Single-Particle Electrodynamics - Assassination Science

B ′d
1 = κ 2 ¨σ ′ ×n + κ 3 (σ ′·n)¨v×n + 2κ 3 ( ˙σ ′·n) ˙v×n + κ 3 (¨σ ′·n)v×n
+ κ 3 ( ˙v·n) ˙σ ′ ×n + 3κ 4 (σ ′·n)( ˙v·n) ˙v×n + κ 4 (σ ′·n)(¨v·n)v×n
+ 3κ 4 ( ˙σ ′·n)( ˙v·n)v×n + 3κ 5 (σ ′·n)( ˙v·n) 2 v×n,
B ′d
2 = κ 2 σ ′ × ˙v + κ 3 γ −2 ˙σ ′ ×n − 2κ 3 (σ ′·v) ˙v×n − κ 3 (σ ′· ˙v)v×n
+ κ 3 (σ ′·n)v× ˙v − 2κ 3 ( ˙σ ′·v)v×n + κ 3 ( ˙v·n)σ ′ ×v
+ 3κ 4 γ −2 (σ ′·n) ˙v×n + 3κ 4 γ −2 ( ˙σ ′·n)v×n − 3κ 4 (σ ′·v)( ˙v·n)v×n
− 3κ 4 (σ ′·n)(v· ˙v)v×n + 6κ 5 γ −2 (σ ′·n)( ˙v·n)v×n,
B ′d
3 = κ 3 γ −2 σ ′ ×v − 3κ 4 γ −2 (σ ′·v)v×n + 3κ 5 γ −4 (σ ′·n)v×n.
G.5.4
The author’s expressions
The final, simplified expressions obtained by the author (on paper) for the
retarded fields are as follows:
where
hence,
E ′q
1 = κ 3 n×E ′′q
1 ,
E ′′q
1 = − ˙v×n ′ ;
E ′q
1 = κ 3 ( ˙v·n)n ′ − κ 3 (n·n ′ ) ˙v;
E ′q
2 = κ 3 γ −2 n ′ ,
E ′d
1 = κ 3 n×E ′′d
1 ,
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