天线圣经(Balanis著)中，第三版中在(4-10b) E θ = j η k I 0 L sin ⁡ θ 4 π ϵ 0 r [ 1 + 1 j k r − 1 ( k r ) 2 ] e − j k r E_\theta = j\eta\frac{kI_0L\sin\theta}{4\pi\epsilon_0 r}\left[1+\frac{1}{jkr}-\frac{1}{(kr)^2}\right]e^{-jkr} Eθ​=jη4πϵ0​rkI0​Lsinθ​[1+jkr1​−(kr)21​]e−jkr

在时域情况下用电荷源表示 E θ = r ^ × ( r ^ × z ^ ) 4 π ϵ 0 c 2 r [ ∂ t 2 f ( t − τ ) ] + 3 ( r ^ ⋅ z ^ ) r ^ − z ^ 4 π ϵ 0 r 3 [ f ( t − τ ) + τ ∂ t f ( t − τ ) ] E_\theta = \frac{\hat{r}\times(\hat{r}\times\hat{z})}{4\pi\epsilon_0 c^2 r}\left[\partial_t^2 f(t-\tau)\right]+\frac{3(\hat{r}\cdot\hat{z})\hat{r}-\hat{z}}{4\pi \epsilon_0 r^3}\left[f(t-\tau)+\tau\partial_t f(t-\tau)\right] Eθ​=4πϵ0​c2rr^×(r^×z^)​[∂t2​f(t−τ)]+4πϵ0​r33(r^⋅z^)r^−z^​[f(t−τ)+τ∂t​f(t−τ)]

对应的频域时用电流源表示 E θ = − j ω μ 0 e − j k r 4 π r [ − r ^ × r ^ × I ⃗ l + ( − j k r + 1 ( k r ) 2 ) ( 3 r ^ r ^ ⋅ I ⃗ l − I ⃗ l ) ] E_\theta = \frac{-j\omega\mu_0e^{-jkr}}{4\pi r}\left[-\hat{r}\times\hat{r}\times\vec{I}l+\left(-\frac{j}{kr}+\frac{1}{(kr)^2}\right)(3\hat{r}\hat{r}\cdot \vec{I}l-\vec{I}l)\right] Eθ​=4πr−jωμ0​e−jkr​[−r^×r^×I l+(−krj​+(kr)21​)(3r^r^⋅I l−I l)]

若考虑在远场时，可以得到常用的场量形式(在球坐标下) E θ = j ω μ 0 e − j k r 4 π r I l sin ⁡ θ E_\theta = \frac{j\omega\mu_0 e^{-jkr}}{4\pi r}Il\sin\theta Eθ​=4πrjωμ0​e−jkr​Ilsinθ