“Solenoidal Field”的概念、定义、习题解题方法及翻译-数学辞典

单词

Solenoidal Field

释义

Solenoidal Field

A solenoidal Vector Field satisfies

(1)

for every Vector

, where

is the Divergence.If this condition is satisfied, there exists a vector

, known as the Vector Potential, such that

(2)

where

is the Curl. This follows from the vector identity

(3)

is an Irrotational Field, then

(4)

is solenoidal. If

and

are irrotational, then

(5)

is solenoidal. The quantity

(6)

where

is the Gradient, is always solenoidal. For a function

satisfying Laplace's Equation

(7)

it follows that

is solenoidal (and also Irrotational).

See also Beltrami Field, Curl, Divergence, Divergenceless Field, Gradient, Irrotational Field,Laplace's Equation, Vector Field

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, pp. 1084, 1980.

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