(A.1) ε_0 ∯▒〖E∙dS=Q〗
Fig. 80. Testing of Gauss’s law using much intermediate matter.
Fig. 81. Gravitational force points inward toward gravitating mass.
(A.6) ∯▒〖g∙dS〗 = -M
(A.7) F=-∇V
(A.8) work done = ∫_(initial point)^(final point)▒〖F∙dx〗
(A.9) ∮_(closed path)▒〖F∙dx〗= ∬_(bounded by closed path)▒〖(∇×F)∙dS〗 =0
(A.10) ∇×F=∇×(-∇V)=0
(A.17) ε_0 ∇∙E=ρ ... (A.21) ε_0 ∇∙E=ρ
(A.18) ∇∙B=0 ... (A.22) ∇∙B=0
(A.19) (∇×B)/μ_0=J+ ε_0 ∂E/∂t
(A.20) ∇×E= -∂B/∂t
(A.23) (∇×B)/μ_0=J+ ε_0 dE/dt
(A.24) ∇×E= -dB/dt
(A.25) E=E_+-E_-
densities, ρ, ... with ρ being zero
Note that ρ_+ and
and ρ_- are both nonnegative.
(A.26) ρ= ρ_+- ρ_-
(A.27) ε_0 ∇∙(E_+- E_- )=ρ_+- ρ_-
(A.28) ε_0 ∇∙E_+=ρ_+
(A.29) ε_0 ∇∙E_-=ρ_-
(A.30) ε_0 ∇∙E_+=ρ_+- {ρ_- δ_(e_(+-) ) (E_+-ρ_- )+ρ_+ δ_(e_(++) ) (E_+-ρ_+ )}
(A.31) ε_0 ∇∙E_-=ρ_-- {ρ_- δ_(e_(--) ) (E_--ρ_- )+ρ_+ δ_(e_(-+) ) (E_--ρ_+ )}
(A.32) B=B_+-B_-
(A.33) ∇∙(B_+-B_- )=0
(A.34) ∇∙B_+=0
(A.35) ∇∙B_-=0
(A.36) ∇∙B_+=- {ρ_- δ_(b_(+-) ) (B_+-ρ_- )+ρ_+ δ_(b_(++) ) (B_+-ρ_+ )}=0
(A.37) ∇∙B_-=- {ρ_- δ_(b_(--) ) (B_--ρ_- )+ρ_+ δ_(b_(-+) ) (B_--ρ_+ )}=0
(A.38) J=J_+-J_-
(A.39) (∇×(B_+-B_- ))/μ_0=(J_+- J_- )+ ε_0 d(E_+-E_- )/dt
(A.40) (∇×(B_+ ))/μ_0=(J_+ )+ ε_0 d(E_+ )/dt
(A.41) (∇×(B_- ))/μ_0=(J_- )+ ε_0 d(E_- )/dt
(A.42) ∇×(E_+-E_- )= -d(B_+-B_- )/dt
(A.43) ∇×(E_+ )= -d(B_+ )/dt
(A.44) ∇×(E_- )= -d(B_- )/dt
The “v” becomes the velocity
The qv×B portions are not needed ... was previously modelled continuously by qE+qv×B.
, and absorption information in qE. The full qE information contains
was previously modelled continuously by qE+qv×B.
(A.45) F=qE+qv×B
(A.46) q= q_+- q_-
(A.47) F=F_++F_-
(A.48) F_++F_-=(q_+- q_- )( E_+-E_- )+(q_+- q_- )v×(B_+-B_- )
(A.49) F_+=(q_+ )( E_+-E_- )+(q_+ )v×(B_+-B_- )
(A.50) F_-=-( q_- )( E_+-E_- )-( q_- )v×(B_+-B_- )
over the volume (vol) of a
charges and the densities, ρ_-=q_-/vol
and ρ_+=q_+/vol, assuming for the moment
(A.51) F_+=(q_+ )( 〖δ_(e_(++) ) (E_+-ρ_+ )e〗_(++) E_+-〖〖δ_(e_(-+) ) (E_--ρ_+ )e〗_(-+) E〗_- )+(q_+ )v×(〖〖δ_(b_(++) ) (B_+-ρ_+ )b〗_(++) B〗_+-〖δ_(b_(-+) ) (B_--ρ_+ ) b_(-+) B〗_- )
(A.52) F_-=-(q_- )( 〖δ_(e_(+-) ) (E_+-ρ_- )e〗_(+-) E_+-〖〖δ_(e_(--) ) (E_--ρ_- )e〗_(--) E〗_- )-(q_- )v×(〖〖δ_(b_(+-) ) (B_+-ρ_- )b〗_(+-) B〗_+-〖〖δ_(b_(--) ) (B_--ρ_- )b〗_(--) B〗_- )
(A.53) F_+=(q_+ )( 〖δ_(e_(++) ) (E_+-ρ_+ )e〗_(++) E_+-〖〖δ_(e_(-+) ) (E_--ρ_+ )e〗_(-+) E〗_- )
(A.54) F_-=-(q_- )( 〖δ_(e_(+-) ) (E_+-ρ_- )e〗_(+-) E_+-〖〖δ_(e_(--) ) (E_--ρ_- )e〗_(--) E〗_- )
A half degree is about .5288≈.5*{360-2*9*〖sin〗^(-1) (1/3)}/9 or half the average available angular gap
Fig. 82. Rendition of Bessler's final figure showing half degree line width.
Fig. 83. Seer lobe rolls without slipping over its lobe-hole.
Fig. 84. Shows the initial geometry of the roller bearing.
Fig. 85. My Orffyreum final figure in Apologia.
Fig. 86. Relationship between Kolob, Oliblish, and the throne of God.
Fig. 87. Yin-yang rotation about horizontal axis, sans dots.
Fig. 88. Yin-yang rotation about horizontal axis, showing dots.
Fig. 89. Sprocket wheels for ED.L.'s Sweet Sixteen family of cylinders.
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