Calculation 3​​​Propagation of a Beam of Light in the z-direction with the speed of light:
c=
1
ϵ0μ0
​within a constant gravitational field, oriented in the z-direction, with accelleration g = G1, resulting in Gravitational Redshift.
Book:
RisingoftheJamesWebbSpaceTelescopeanditsFundamentalBlindnes
:Page46,Equation(73)​​ExampleofaSphericalBeamofLight ,propagatingintheradial-direction(r-direction)​​withthespeedoflightc=
1
ϵ0μ0
.​​TheinputfortheElectricFieldIntensity{E(x,y,z,)=ev}andtheMagneticFieldIntensity{H(x,y,z,)=mv}havebeensubstitutedintheFieldEquationfortheElectromagneticFieldwithinaconstantgravitationalfieldwithaccellerationginthez-direction.(BookEquation73,page46).​​​​
Book:
RisingoftheJamesWebbSpaceTelescopeanditsFundamentalBlindnes
:Page15,Equation(19)​​ExampleofaLASER-BEAMwithaGaussianIntensitydivison
-K2
2
x
+
2
y

,combinedwithanarbitrarydivisiong[x,y]inthe(x,y)plane,propagatinginthez-directionwiththespeedoflightc=
1
ϵ0μ0
.​​TheinputfortheElectricFieldIntensity{E(x,y,z,)=ev}andtheMagneticFieldIntensity{H(x,y,z,)=mv}hasbeensubstitutedintheFieldEquationfortheElectromagneticField(BookEquation19,page16).​​​​
- 
1
2
c
∂
¯
E
×
¯
Η

∂t
+
ε
0
¯
E
∇. 
¯
E
−
ε
0
¯
E
×∇×
¯
E
+
μ
0
¯
Η
∇. 
¯
Η
−
μ
0
¯
Η
×∇×
¯
Η

= 0
Equation(19)​​​​Whichcanbewrittenas:​​​​term1=-
1
2
c
∂
¯
E
×
¯
Η

∂t
​​​​term2=
ε
0
¯
E
(∇. 
¯
E
)​​​​term3=−
ε
0
¯
E
×(∇×
¯
E
)​​​​term4=
μ
0
¯
Η
∇. 
¯
Η
​​​​term5=−
μ
0
¯
Η
×∇×
¯
Η
​​​​Equation(19)equals:​​​​term1+term2+term3+term4+term5=0
​​Whichcanbewrittenas:​​​​term1=-
1
2
c
∂
¯
E
×
¯
Η

∂t
​​​​term2=
ε
0
¯
E
(∇. 
¯
E
)​​​​term3=−
ε
0
¯
E
×(∇×
¯
E
)​​​​term4=
μ
0
¯
Η
∇. 
¯
Η
​​​​term5=−
μ
0
¯
Η
×∇×
¯
Η
​​​​term6=-
1
2

2
ε
μ(
¯
E
 . 
¯
E
)
+
ε
2
 μ
(
¯
H
 . 
¯
H
)
¯
g
​​​​Equation(73)equals:​​​​term1+term2+term3+term4+term5+term6=0
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
x=.
In[]:=
y=.
In[]:=
z=.
In[]:=
t=.
In[]:=
Get["VectorAnalysis`"]
General
:VectorAnalysis` is now obsolete. The legacy version being loaded may conflict with current functionality. See the Compatibility Guide for updating information.
In[]:=
Get["Calculus`DSolve`"]
Get
:Cannot open Calculus`DSolve`.
Out[]=
$Failed
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
Get["Calculus`DSolveIntegrals`"]
Get
:Cannot open Calculus`DSolveIntegrals`.
Results for the electromagnetic force densities in resp x-direction, y-direction, z-direction: