Amperning aylanish qonuni

Klassik elektromagnetizmda Amperning aylanish qonuni ( Amperning kuch qonuni bilan adashtirmaslik kerak) ^[1] yopiq halqa atrofidagi integral magnit maydonni halqadan oʻtuvchi elektr toki bilan bogʻlaydi. Jeyms Klerk Maksvell (Amper emas) 1861 yilda nashr etilgan " Kuchning jismoniy chiziqlari to'g'risida " ^[2] maqolasida uni gidrodinamikadan foydalangan holda chiqargan [2] 1865 yilda u o'zgaruvchan tok atamasini qo'shish orqali vaqt o'zgaruvchan toklarga qo'llaniladigan tenglamani umumlashtirdi, natijada zamonaviy qonunning shakli, ba'zan Amper-Maksvell qonuni deb ataladi, ^[3] ^[4] ^[5] bu klassik elektromagnetizmning asosini tashkil etuvchi Maksvell tenglamalaridan biridir.Shunday qilib, tokli o‘tkazgich va uni qurshab olgan magnit maydoni bir butun elektromagnit hodisaning bir-biridan ajratib bo‘lmaydigan tomonlaridir. Elektromagnit hodisalari asosida yaratilgan elektr dviga-tellari, generatorlar, transformatorlar va shu kabilardan keng foyda-laniladi.

Maksvellning dastlabki aylanish qonuni[tahrir | manbasini tahrirlash]

1820 yilda daniyalik fizik Xans Kristian Orsted elektr toki uning atrofida magnit maydon hosil qilishini aniqladi, u tok o'tkazuvchi sim yonidagi kompas ignasi igna simga perpendikulyar bo'ladigan tarzda burilganini payqadi. ^[6] ^[7] U toʻgʻri oqim oʻtkazuvchi sim atrofidagi maydonni boshqaradigan qoidalarni oʻrganib chiqdi va kashf qildi: ^[8] Magnit maydonni rasmda magnit kuch chiziqlari tufayli tasvirlash mumkin (3 a, b - rasm). Doimiy magnitning N va S qutblari bo‘ylab yo‘nalgan berk uzluksiz chiziqlarni magnit kuch chiziqlari deb ataladi (3a - rasm). To‘g‘ri o‘tkazgich-dagi tok atrofida hosil bo‘lgan aylanalardan iborat (3b - rasm). Magnit kuch chiziqlarining boshi va oxiri bo‘lmaydi. Elektr maydon kuch chiziqlari ochiq, uzlukli bo‘lib, musbat zaryadda boshlanadi va manfiy zaryadda tugaydi. Magnit kuch chiziqlarining uzluksizligi tabiatda magnit zaryadlari yo‘qligi va binobarin, magnit tokining sodir bo‘laolmasligidan dalolat beradi.

Magnit maydon chiziqlari oqim o'tkazuvchi simni o'rab oladi.
Magnit maydon chiziqlari simga perpendikulyar tekislikda yotadi.
Agar oqim yo'nalishi teskari bo'lsa, magnit maydonning yo'nalishi teskari bo'ladi.
Maydonning kuchi oqimning kattaligiga to'g'ridan-to'g'ri proportsionaldir.
Har qanday nuqtadagi maydonning kuchi nuqtaning simdan masofasiga teskari proportsionaldir.

Bu elektr va magnitlanish o'rtasidagi bog'liqlik bo'yicha ko'plab tadqiqotlarni keltirib chiqardi. André-Marie Amper ikkita tok o'tkazuvchi simlar orasidagi magnit kuchni o'rganib, Amperning kuch qonunini kashf etdi. 1850-yillarda shotlandiyalik matematik fizigi Jeyms Klerk Maksvell bu va boshqa natijalarni yagona matematik qonunga umumlashtirdi. Maksvellning aylanma qonunining asl shakli, u 1855 yilda o'zining "Faraday kuch chiziqlari to'g'risida" ^[9] maqolasida gidrodinamikaga o'xshatish asosida olingan bo'lib, magnit maydonlarni ularni hosil qiluvchi elektr toklari bilan bog'laydi. U ma'lum bir oqim bilan bog'liq magnit maydonni yoki ma'lum bir magnit maydon bilan bog'liq bo'lgan oqimni aniqlaydi.

Dastlabki elektron qonun faqat magnitostatik vaziyatga, yopiq kontaktlarning zanglashiga olib keladigan doimiy barqaror oqimlarga nisbatan qo'llaniladi. Vaqt o'tishi bilan o'zgarib turadigan elektr maydonlari bo'lgan tizimlar uchun dastlabki qonun (ushbu bo'limda keltirilganidek) Maksvell tuzatishi deb nomlanuvchi atamani o'z ichiga olishi uchun o'zgartirilishi kerak (pastga qarang).

Ekvivalent shakllar[tahrir | manbasini tahrirlash]

“Integral shakl” va “differensial shakl”. Shakllar mutlaqo ekvivalent va Kelvin-Stokes teoremasi bilan bog'liq (quyidagi " isbot " bo'limiga qarang).
SI birliklaridan foydalanadigan shakllar va cgs birliklaridan foydalanadiganlar. Boshqa birliklar mumkin, ammo kamdan-kam hollarda. Ushbu bo'lim SI birliklaridan foydalanadi, cgs birliklari keyinroq muhokama qilinadi.
$B$ yoki $H$ magnit maydonlaridan foydalangan holda shakllar. Ushbu ikki shakl mos ravishda umumiy oqim zichligi va erkin oqim zichligidan foydalanadi. $B$ va $H$ maydonlari konstitutsiyaviy tenglama bilan bog'langan: magnit bo'lmagan materiallarda $B = μ 0 H$ , bu erda $μ 0$ magnit doimiydir .

Tushuntirish[tahrir | manbasini tahrirlash]

Dastlabki elektron qonunining integral shakli magnit maydonning qandaydir yopiq egri $C$ atrofidagi chiziqli integralidir (ixtiyoriy, lekin yopiq bo'lishi kerak). $C$ egri chizig'i o'z navbatida elektr toki o'tadigan $S$ sirtini ham chegaralaydi (yana o'zboshimchalik bilan, lekin yopiq emas, chunki hech qanday uch o'lchovli hajm $S$ bilan o'ralgan emas) va oqimni o'rab oladi. Qonunning matematik bayoni - bu yopiq yo'ldan (sirt integrali) o'tgan oqim tufayli qandaydir yo'l atrofidagi magnit maydonning umumiy miqdori (chiziq integrali) o'rtasidagi bog'liqlik. ^[10] ^[11] 4. Amper qonuni. Lorens kuchi. Elektr toki magnit maydoni. Magnit maydoni – elektromagnit maydon namoyon bo‘lishining bir ko‘rinishi bo‘lib, shu bilan farq qiladiki, u harakatdagi elektr bilan zaryadlangan zarra va jismlarga, tokli o‘tkazgichlarga hamda magnit momen-tiga ega bo‘lgan zarra va jismlargina kuch bilan ta’sir qiladi.

1819 yilda Ersted tokning magnit sterlkasiga ta’sir etish hodisasini, 1820 yilda Amper toklarning o‘zaro ta’sir etish hodisasini topdilar. 1831 yilda Faradey elektromagnit induksiya hodisasini kashf etdi. 1834 yilda Lens induktivlangan magnit oqimining teskari ta’sir etish qonunini ifodalab berdi. Fanning shu sohalaridagi taraqqiyoti elektr va magnit hodisalari bir-biridan ajralmas ekanligini isbot etdi. Elektr tokisiz magnit hodisasi va aksincha, magnit hodisasiz elektr toki bo‘lmaydi. Elektr toki tarzida sodir bo‘lgani uchun, albatta, magnit hodisalari ham elektr hodisalari bilan birgalikda sodir bo‘ladi.

SI birliklarida yozilgan dastlabki aylanish qonunining shakllari
	Integral shakl	Differensial shakl
$B$ -maydon va umumiy oqimdan foydalanish	$\oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {l}}=\mu _{0}\iint _{S}\mathbf {J} \cdot \mathrm {d} \mathbf {S} =\mu _{0}I_{\mathrm {enc} }$	$\mathbf {\nabla } \times \mathbf {B} =\mu _{0}\mathbf {J}$
$H$ -maydon va erkin oqimdan foydalanish	$\oint _{C}\mathbf {H} \cdot \mathrm {d} {\boldsymbol {l}}=\iint _{S}\mathbf {J} _{\mathrm {f} }\cdot \mathrm {d} \mathbf {S} =I_{\mathrm {f,enc} }$	$\mathbf {\nabla } \times \mathbf {H} =\mathbf {J} _{\mathrm {f} }$

$J$ is the total current density (in amperes per square metre, A·m⁻²),
$J f$ is the free current density only,
$\oint C$ is the closed line integral around the closed curve $C$ ,
$\iint S$ denotes a 2-D surface integral over $S$ enclosed by $C$ ,
$\cdot$ is the vector dot product,
$d l$ is an infinitesimal element (a differential) of the curve $C$ (i.e. a vector with magnitude equal to the length of the infinitesimal line element, and direction given by the tangent to the curve $C$ )
$d S$ is the vector area of an infinitesimal element of surface $S$ (that is, a vector with magnitude equal to the area of the infinitesimal surface element, and direction normal to surface $S$ . The direction of the normal must correspond with the orientation of $C$ by the right hand rule), see below for further explanation of the curve $C$ and surface $S$ .
$\nabla \times$ is the curl operator.

↑ Ampère never utilized the field concept in any of his works; cf. Assis, André Koch Torres. Ampère's electrodynamics: analysis of the meaning and evolution of Ampère's force between current elements, together with a complete translation of his masterpiece: Theory of electrodynamic phenomena, uniquely deduced from experience. Montreal, QC: Apeiron, 2015. ISBN 978-1-987980-03-5. The "Ampère circuital law" is thus more properly termed the "Ampère–Maxwell law." It is named after Ampère because of his contributions to understanding electric current. Maxwell does not take Ampère's force law as a starting point in deriving any of his equations, although he mentions Ampère's force law in his A Treatise on Electricity and Magnetism vol. 2, part 4, ch. 2 (§§502-527) & 23 (§§845-866).
↑ Clerk Maxwell. „On Physical Lines of Force“. New York, Dover Publications (1890).
↑ Fleisch, Daniel. A Student's Guide to Maxwell's Equations. Cambridge University Press, 2008 — 83 bet. ISBN 9781139468473.
↑ Garg, Anupam. Classical Electromagnetism in a Nutshell. Princeton University Press, 2012 — 125 bet. ISBN 9780691130187.
↑ Katz, Debora M.. Physics for Scientists and Engineers: Foundations and Connections, Extended Version. Cengage Learning, 2016 — 1093 bet. ISBN 9781337364300.
↑ Oersted, H. C. (1820). "Experiments on the effect of a current of electricity on the magnetic needles". Annals of Philosophy (London: Baldwin, Craddock, Joy) 16: 273.
↑ H. A. M. Snelders, "Oersted's discovery of electromagnetism" in Cunningham, Andrew Cunningham. Romanticism and the Sciences. CUP Archive, 1990 — 228 bet. ISBN 0521356857.
↑ Dhogal. Basic Electrical Engineering, Vol. 1. Tata McGraw-Hill, 1986 — 96 bet. ISBN 0074515861.
↑ Clerk Maxwell. „On Faraday's Lines of Force“. New York, Dover Publications (1890).
↑ Knoepfel, Heinz E.. Magnetic Fields: A comprehensive theoretical treatise for practical use. Wiley, 2000 — 4 bet. ISBN 0-471-32205-9.
↑ Owen, George E.. Electromagnetic Theory, Reprint of 1963, Courier-Dover Publications, 2003 — 213 bet. ISBN 0-486-42830-3.

[1] Ampère never utilized the field concept in any of his works; cf. Assis, André Koch Torres. Ampère's electrodynamics: analysis of the meaning and evolution of Ampère's force between current elements, together with a complete translation of his masterpiece: Theory of electrodynamic phenomena, uniquely deduced from experience. Montreal, QC: Apeiron, 2015. ISBN 978-1-987980-03-5. The "Ampère circuital law" is thus more properly termed the "Ampère–Maxwell law." It is named after Ampère because of his contributions to understanding electric current. Maxwell does not take Ampère's force law as a starting point in deriving any of his equations, although he mentions Ampère's force law in his A Treatise on Electricity and Magnetism vol. 2, part 4, ch. 2 (§§502-527) & 23 (§§845-866).

[2] Clerk Maxwell. „On Physical Lines of Force“. New York, Dover Publications (1890).

[Fleisch-3] Fleisch, Daniel. A Student's Guide to Maxwell's Equations. Cambridge University Press, 2008 — 83 bet. ISBN 9781139468473.

[Garg-4] Garg, Anupam. Classical Electromagnetism in a Nutshell. Princeton University Press, 2012 — 125 bet. ISBN 9780691130187.

[Katz-5] Katz, Debora M.. Physics for Scientists and Engineers: Foundations and Connections, Extended Version. Cengage Learning, 2016 — 1093 bet. ISBN 9781337364300.

[6] Oersted, H. C. (1820). "Experiments on the effect of a current of electricity on the magnetic needles". Annals of Philosophy (London: Baldwin, Craddock, Joy) 16: 273.

[Cunningham-7] H. A. M. Snelders, "Oersted's discovery of electromagnetism" in Cunningham, Andrew Cunningham. Romanticism and the Sciences. CUP Archive, 1990 — 228 bet. ISBN 0521356857.

[Dhogal-8] Dhogal. Basic Electrical Engineering, Vol. 1. Tata McGraw-Hill, 1986 — 96 bet. ISBN 0074515861.

[9] Clerk Maxwell. „On Faraday's Lines of Force“. New York, Dover Publications (1890).

[Knoepfel-10] Knoepfel, Heinz E.. Magnetic Fields: A comprehensive theoretical treatise for practical use. Wiley, 2000 — 4 bet. ISBN 0-471-32205-9.

[Owen-11] Owen, George E.. Electromagnetic Theory, Reprint of 1963, Courier-Dover Publications, 2003 — 213 bet. ISBN 0-486-42830-3.

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