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**Extra info for A Kinematical Interpretation of Electromagnetism (1919)(en)(8s)**

**Example text**

The ﬁrst root λ∗1 of Eq. 5 l (m) Fig. 8. The ﬁrst root λ∗1 of Eq. 5 l (m) Fig. 9. 6, and subject to the condition k02 , the second terms in Eqs. 5 l (m) Fig. 10. 001i wave terms addressed in the paper by King and Sandler (1994). 85) where ε = −ik0 l and p are given in the paper by King and Sandler (1994). Then, the second term in Eq. 79) reduces to −ik03 lμ0 2 1 ik0 r2 −ip∗ e e F(p∗ ). 86) It is seen that the corresponding term in the paper by King and Sandler (1994) is written in the form k02 εμ0 2π π ik0 r2 −ip e e F(p).

142) r02 , it is known that r1 ∼ r0 − d cos Θ, r2 ∼ Taking into account d2 r0 + d cos Θ in phase and r1 ∼ r2 ∼ r0 in amplitudes. 144) z+d d z+d ∼ = cos Θ + . 147) ωμ0 ik0 r0 e 2k0 π × ik0 r0 sin Θ(ε∗ sin Θ + cos Θ + d r0 ) × − iε∗ sin Θ sin(k0 d cos Θ) + cos(k0 d cos Θ) sin Θ × ε∗ sin3 Θ + sin2 Θ cos Θ + − sin Θeik0 d cos Θ ε∗ r02 (ε∗ sin Θ + cos Θ + d sin2 Θ − ε∗ r0 − d 3 r0 ) ωμ0 i π e4 2k02 2 πr0 sin Θ 5/2 × j A(λj )λj eiγ0 (λj )(r0 cos Θ+d)+iλj r0 sin Θ . 148) After considerable algebraic manipulation, the ﬁeld components in spherical coordinates r0 , Θ, Φ can be expressed as follows: r (r0 , Θ) = − E0Θ × ωμ0 ik0 r0 e 2πk0 ik0 cos(k0 d cos Θ) r0 sin Θ(ε∗ sin Θ + cos Θ + d r0 ) × (ε∗ sin3 Θ + sin2 Θ cos Θ − ε∗ ) + + d(sin2 Θ − ε∗ cos Θ) r0 dε∗ cos Θ sin3 Θ r0 + ik0 [i sin(k0 d cos Θ)] r0 sin Θ(ε∗ sin Θ + cos Θ + + d sin2 Θ cos2 Θ + r0 + ε∗ sin Θ(ε∗ cos Θ − sin Θ)eik0 d cos Θ r02 (ε∗ sin Θ + cos Θ + d/r0 )3 ωμ0 i π e4 2k02 × cos Θ + 2 πr0 sin Θ j d r0 d r0 ) 2 sin2 Θ cos Θ − ε∗ − dε∗ cos Θ r0 A(λj )λ3/2 q (λj ) λj sin Θ eiγ0 (λj )(r0 cos Θ+d)+iλj r0 sin Θ .

IEEE Transactions on Antennas and Propagation, 46(12): 1745–1946. Sommerfeld A (1909) Propagation of waves in wireless telegraphy. Annalen der Physik (Leipzig), 28: 665–736. Sommerfeld A (1926) Propagation of waves in wireless telegraphy. Annalen der Physik (Leipzig), 81: 1135–1153. Wait JR (1953) Radiation from a vertical electric dipole over a stratiﬁed ground. IRE Transactions on Antennas and Propagation, AP-1: 9-12. Wait JR (1954) Radiation from a vertical electric dipole over a stratiﬁed ground.

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