Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 9.11

Radiation of Electromagnetic Waves

Physics — Landau & Lifshitz · radiation-fields-potentials

Problem

Starting from the general expressions for the retarded potentials, derive the electric and magnetic fields in the radiation zone for an oscillating electric dipole p(t)=p0cos⁡(ωt) z^\mathbf{p}(t) = p_0 \cos(\omega t)\, \hat{z}. Show that in the radiation zone B=−μ0p0ω24πcsin⁡θrcos⁡[ω(t−r/c)] ϕ^\mathbf{B} = -\frac{\mu_0 p_0 \omega^2}{4\pi c} \frac{\sin\theta}{r} \cos[\omega(t - r/c)]\, \hat{\phi} and E=c B×r^\mathbf{E} = c\, \mathbf{B} \times \hat{r}.

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