**X1-081 (2012/01/19)**

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Transverse-electric and transverse-magnetic fields
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Using a sufficiently smooth function, one can decompose the space into subsets (level surfaces of that function) the dimensions of whixh are one less that that of the space. Vector fields tangent (perpendicular) to these surfaces are called transverse (longitudinal). Electromagnetic fields are written in terms of transverse-electric and transverse-magnetic fields, and each of these are written in terms of nonzero longitudinal components.