Tiān-tiûⁿ (電場 ) sī chûn-chāi tī tiān-hō chiu-ûi ē-sái thôan-tē tiān-hô kap tiān-hô chi-kan kau-hō͘ chok-iōng ê bu̍t-lí-tiûⁿ . Tiān-tiûⁿ sī sán-seng chū tiān-hô, ia̍h-sī sûi sî-kan piàn-hòa ê chû-tiûⁿ . Tiān-tiûⁿ kap chû-tiûⁿ lóng sī tiān-chû-la̍t ê tián-hiān, jî-chhiáⁿ tiān-chû-la̍t chū-jiân ê sì chióng ki-pún-la̍t ê chi̍t chióng.
Tiān-tiûⁿ ê chok-iōng chêng-hêng. Tiān-tiûⁿ tī bu̍t-lí léng-e̍k ê chin-chē hong-bīn lóng chiok tiōng-iàu, tī tiān-ki kho-ki mā ū si̍t-chè ê èng-iōng. Tùi goân-chú ê chhioh-tō͘ lâi khòaⁿ, tiān-tiûⁿ sī chō-sêng goân-chú-hu̍t kap tiān-chú hō͘-siong khip-ín ê goan-in, i kā chit nn̄g hāng pa̍k chò-hóe, jiân-āu goân-chú chi-kan ê la̍t iū sán-seng hòa-ha̍k-kiat-ha̍p .
Tiān-tiûⁿ tī sò͘-ha̍k-siōng ê tēng-gī sī chi̍t-ê kap khong-kan tiong kok tiám ū koan-hē ê hiòng-liōng-tiûⁿ ; i ê liōng sī si-ka tī chhì-giām-tiān-hô téng, múi tan-ūi tiān-hô ê la̍t; i ê hong-hiòng tō sī chit-ê la̍t ê hong-hiòng. Tiān-tiûⁿ ê tō-chhut SI tan-ūi sī bó͘-lú-to͘h múi kong-chhioh (V/m), che mā tú-á-hó sī netwon múi coulomb (N/C).
It-poaⁿ biâu-su̍t
siu-kái
Tiān-tiûⁿ-sòaⁿ
siu-kái
Tiān-tiûⁿ-sòaⁿ sī chi̍t tiâu chi̍t tiâu hi-kò͘ ê sòaⁿ, sī têng-hiān tiān-tiûⁿ ê chi̍t chióng hong-sek.
Tī tiān-tiûⁿ-sòaⁿ téng-koân jīm-hô chi̍t tiàm ê hong-hiòng tō sī tiān-tiûⁿ ê hong-hiòng.
Tiān-tiûⁿ-sòaⁿ tī khong-kan tiong ê bi̍t-tō͘ tāi-piáu tiān-tiûⁿ ê kiông-tō͘.
Tī tiān-tiûⁿ-sòaⁿ ê hoān-ûi lāi chēng-chí sek-hòng ê chiàⁿ tiám-tiān-hō, i ê lō͘-kèng tō sī tiān-tiûⁿ-sòaⁿ. Chēng-thài tiān-hō sán-seng ê tiān-tiûⁿ-sòaⁿ, koh ū kúi-nā tiōng-iàu ê sèng-chit:
Tiān-tiûⁿ-sòaⁿ sī hoat-goân chū chiàⁿ tiān-hō, soah-bóe î hū tiān-hō.
Tiān-tiûⁿ-sòaⁿ kap tō-thé ê piáu-bīn sûi-ti̍t. Chit ê kài-liām sī Eng-kok bu̍t-lí-ha̍k-ka Michael Faraday hoat-bêng--ê. I khah-chá sī iōng le̍k-sòaⁿ
Sò͘-ha̍k-biâu-su̍t
siu-kái
Gauss tēng-lu̍t sī teh kóng tiān-hô án-chóaⁿ sán-seng tiān-tiûⁿ. Faraday kám-èng tēng-lu̍t sī teh kóng sûi sî-kan teh piàn-hòa ê chû-tiûⁿ án-chóaⁿ sán-seng tiān-tiûⁿ. Chit nn̄g tiâu tēng-lu̍t ha̍p chò-hóe, tō kàu lán tēng-gī tiān-tiûⁿ ê hêng-ûi--ah. Put-lî-kò, kì-jiân chû-tiûⁿ mā ē-sái piáu-ta̍t chò tiān-tiûⁿ ê hâm-sò͘, che nn̄g chióng tiûⁿ tio̍h-ài thàu-lām chò-hóe, piàn-sêng Maxwell hong-têng-cho͘ , i kā nn̄g ê tiûⁿ khòaⁿ sī tiān-hô kap tiān-liû ê hâm-sò͘.
Chēng-tiān-ha̍k
siu-kái
Chēng-tiān-ha̍k sī gián-kiú tiān-hō chēng-thāi (tiān-hô lóng bōe tín-tāng) chit khoán te̍k-sû chōng-hóng ê ha̍k-būn. Chēng-tiān-ha̍k, tō bōe chhut-hiān Maxwell-Faraday kám-èng hāu-èng. Chhun--ê nn̄g tiâu hong-têng-sek (Gauss tēng-lu̍t
∇
⋅
E
=
ρ
ε
0
{\textstyle {\boldsymbol {\nabla }}\,{\boldsymbol {\cdot }}\,{\boldsymbol {E}}={\frac {\rho }{\varepsilon _{0}}}}
∇
×
E
=
0
{\displaystyle {\boldsymbol {\nabla }}\,{\boldsymbol {\times }}\,{\boldsymbol {E}}=0}
Coulomb tēng-lu̍t , i kóng chi̍t ê khiā tī
x
1
{\displaystyle {\boldsymbol {x}}_{1}}
q
1
{\displaystyle q_{1}}
x
0
{\displaystyle {\boldsymbol {x}}_{0}}
q
0
{\displaystyle q_{0}}
F
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{\displaystyle {\boldsymbol {F}}={\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{0}}{\left\vert {\boldsymbol {x}}_{1}-{\boldsymbol {x}}_{0}\right\vert ^{3}}}({\boldsymbol {x}}_{1}-{\boldsymbol {x}}_{0}),}
ε
0
{\displaystyle \varepsilon _{0}}
chin-khong tiān-iông-lu̍t , tan-ūi sī C2 m−2 N−1 . Nā tiān-hō sī hun-pò͘ tī kài-chit lāi-bīn,
ε
0
{\displaystyle \varepsilon _{0}}
tiān-iông-lu̍t ,
ε
{\displaystyle \varepsilon }
Sio-tha̍h goân-lí
siu-kái
In-ūi Maxwell hong-têng-cho͘ sī sòaⁿ-sèng--ê, só͘-í tiān-tiûⁿ ē-sái àn-chiàu hiòng-liōng ê hong-sek sio-tha̍h, iā tō sī boán-chiok sio-tha̍h goân-lí . Chit-ê goân-lí sī teh kóng: in-ūi chit-tui tiān-hô tī bó͘ chi̍t tiám só͘ chō-sêng ê chóng tiān-tiûⁿ, téng-î kok-piat tiān-hô tan-to̍k chûn-chāi sî tī hit chi̍t tiám só͘ chō-sêng ê tiān-tiûⁿ chi chóng-hô. Kè-sǹg kúi-nā tiám-tiān-hô só͘ chō-sèng chi tiān-tiûⁿ ê sî, chit chióng goân-lí tō piàn-kah chin hó ēng. Iōng sò͘-ha̍k-sek lâi siá, siat-sú tiān-hô
q
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,
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q
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{\displaystyle q_{1},q_{2},\ldots ,q_{n}}
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{\displaystyle {\boldsymbol {x}}_{1},{\boldsymbol {x}}_{2},\ldots ,{\boldsymbol {x}}_{n}}
E
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{\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})}
q
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{\displaystyle q_{i}}
E
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{\displaystyle {\boldsymbol {E}}_{i}({\boldsymbol {x}})}
E
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{\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})={\boldsymbol {E}}_{1}({\boldsymbol {x}})+{\boldsymbol {E}}_{2}({\boldsymbol {x}})+\cdots +{\boldsymbol {E}}_{n}({\boldsymbol {x}})=\sum _{i=1}^{n}{\boldsymbol {E}}_{i}({\boldsymbol {x}}),}
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{\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})={\frac {1}{4\pi \varepsilon _{0}}}\sum _{i=1}^{n}{\frac {q_{i}({\boldsymbol {x}}_{i}-{\boldsymbol {x}})}{\left\vert {\boldsymbol {x}}_{i}-{\boldsymbol {x}}\right\vert ^{3}}}.}
ρ
(
x
)
{\displaystyle \rho ({\boldsymbol {x}})}
ρ
{\displaystyle \rho }
tiān-hō bi̍t-tō͘ , i ê SI tan-ūi sī coulomb múi li̍p-hong kong-chhioh (C/m3 ). Khiā tī tiám
x
′
{\displaystyle {\boldsymbol {x}}'}
d
V
{\displaystyle {\text{d}}V}
ρ
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d
V
{\displaystyle \rho ({\boldsymbol {x}}'){\text{d}}V}
x
{\displaystyle {\boldsymbol {x}}}
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{\displaystyle {\text{d}}{\boldsymbol {E}}({\boldsymbol {x}})={\frac {1}{4\pi \varepsilon _{0}}}{\frac {\rho ({\boldsymbol {x}}'){\text{d}}V}{\left\vert {\boldsymbol {x}}'-{\boldsymbol {x}}\right\vert ^{3}}}({\boldsymbol {x}}'-{\boldsymbol {x}}),}
V
{\displaystyle V}
chek-hun , tō sī kui-ē tiān-hō hun-pò͘ chō-sêng ê tiān-tiûⁿ:
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{\displaystyle {\boldsymbol {E}}({\boldsymbol {x}})={\frac {1}{4\pi \varepsilon _{0}}}\iiint _{V}{\frac {\rho ({\boldsymbol {x}}'){\text{d}}V}{\left\vert {\boldsymbol {x}}'-{\boldsymbol {x}}\right\vert ^{3}}}({\boldsymbol {x}}'-{\boldsymbol {x}}).}
Jû-kó hē-thóng sī ún-tēng-thài--ê (Eng-gí : steady state), chû-tiûⁿ mā bōe sûi sî-kan piàn-hòa, án-ne àn-chiàu bô tiān-chû kám-èng sî ê Faraday tēng-lu̍t,
∇
×
E
=
0
{\displaystyle {\boldsymbol {\nabla }}\,{\boldsymbol {\times }}\,{\boldsymbol {E}}=0}
bô-soân-ê . Nā sī chit khoán chêng-hêng, lán ē-tàng tēng-gī tiān-ūi ,
Φ
{\displaystyle \Phi }
sûn-liōng tiûⁿ , pēng-chhiáⁿ boán-chiok
E
=
−
∇
Φ
{\displaystyle {\boldsymbol {E}}=-{\boldsymbol {\nabla }}\Phi }
tiān-ūi-chha (ia̍h tiān-ap).
Iáu-m̄-koh it-poaⁿ ê tiān-tiûⁿ bô-hoat-tō͘ kap chû-tiûⁿ hun-khui lâi biâu-siá. Lán ài tēng-gī chi̍t ê hiòng-liōng-tiûⁿ , kiò-chò chû-hiòng-liōng-ūi ,
A
{\displaystyle {\boldsymbol {A}}}
B
=
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×
A
{\displaystyle {\boldsymbol {B}}={\boldsymbol {\nabla }}\,{\boldsymbol {\times }}\,{\boldsymbol {A}}}
E
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Φ
−
∂
A
∂
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{\displaystyle {\boldsymbol {E}}=-{\boldsymbol {\nabla }}\Phi -{\frac {\partial {\boldsymbol {A}}}{\partial t}},}
∇
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{\displaystyle {\boldsymbol {\nabla }}\Phi }
Φ
{\displaystyle \Phi }
thui-tō͘ ,
∂
A
∂
t
{\textstyle {\frac {\partial {\boldsymbol {A}}}{\partial t}}}
A
{\displaystyle {\boldsymbol {A}}}
phian-tō-sò͘ .
Tùi í-siōng ê sek chhú soân-tō͘, tō ê tit-tio̍h Faraday kám-èng tēng-lu̍t :
∇
×
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∂
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∇
×
A
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∂
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∂
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∂
t
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{\displaystyle {\boldsymbol {\nabla }}\,{\boldsymbol {\times }}\,{\boldsymbol {E}}=-{\frac {\partial ({\boldsymbol {\nabla }}\,{\boldsymbol {\times }}\,{\boldsymbol {A}})}{\partial t}}=-{\frac {\partial {\boldsymbol {B}}}{\partial t}},}
