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純量勢

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純量勢(scalar potential)或稱純量位,在向量分析物理學中是一個基本概念,将矢量场的无旋部分表示为标量场梯度,该标量场称为标量势[1]。一般只要不會與向量勢發生混淆,前綴形容「純量」常省略,而簡稱「勢」或「位勢」。

給定一向量場F,其純量勢V為一純量場;對此純量場取負值梯度則得到F

相反過來,給定一函數V,這個式子定義了一個向量場F,其純量勢為V。純量勢也常常標記為希臘字母Φ,比如在電動力學的場合。

純量勢的物理意義和場的類型有關。對一流體或氣體流的向量場,定義純量勢暗示了任一點的流向與該點純量勢的最陡降方向相同,而對於力場,在一點的加速度也是一樣的情況。力場的純量勢跟力場的勢能(或稱位能)密切相關。

不是每個向量場都有一純量勢;有純量勢的向量場稱作是保守向量場,相應於物理學中保守力的稱呼。在各種速度場中,任何的層狀場(lamellar field)皆有一純量勢,而一螺線向量場可有純量勢的情況只發生在拉普拉斯場(Laplacian field)。

參考

[编辑]
  1. ^ 存档副本. [2024-01-26]. (原始内容存档于2024-01-26). 
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純量勢
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