James Clerk Maxwell
James Clerk Maxwell

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James Clerk Maxwell

5.1.2 Getting agreement with Gauss's law

Substituting the assumed form of the electric field (Equation 7.20) into the empty-space version of Gauss's law (Equation 7.16) gives

The first two partial derivatives are equal to zero because f does not depend on x or y. So we obtain

We are interested in disturbances that propagate in the z-direction, so can ignore the possibility that ∂f/∂z = 0 everywhere. It follows that uz = 0. This means that u is a unit vector perpendicular to the z-direction. With no loss in generality, we can choose u to be equal to ex. It is then appropriate to replace f by Ex, and write Equation 7.20 in the form

A wave of this type, in which the variable of interest oscillates perpendicular to the direction of propagation, is said to be transverse.


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