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Divergence of the electric flux density in free space is
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According to Gauss's Law in differential form, the divergence of the electric flux density (D) is equal to the volume charge density (╧БvтАЛ). In free space, there are no charges present, therefore ╧БvтАЛ=0, which results in a divergence of zero.
According to Gauss's Law in differential form, the divergence of the electric flux density (D) is equal to the volume charge density (╧БvтАЛ). In free space, there are no charges present, therefore ╧БvтАЛ=0, which results in a divergence of zero.
тИЗтЛЕD=╧БvтАЛ тАФ Differential form of Gauss's Law
тИЗтЛЕD=0 тАФ Divergence in free space
Maxwell's first equation for electrostatic fields is derived from Gauss's Law, which states that the net electric flux emanating from a closed surface is proportional to the enclosed charge. In free space (vacuum), the net charge density is zero everywhere. Consequently, the divergence operator acting on the electric flux density field must yield a scalar value of zero, indicating the absence of sources or sinks (charges) in the region.
Electric flux density D is related to electric field intensity by D=╧╡0тАЛE
A zero divergence field is often called a solenoidal field
In free space, ╧БvтАЛ=0 as there are no free charges
Simplifies Maxwell's equations for electromagnetic wave propagation
Confirms that electric fields in vacuum are continuous
Analysis of plane wave propagation in vacuum
Calculation of field distribution in transmission lines
If charges were present, divergence would be non-zero and equal to the local charge density.
This condition is essential for deriving the Helmholtz wave equation for the electric field.
B is correct тАФ The divergence of electric flux density in free space is 0 because there are no free charges to act as sources or sinks for the flux.
Remember that the divergence of magnetic flux density (тИЗтЛЕB) is always 0 everywhere, not just in free space, due to the non-existence of magnetic monopoles.