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This rule can be generalized to the case where more components are present. The direction of propagation of the wave is then given by the corkscrew rule for rotation from the resultant electric field to the resultant magnetic field through the smallest possible angle. 2 dipole). In this case, the function f(t-xfv) will have a more closely defined form. 20) Ex= Ez = 0 where w = 2rrf, and Em is the amplitude of the electric field strength. Mathematically, Em and ware arbitrary constants. e. if the disturbance starts off in a harmonic form (a cosine wave), then it will be propagated in the same form.
The wave is propagated from left to right along the x axis, its general form being preserved. This wave is called a transverse wave, because the field only has components at right angles to the direction of propagation. 3 perpendicular to the direction of propagation. At a given moment, the electric field has the same value at all points of a given plane at right angles to the direction of propagation. 8). This gives oHz = ox - oEy ot - ~ = . ; ;. 25) Hz= J~ Em COS (wt-Px) = J! 26) These represent an electromagnetic wave propagated to the right along the x axis with a velocity v = 1/--/BJl.
6), relating to the electric flux, to the parallelepiped gives f Dn dS = p(x, y, z) dv = -Dz~x~y+(Dz)z+dz~x~y-Dy~X~Z Jv oDx = ( fu + (Dy)y+dy~X~Z- Dx~Y~Z + (Dx)x+dx~Y~Z oDy oDz) + oy + oz ~x~y~z = p(x, y, z)~x~y~z or ( oDx + ~_! 24) ax oy oz which represents the description of the behaviour of magnetic flux in differential notation. 19) with respect to x, y and z respectively, and adding the results. 25) ox oy az ar The sets of partial differential equations derived in this section form the basis of the study of the electromagnetic field.