Example 20 Introduction to Black Holes
ABlackHolerepresentsaperfectequilibriumbetweentheElectricForces,MagneticForcesandGravitationalForces.​​​​term1+term2+term3+term4+term5+term6=0
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
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
r=.
In[]:=
θ=.
In[]:=
φ=.
In[]:=
t=.
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
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[]:=
r=.
In[]:=
SetCoordinates[Spherical[r,θ,φ]]
Out[]=
Spherical[r,θ,φ]
In[]:=
{Coordinates[Spherical],CoordinateRanges[Spherical]}
Out[]=
{{r,θ,φ},{0≤r<∞,0≤θ≤π,-π<φ≤π}}
In[]:=
CoordinatesToCartesian[Coordinates[Spherical],Spherical]
Out[]=
{rCos[φ]Sin[θ],rSin[θ]Sin[φ],rCos[θ]}
In[]:=
f[r]=.
In[]:=
n=.
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
Q1=.
In[]:=
G1=6.67408
-11
10
Out[]=
6.67408×
-11
10
In[]:=
Q1=1.6021765
-19
10
Out[]=
1.60218×
-19
10
In[]:=
ϵ0=8.85
-12
10
Out[]=
8.85×
-12
10
In[]:=
μ0=4π
-7
10
//N
Out[]=
1.25664×
-6
10
In[]:=
G1=.
In[]:=
Q1=.