Simple Nature - Light and Matter

and Maxwell’s equations becomeΦ E = 0Φ B = 0Γ E = − ∂Φ B∂tc 2 Γ B = ∂Φ E∂t.The equation Φ = 0 has already been verified for this type ofwave pattern in example 36 on page 630. Even if you haven’t learnedthe techniques from that section, it should be visually plausible thatthis field pattern doesn’t diverge or converge on any particular point.Geometry of the electric and magnetic fieldsThe equation c 2 Γ B = ∂Φ E /∂t tells us that there can be no suchthing as a purely magnetic wave. The wave pattern clearly does havea nonvanishing circulation around the edge of the surface suggestedin figure g, so there must be an electric flux through the surface.This magnetic field pattern must be intertwined with an electricfield pattern that fills the same space. There is also no way that thetwo sides of the equation could stay synchronized with each otherunless the electric field pattern is also a sine wave, and one thathas the same wavelength, frequency, and velocity. Since the electricfield is making a flux through the indicated surface, it’s plausiblethat the electric field vectors lie in a plane perpendicular to thatof the magnetic field vectors. The resulting geometry is shown infigure h. Further justification for this geometry is given later in thissubsection.i / An impossible wave pattern.h / The geometry of an electromagnetic wave.One feature of figure h that is easily justified is that the electricand magnetic fields are perpendicular not only to each other, butalso to the direction of propagation of the wave. In other words, thevibration is sideways, like people in a stadium “doing the wave,”not lengthwise, like the accordion pattern in figure i. (In standard698 Chapter 11 Electromagnetism