最新电磁场与电磁波英文版

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电磁场与电磁波英文版
1. Directional Derivative & Gradient
The directional derivative of a scalar at a point indicates the spatial
rate of change of the scalar at the point in a certain direction.
be positive. If the electric charge is negative, the flux will be negative.
In a source-free region where there is no charge, the flux through
any closed surface becomes zero.
The direction of a closed surface is defined as the outward normal on the closed surface. Hence, if there is a source in a closed surface, the flux of the vectors must be positive; conversely, if there is a sink, the flux of the vectors will be negative.
In rectangular coordinate system, the operator算符 is denoted as
来自百度文库ex
xey
yez
z
Then the grad of scalar field can be denoted as
grad
2. Flux & Divergence The surface integral面积分 of the vector field A evaluated over a directed surface S is called the flux through the directed surface S,
The flux通量 of the vectors through a closed surface can reveal the properties of the sources and how the sources existed within the closed surface.
The flux only gives the total source in a closed surface, and it cannot describe the distribution 分布of the source. For this reason, the divergence is required.
In rectangular coordinate system直角坐标系, the gradient of a
scalar field can be expressed as
gr a dex xey yez z
Where “grad” is the observation of the word “gradient”.
scalar field at a point is the maximum directional derivative at the
point, and its direction is that in which the directional derivative will
be maximum.
We introduce the ratio比率 of the flux of the vector field A at the point through a closed surface to the volume enclosed by that surface, and the limit极限 of this ratio, as the surface area is made to become vanishingly small at the point, is called the divergence of the vector field at that point, denoted by divA, given by
The source a positive source; The sink a negative source.
From physics we know that
EdS q
S
0
If there is positive electric charge in the closed surface, the flux will
divA limSAdS ΔV0 ΔV
Where “div” is the observation of the word “divergence, and V is the volume closed by the closed surface. It shows that the divergence of a vector field is a scalar field, and it can be considered as the flux through the surface per unit volume.
l
Δl P
P
The directional derivative of scalar l P
at point P in the direction of l is defined as
lim (P)(P)
l P Δl 0
Δl
The gradient is a vector. The magnitude幅度 of the gradient of a
and it is denoted by scalar , i.e.
S AdS
The flux could be positive, negative, or zero.
A source in the closed surface produces a positive integral, while a sink gives rise to a negative one.
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