We can see in many publications that in the ionosphere, the zonal electrical field is directed eastward on the dayside and westward on the nightside. Why exactly that happens? What are the physics involved?
The zonal electric fields are produced by the effects of the F disturbance dynamo effects. The F dynamo effects is cussed by the energy input from the magnetosphric disturbances which alters the global circulation of nuetral winds over the F2 layer. Therefore the electric fields are height dependant and have diurnal varriations
A modern (although now classic) book on the ionosphere, discusses the reasons for the existence of an electric field in the ionosphere. This book is: "The Earth´s Ionsphere by M.C. Kelley. I'm going to refer you to the sections that you should read based on the 2nd edition of this book (2009). Read Secion 2.3 (page 47-48) for a first principle based discussion on the origin of ionosphere´s electric field. Them, for the zonal electric field, read first Section 3.1 (pag 71) and in the equatorial region case (the F dynamo) read Section 3.2 (pag 77). The Figure 3.5 explain clearly the origin of zonal eletric field.