2 μ0
=
E0 2 c ϵ0
2
=
B0 2 c
2 μ0
And the definitions of power
P=ϵ
0 c E2=ϵ0 c2 EB= EB
μ0
And energy stored per unit volume
ϖ=
ϵ0 E2
2
+
B2
2 μ0
=
ϵ0 E2
2
+
E2
2 μ0 c2=
ϵ0 E2
2
+
ϵ0 E2
2
=ϵ
0 E2
Pressure, Intensity, and their relation with Electric field didn’t show up in the Masteringphysics example,
but it’s in a former final, so I have no idea if this is relevant, but just in case
.
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