Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction

4.3 Time Varying Fields 97field E ⊥ as the sum of left and right hand circularly fields:E ⊥ = E L + E R (4.40)E L = 1 (E⊥ − i2)⊥ (4.41)E R = 1 ( )E⊥ +iˆB×E ⊥2(4.42)where ˆB ≡ ˆk. The imaginary term is the orthogonal electric field componentretarded or advanced in phase by 90 ◦ compared with E ⊥ as shown in Fig. 4.6.The linearly polarized field E ⊥ is equivalent to the sum of left and right circularlyFigure 4.6: The decomposition of E ⊥ into left and right handed components.polarized fields.To solve Eq. (4.38) we first note the result that BB ∗ is a scalar operator:BB ∗ v P ⊥≡(iω + q m B× )(−iω + q m B× )v P ⊥= ω 2 v P ⊥ + q2m B×B×v 2 P ⊥= (ω 2 − ωc 2 )v P ⊥. (4.43)