静電界と電磁界の比較

By 平野拓一

rhat[θ_, ϕ_] := {Sin[θ]*Cos[φ], 
          Sin[θ]*Sin[φ], 
          Cos[θ]};
θhat[θ_, ϕ_] := {Cos[θ]*Cos[φ], 
          Cos[θ]*
            Sin[φ], -Sin[θ]};
φ = 0;
λ = 1;
z0 = 120*π;
k = ((2*π)/λ);
VecAbs[a_] := (Sqrt[a . Conjugate[a]]);

電磁波テキストp.52の電界の式

er1[
          r_, θ_] := θhat[θ, ϕ]*((I*z0)/(2*λ*r))*Exp[-I*k*r]*Sin[θ];
er2a[r_, θ_] := 
        rhat[θ, ϕ]*(z0/(2*π*(r^2)))*Exp[-I*k*r]*
          Cos[θ];
er2b[
          r_, θ_] := θhat[θ, ϕ]*((I*z0)/(2*λ*r))*(1/(I*k*r))*Exp[-I*k*r]*
          Sin[θ];
er3a[r_, θ_] := 
        rhat[θ, ϕ]*(z0/(2*π*(r^2)))*(1/(I*k*r))*
          Exp[-I*k*r]*Cos[θ];
er3b[
          r_, θ_] := θhat[θ, ϕ]*((I*z0)/(2*λ*r))*(1/(((I*k*r))^2))*Exp[-I*k*r]*
          Sin[θ];

<< Graphics`Legend`;
θ = (π/2);
\(Plot[{VecAbs[\ er1[r, θ]\ ], 
VecAbs[\ 
          er2a[r, θ]\ ], 
VecAbs[\ 
          er2b[r, θ]\ ], 
VecAbs[\ 
          er3a[r, θ]\ ], 
VecAbs[\ 
          er3b[r, θ]\ ]}, 
{r, 0, 
        1}, 
PlotRange -> {0, 
          10000}, 
PlotStyle -> {{RGBColor[1, 0, 
              0]}, 
{RGBColor[0, 1, 
              0]}, 
{RGBColor[0, 0, 
              1]}, 
{RGBColor[0, 1, 
              1]}, 
{RGBColor[1, 0, 
              1]}}, 
Frame -> 
        True, 
FrameLabel -> {"r (λ)", "Relative intensity"}, 
PlotLegend -> {\*""放射界 \!\(θ\&^\)"", 
\*""誘導界 \!\(r\&^\)"", 
\*""ビオサバール界 \!\(θ\&^\)"", 
\*""準静電界 \!\(r\&^\)"", 
\*""準静電界 \!\(θ\&^\)""}, 
LegendSize -> {1, 
          1}, 
LegendPosition -> {\(-0.3\), \(-0.3\)}]\)

θ = (π/2);
FindRoot[
      VecAbs[ er1[r, θ] ] == VecAbs[ er3b[r, θ] ], {r, 0.1, 
        0.11}]

θ = (π/2);
FindRoot[
      VecAbs[ er1[r, θ] ] == VecAbs[ er2b[r, θ] ], {r, 0.1, 
        0.11}]