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zb23
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Why is the divergence of an amplitude of an electric field of a monochromatic plane wave zero?
DaveE said:Divergence is a vector function, not just amplitude, which is why we can use it on E-fields, which are vectors.
yes. I was also kind of sloppy in mixing the derivative and integral forms when I said "measured over a region...".PeterDonis said:The way you are saying this is a bit confusing. Divergence is an operator that can be applied to vectors; the result of applying this operator to a vector is a scalar.
Right, so if I can say ## \nabla \cdot \bf E = 0 ## for any electric field E in the absence of charge, am I home or not?PeterDonis said:The way you are saying this is a bit confusing. Divergence is an operator that can be applied to vectors; the result of applying this operator to a vector is a scalar.
rude man said:if I can say ## \nabla \cdot \bf E = 0 ## for any electric field E in the absence of charge, am I home or not?
rude man said:So,question: can you say that? Did someone say it about 140 years ago?
zb23 said:So is divergence of a complex vector amplitude of electric field of a monochromatic plane wave always zero?
zb23 said:if I write my solution as E*e^i(wt-k*r), where my E is my amplitude written as complex vector
zb23 said:I understand but E is not longer a vector field it is just an amplitude vector that doesn't have to satisfy maxwell equation.
zb23 said:E is not a vector field that represent electric field*
The electric field divergence of a monochromatic plane wave is a measure of the change in electric field intensity at a given point in space. It is a vector quantity that describes the amount and direction of electric field flow at that point.
The electric field divergence of a monochromatic plane wave is zero because the electric field is constant and does not change with respect to time or space. This means that there is no source or sink of electric field, resulting in a net flow of zero.
The electric field divergence of a monochromatic plane wave is a fundamental concept in Maxwell's equations. It is represented by the first equation, known as Gauss's law, which states that the net electric flux through a closed surface is equal to the charge enclosed by that surface.
In theory, the electric field divergence of a monochromatic plane wave can be non-zero if there is a source or sink of electric field, such as a point charge or dipole. However, in most practical applications, the electric field divergence is assumed to be zero due to the absence of these sources.
The electric field divergence of a monochromatic plane wave does not affect the propagation of the wave itself. However, it is an important concept in understanding the behavior and interactions of electromagnetic waves with matter, as it is related to the distribution of charges and currents in a given medium.