Tiān-tiûⁿ

連結=https://zh-min-nan.wikipedia.org/wiki/t%C3%B3ng-%C3%A0n:VFPt_charges_plus_minus_thumb.svg|右|縮圖|250x250像素|Tiān-tiûⁿ ê chok-iōng chêng-hêng.

**Tiān-tiûⁿ** (Hàn-jī: ; Eng-gí: ) 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 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

### Tiān-tiûⁿ-sòaⁿ

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
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
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 \boldsymbol\nabla\,\boldsymbol\cdot\,\boldsymbol{E}=\frac{\rho}{\varepsilon_0} í-kip bô kám-èng hāng ê Faraday tēng-lu̍t \boldsymbol\nabla\,\boldsymbol\times\,\boldsymbol{E}=0) tàu-chò-hóe tō téng-î Coulomb tēng-lu̍t, i kóng chi̍t ê khiā tī \boldsymbol{x}_1, tiān-hō-liōng sī q_1 ê chit-tiám tùi chi̍t ê khiā tī \boldsymbol{x}_0, tiān-hō-liōng sī q_0 chhut-la̍t:\boldsymbol{F}=\frac{1}{4\pi\epsilon_0}\frac{q_1q_0}{\left\vert\boldsymbol{x}_1-\boldsymbol{x}_0\right\vert^3}(\boldsymbol{x}_1-\boldsymbol{x}_0),kî-tiong \varepsilon_0 sī chin-khong tiān-iông-lu̍t, tan-ūi sī C2 m−2 N−1. Nā tiān-hō sī hun-pò͘ tī kài-chit lāi-bīn, \varepsilon_0 tio̍h-ài ōaⁿ-chò sī kài-chit ê tiān-iông-lu̍t, \varepsilon.
### Sio-tha̍h goân-lí
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_1, q_2,\ldots,q_n hun-pia̍t khiā tī khong-kan-tiong ê \boldsymbol{x}_1,\boldsymbol{x}_2,\ldots,\boldsymbol{x}_n bōe tín-tāng, mā bô tiān-liû ê chûn-chāi, nā-án-ne sio-tha̍h goân-lí kóng, kiat-kó ê tiān-tiûⁿ \boldsymbol{E}(\boldsymbol{x}) sī ta̍k-ê tiám-tiān-hô q_i sán-seng ê tiān-tiûⁿ \boldsymbol{E}_i(\boldsymbol{x}) ê chóng-hô,\boldsymbol{E}(\boldsymbol{x})=\boldsymbol{E}_1(\boldsymbol{x})+\boldsymbol{E}_2(\boldsymbol{x})+\cdots+\boldsymbol{E}_n(\boldsymbol{x})=\sum^n_{i=1}\boldsymbol{E}_i(\boldsymbol{x}),kî-tiong ê tiān-tiûⁿ ē-sái iōng Coulomb tēng-lu̍t siá, só͘-í\boldsymbol{E}(\boldsymbol{x})=\frac{1}{4\pi\varepsilon_0}\sum^n_{i=1}\frac{q_i(\boldsymbol{x}_i- \boldsymbol{x})}{\left\vert \boldsymbol{x}_i- \boldsymbol{x}\right\vert^3}.Chit tiâu kong-sek mā hō͘ lán ē-tàng kè-sǹg liân-sio̍k tiān-hô hun-pò͘ \rho(\boldsymbol{x}) só͘ tì ê tiān-tiûⁿ, tī chiah ê \rho  sī tiān-hō bi̍t-tō͘, i ê SI tan-ūi sī coulomb múi li̍p-hong kong-chhioh (C/m3). Khiā tī tiám \boldsymbol{x}' ê sè-lia̍p-á thé-chek \text{d}V tiong, ū tiān-hō-liōng \rho(\boldsymbol{x}')\text{d}V, i sán-seng ê tiān-tiûⁿ ē-sái khòaⁿ-chò sī tiám-tiān-hō sán-seng--ê, só͘-í i tī tiám \boldsymbol{x} chō-sêng ê tiān-tiûⁿ tō sī\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}),kā só͘-ū chit khoán sè-lia̍p-á thé-chek kòng-hiàn ê tiān-tiûⁿ ka-ka--khí-lâi, khiā-sǹg-kóng sī tùi choân-pō͘ thé-chek V chò chek-hun, tō sī kui-ē tiān-hō hun-pò͘ chō-sêng ê tiān-tiûⁿ: \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}).

### Tiān-ūi

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, \boldsymbol\nabla\,\boldsymbol\times\,\boldsymbol{E}=0, tiān-tiûⁿ sī bô-soân-ê. Nā sī chit khoán chêng-hêng, lán ē-tàng tēng-gī tiān-ūi, \Phi, i sī chi̍t ê sûn-liōng tiûⁿ, pēng-chhiáⁿ boán-chiok \boldsymbol{E}=-\boldsymbol\nabla\Phi. Khong-kan tiong nn̄g tiám tiān-ūi ê chha kiò-chò 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, \boldsymbol{A}, i boán-chiok \boldsymbol{B}=\boldsymbol{\nabla}\,\boldsymbol\times\,\boldsymbol{A}, án-ne iáu-koh ū hoat-tō͘ kā tiān-tiûⁿ piáu-ta̍t chò\boldsymbol{E}=-\boldsymbol\nabla\Phi-\frac{\partial\boldsymbol{A}}{\partial t},kî-tiong \boldsymbol\nabla\Phi sī   tiān-ūi \Phi ê thui-tō͘, \frac{\partial\boldsymbol{A}}{\partial t} sī chû-hiòng-liōng-ūi \boldsymbol{A} tùi sî-kan ê phian-tō-sò͘.

Tùi í-siōng ê sek chhú soân-tō͘, tō ê tit-tio̍h Faraday kám-èng tēng-lu̍t: \boldsymbol\nabla\,\boldsymbol\times\,\boldsymbol{E}
=-\frac{\partial (\boldsymbol\nabla\,\boldsymbol\times\,\boldsymbol{A})}{\partial t}
=-\frac{\partial \boldsymbol{B}}{\partial t},

Lūi-pia̍t:Tiān-chû-ha̍k