Single-Particle Electrodynamics - Assassination Science

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.5.5
Comparison of expressions
To compare these two sets of results quickly, we simply subtract the latter
from the former; we find
∆E ′q
1 = 0,
∆E ′q
2 = 0,
∆E ′d
1 = 0,
∆E ′d
2 = 0,
∆E ′d
3 = 0,
∆B ′q
1 = 0,
∆B ′q
2 = 0,
∆B ′d
1 = 0,
∆B ′d
2 = 0,
∆B ′d
3 = 0.
Hence, the author’s simplified expressions for the retarded fields have been
explicitly verified.
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