Lorents-Heaviside birliklari (yoki Heaviside-Lorents birliklari) tarkibidagi birliklar tizimini (xususan, elektromagnit birliklarni) tashkil qiladi CGS uchun nomlangan Xendrik Antuan Lorents va Oliver Heaviside. Ular bilan bo'lishadilar CGS-Gauss birliklari bo'lgan mulk elektr doimiy ε0 va magnit doimiy µ0 paydo bo'lmasligi, ularning aniqlanishi bilan elektromagnit miqdorlarga bevosita kiritilgan. Lorents-Heaviside birliklari normallashgan deb hisoblanishi mumkin ε0 = 1 va µ0 = 1, shu bilan birga qayta ko'rib chiqish Maksvell tenglamalari dan foydalanish yorug'lik tezligi v o'rniga.[1]
Lorents-Heaviside birliklari, shunga o'xshash SI birliklar, ammo farqli o'laroq Gauss birliklari, bor ratsionalizatsiya qilingan, degan ma'noni anglatuvchi omillar mavjud emas 4π ichida aniq ko'rinadigan Maksvell tenglamalari.[2] Ushbu birliklarning ratsionalizatsiyasi qisman ularning jozibadorligini tushuntiradi kvant maydon nazariyasi: the Lagrangian nazariyasi asosida hech qanday omil mavjud emas 4π ushbu birliklarda.[3] Binobarin, Lorents-Heaviside birliklari omillarga ko'ra farqlanadi √4π elektr va magnit maydonlarining ta'riflarida va elektr zaryadi. Ular ko'pincha ishlatiladi relyativistik hisob-kitoblar,[eslatma 1] va ishlatiladi zarralar fizikasi. Ular uchtadan kattaroq fazoviy o'lchamlarda hisob-kitoblarni amalga oshirishda ayniqsa qulaydir torlar nazariyasi.
Uzunlik-massa-vaqt doirasi
Gauss birliklarida bo'lgani kabi, Heaviside-Lorents birliklari (ushbu maqoladagi HLU) uzunlik-massa-vaqt o'lchamlari. Bu shuni anglatadiki, barcha elektr va magnit birliklar uzunlik, vaqt va massaning asosiy birliklari bo'yicha ifodalanadi.
Ushbu tizimlarda zaryadni aniqlash uchun ishlatiladigan Kulon tenglamasi quyidagicha F = qG
1qG
2/r2 Gauss tizimida va F = qLH
1qLH
2/4.r2 HLUda. Keyin zaryad birligi ulanadi 1 din⋅sm2 = 1 esu2 = 4π hlu. HLU miqdori qLH zaryadni tavsiflash u holda √4π mos keladigan Gauss miqdoridan kattaroq (pastga qarang), qolganlari quyidagicha.
SI birliklari uchun o'lchovli tahlildan foydalanilganda, shu jumladan ε0 va m0 birliklarni konvertatsiya qilish uchun ishlatiladi, natijada Heaviside-Lorentz birliklariga va undan konversiyani beradi. Masalan, zaryad √ε0L3MT−2. Qachon qo'yadi ε0 = 8.854 pF / m, L = 0,01 m, M = 0,001 kgva T = 1 ikkinchidan, bu quyidagicha baholanadi 9.409669×10−11 C. Bu HLU zaryad birligining kattaligi.
Maksvellning manbalari bilan tenglamalari
Lorents-Heaviside birliklari bilan, Maksvell tenglamalari yilda bo'sh joy manbalar bilan quyidagi shaklga ega:
![{displaystyle abla cdot mathbf {E} ^ {extsf {LH}} = ho ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86ce6fdbd667afc37c7e63d55c7fa891ad039694)
![{displaystyle abla cdot mathbf {B} ^ {extsf {LH}} = 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c7463e2f1f3172fb778bf6f230f658f623b0a4)
![{displaystyle abla imes mathbf {E} ^ {extsf {LH}} = - {frac {1} {c}} {frac {qisman mathbf {B ^ {extsf {LH}}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9f627cdb2c98021792ff7af58ec80a33b4dd363)
![{displaystyle abla imes mathbf {B} ^ {extsf {LH}} = {frac {1} {c}} {frac {qisman mathbf {E} ^ {extsf {LH}}} {qisman t}} + {frac { 1} {c}} mathbf {J} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9a75573d3e8f0a83ed185623b4e3796cce80983)
qayerda v bo'ladi vakuumdagi yorug'lik tezligi. Bu yerda ELH = D.LH bo'ladi elektr maydoni, HLH = BLH bo'ladi magnit maydon, rLH bu zaryad zichligi va JLH bu joriy zichlik.
The Lorents kuchi tenglama:
![{displaystyle mathbf {F} = q ^ {extsf {LH}} chap (mathbf {E} ^ {extsf {LH}} + {frac {mathbf {v}} {c}} imes mathbf {B} ^ {extsf { LH}} ight),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/832e88947e327e1f33c2a5487d7de904d6829ddb)
Bu yerga qLH vektor tezligi bilan sinov zarrachasining zaryadidir v va F bu sinov zarrachasiga ta'sir qiluvchi birlashgan elektr va magnit kuchdir.
Gauss va Heaviside-Lorents tizimlarida elektr va magnit birliklar mexanik tizimlardan kelib chiqadi. Zaryad Coulomb tenglamasi orqali aniqlanadi ε = 1. Gauss tizimida Kulon tenglamasi quyidagicha F = qG
1qG
2/r2. Lorents-Heaviside tizimida, F = qLH
1qLH
2/4.r2. Bundan odam buni ko'radi qG
1qG
2 = qLH
1qLH
2/4π, Gauss zaryadlarining miqdori Lorents-Heaviside miqdorlariga nisbatan kichik bo'lganligi √4π. Boshqa miqdorlar quyidagicha bog'liqdir.
![{displaystyle q ^ {extsf {LH}} = {sqrt {4pi}} q ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3751aefd73cd1b484b83a8500e9488acc9dde5a2)
![{displaystyle mathbf {E} ^ {extsf {LH}} = {mathbf {E} ^ {extsf {G}} ustidan {sqrt {4pi}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/144f23800732293052be4cd4cf832a50517a323f)
.
Tenglamalar ro'yxati va boshqa birliklar tizimlari bilan taqqoslash
Ushbu bo'limda Lorents-Heaviside, Gaussian va SI birliklarida berilgan elektromagnetizmning asosiy formulalari ro'yxati keltirilgan. Aksariyat ramz nomlari berilmagan; to'liq tushuntirishlar va ta'riflar uchun har bir tenglama uchun tegishli maxsus maqolani bosing.
Maksvell tenglamalari
Bu erda Maksvell tenglamalari ham makroskopik, ham mikroskopik shakllarda keltirilgan. Tenglamalarning faqat "differentsial shakli" berilgan, "integral shakli" emas; integral shakllarini olish uchun divergensiya teoremasi yoki Kelvin - Stoks teoremasi.
Ism | SI miqdorlar | Lorents-Heaviside miqdorlari | Gauss miqdorlar |
---|
Gauss qonuni (makroskopik) | ![{displaystyle abla cdot mathbf {D} ^ {extsf {SI}} = ho _ {ext {f}} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e3c13ca29b0d5e4d6f0b80379d257c6a327cb6b8) | ![{displaystyle abla cdot mathbf {D} ^ {extsf {LH}} = ho _ {ext {f}} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/96c61928a4d14bd2dcc9db83fe913431147fee8d) | ![{displaystyle abla cdot mathbf {D} ^ {extsf {G}} = 4pi ho _ {ext {f}} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f6369fd2926ef4809b87e394b8e14bf9fffc9246) |
Gauss qonuni (mikroskopik) | ![{displaystyle abla cdot mathbf {E} ^ {extsf {SI}} = ho ^ {extsf {SI}} / epsilon _ {0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd50a5f3d3b85f21f825070ff110947b9846d236) | ![{displaystyle abla cdot mathbf {E} ^ {extsf {LH}} = ho ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86ce6fdbd667afc37c7e63d55c7fa891ad039694) | ![{displaystyle abla cdot mathbf {E} ^ {extsf {G}} = 4pi ho ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e710aff0c58830160e835ec55670272980059e51) |
Magnetizm uchun Gauss qonuni: | ![{displaystyle abla cdot mathbf {B} ^ {extsf {SI}} = 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee84f2beb068185891cba01e2044e5c614e1e216) | ![{displaystyle abla cdot mathbf {B} ^ {extsf {LH}} = 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c7463e2f1f3172fb778bf6f230f658f623b0a4) | ![{displaystyle abla cdot mathbf {B} ^ {extsf {G}} = 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9869bdd81918ec8852a1ee84d3fed4539e41b1d2) |
Maksvell - Faradey tenglamasi (Faradey induksiya qonuni ): | ![{displaystyle abla imes mathbf {E} ^ {extsf {SI}} = - {frac {qisman mathbf {B} ^ {extsf {SI}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b6db116ef8f81662f223a011904a795365a1c8f6) | ![{displaystyle abla imes mathbf {E} ^ {extsf {LH}} = - {frac {1} {c}} {frac {qisman mathbf {B} ^ {extsf {LH}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e399b7c55d7bb633ad2f5b45f2618dba70f0317d) | ![{displaystyle abla imes mathbf {E} ^ {extsf {G}} = - {frac {1} {c}} {frac {qisman matematik {B} ^ {extsf {G}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2344788cc4fb4374890dd2136b263565bab1a578) |
Amper - Maksvell tenglamasi (makroskopik): | ![{displaystyle abla imes mathbf {H} ^ {extsf {SI}} = mathbf {J} _ {ext {f}} ^ {extsf {SI}} + {frac {qisman mathbf {D} ^ {extsf {SI}} } {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f75ab63ec6edc79d20cb66ada4e958d9b53fffd0) | ![{displaystyle abla imes mathbf {H} ^ {extsf {LH}} = {frac {1} {c}} mathbf {J} _ {ext {f}} ^ {extsf {LH}} + {frac {1} { c}} {frac {qisman mathbf {D} ^ {extsf {LH}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4a1d9c431e2229ab34dca6b54c24a94cd4d2122) | ![{displaystyle abla imes mathbf {H} ^ {extsf {G}} = {frac {4pi} {c}} mathbf {J} _ {ext {f}} ^ {extsf {G}} + {frac {1} { c}} {frac {qisman mathbf {D} ^ {extsf {G}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ea562c2623912489ac2508ac6e72d40a90a89ac) |
Amper - Maksvell tenglamasi (mikroskopik): | ![{displaystyle abla imes mathbf {B} ^ {extsf {SI}} = mu _ {0} mathbf {J} ^ {extsf {SI}} + {frac {1} {c ^ {2}}} {frac {qisman mathbf {E} ^ {extsf {SI}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6b7016da4584dcbaf7ae0bd86c6fc19d38e0631e) | ![{displaystyle abla imes mathbf {B} ^ {extsf {LH}} = {frac {1} {c}} mathbf {J} ^ {extsf {LH}} + {frac {1} {c}} {frac {qisman mathbf {E} ^ {extsf {LH}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0fbf356a7b5e01019abc8b072e83627a1bded37d) | ![{displaystyle abla imes mathbf {B} ^ {extsf {G}} = {frac {4pi} {c}} mathbf {J} ^ {extsf {G}} + {frac {1} {c}} {frac {qisman mathbf {E} ^ {extsf {G}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/894b3a12cdc3f88054c50c9e048cd57577fd7735) |
Boshqa asosiy qonunlar
Ism | SI miqdori | Lorents-Heaviside miqdorlari | Gauss miqdori |
---|
Lorents kuchi | ![{displaystyle mathbf {F} = qleft (mathbf {E} ^ {extsf {SI}} + mathbf {v} imes mathbf {B} ^ {extsf {SI}} ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f2d0802ff6dd2a33d695a43fce2981e8b9026aa) | ![{displaystyle mathbf {F} = qleft (mathbf {E} ^ {extsf {LH}} + {frac {1} {c}} mathbf {v} imes mathbf {B} ^ {extsf {LH}} ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a981e34ef6b060cc7fff3e9081e6977e1546d75) | ![{displaystyle mathbf {F} = qleft (mathbf {E} ^ {extsf {G}} + {frac {1} {c}} mathbf {v} imes mathbf {B} ^ {extsf {G}} ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0ad92a15e363b61587abf3490c5e3296cb141a9) |
Kulon qonuni |
| ![{displaystyle mathbf {F} = {frac {1} {4pi}} {frac {q_ {1} ^ {extsf {LH}} q_ {2} ^ {extsf {LH}}} {r ^ {2}}} mathbf {hat {r}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9c64a9060e9b438a0d8da128dce9d46a2a1dc10) | ![{displaystyle mathbf {F} = {frac {q_ {1} ^ {extsf {G}} q_ {2} ^ {extsf {G}}} {r ^ {2}}} mathbf {hat {r}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b268f70a9479a4286bb0b997ba8b4227dfc46587) |
Ning elektr maydoni statsionar nuqtali zaryad | ![{displaystyle mathbf {E} ^ {extsf {SI}} = {frac {1} {4pi epsilon _ {0}}} {frac {q ^ {extsf {SI}}} {r ^ {2}}} mathbf { shapka {r}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fcef214b0e10e2cc49cdfccbc76e45121b1b4357) | ![{displaystyle mathbf {E} ^ {extsf {LH}} = {frac {1} {4pi}} {frac {q ^ {extsf {LH}}} {r ^ {2}}} mathbf {hat {r}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a284ae54f76c8924198d446c18b3c62898378ff) | ![{displaystyle mathbf {E} ^ {extsf {G}} = {frac {q ^ {extsf {G}}} {r ^ {2}}} mathbf {hat {r}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2cdc6ac038096a5e6272b7c6fb497121beff9ea3) |
Bio-Savart qonuni | ![{displaystyle mathbf {B} ^ {extsf {SI}} = {frac {mu _ {0}} {4pi}} oint {frac {I ^ {extsf {SI}} dmathbf {l} imes mathbf {hat {r} }} {r ^ {2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/59a85afc7494ee6de62d059a8bc0aa3f374b0602) | ![{displaystyle mathbf {B} ^ {extsf {LH}} = {frac {1} {4pi c}} malham {frac {I ^ {extsf {LH}} dmathbf {l} imes mathbf {hat {r}}} { r ^ {2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77e23db5698b6689f26e22c094a643253734c48b) | ![{displaystyle mathbf {B} ^ {extsf {G}} = {frac {1} {c}} malham {frac {I ^ {extsf {G}} dmathbf {l} imes mathbf {hat {r}}} {r ^ {2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/486e76c565ab09f94c860727876cdf3151c33702) |
Dielektrik va magnit materiallar
Quyida dielektrik muhitdagi turli sohalar uchun ifodalar mavjud. Bu erda oddiylik uchun muhit bir hil, chiziqli, izotrop va noan'anaviy bo'lishi kerak, shuning uchun o'tkazuvchanlik oddiy doimiy.
SI miqdori | Lorents-Heaviside miqdorlari | Gauss miqdori |
---|
![{displaystyle mathbf {D} ^ {extsf {SI}} = epsilon _ {0} mathbf {E} ^ {extsf {SI}} + mathbf {P} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f533fedf6ab75094c7885443423363085f80ffd) | ![{displaystyle mathbf {D} ^ {extsf {LH}} = mathbf {E} ^ {extsf {LH}} + mathbf {P} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/980345023713e80b25f20e9e85186d3cbd674a3f) | ![{displaystyle mathbf {D} ^ {extsf {G}} = mathbf {E} ^ {extsf {G}} + 4pi mathbf {P} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1725589f46d1cd684007c0f7c77fa79aad76dcaf) |
![{displaystyle mathbf {P} ^ {extsf {SI}} = chi _ {ext {e}} ^ {extsf {SI}} epsilon _ {0} mathbf {E} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4e9dc976911e2db57cf10e080a3c32938bcde92) | ![{displaystyle mathbf {P} ^ {extsf {LH}} = chi _ {ext {e}} ^ {extsf {LH}} mathbf {E} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/deb5f8d95e92b10a949c6c0f44078c7573411197) | ![{displaystyle mathbf {P} ^ {extsf {G}} = chi _ {ext {e}} ^ {extsf {G}} mathbf {E} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13965d25c91efeb9818b72ea3b01c0bffc2cad71) |
![{displaystyle mathbf {D} ^ {extsf {SI}} = epsilon mathbf {E} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d1cfff0d77529d46ac43e9d95a20b3f75aeca57) | ![{displaystyle mathbf {D} ^ {extsf {LH}} = epsilon mathbf {E} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7649e5cf951595dccc162ff9f695d42044107704) | ![{displaystyle mathbf {D} ^ {extsf {G}} = epsilon mathbf {E} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/986682b9413e079279d84aadfbe0000171abb018) |
![{displaystyle epsilon ^ {extsf {SI}} / epsilon _ {0} = 1 + chi _ {ext {e}} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/acefb183ed451cde20afd107be4c27e5ce07c359) | ![{displaystyle epsilon ^ {extsf {LH}} = 1 + chi _ {ext {e}} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76f1c67a1cd6d5866720ac626a696990d4ccd8e5) | ![{displaystyle epsilon ^ {extsf {G}} = 1 + 4pi chi _ {ext {e}} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a9b2982d40dd81b0022b35d82442a851cc8e486d) |
qayerda
Miqdorlar
,
va
o'lchovsiz va ularning soni bir xil qiymatga ega. Aksincha, elektr sezuvchanligi
barcha tizimlarda o'lchovsiz, ammo mavjud turli xil raqamli qiymatlar xuddi shu material uchun:
![{displaystyle chi _ {ext {e}} ^ {extsf {SI}} = chi _ {ext {e}} ^ {extsf {LH}} = 4pi chi _ {ext {e}} ^ {extsf {G}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9bfb1e6627a0149f547f8fcb6bf088c8539d8dfa)
Keyinchalik, bu erda magnit muhitdagi turli xil maydonlarning ifodalari mavjud. Shunga qaramay, muhit bir hil, chiziqli, izotropik va noan'anaviydir, shuning uchun o'tkazuvchanlik skalar doimiysi sifatida ifodalanishi mumkin.
SI miqdori | Lorents-Heaviside miqdorlari | Gauss miqdori |
---|
![{displaystyle mathbf {B} ^ {extsf {SI}} = mu _ {0} (mathbf {H} ^ {extsf {SI}} + mathbf {M} ^ {extsf {SI}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9df3dd64cf7d54d606915253c013959778802975) | ![{displaystyle mathbf {B} ^ {extsf {LH}} = mathbf {H} ^ {extsf {LH}} + mathbf {M} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ab843e6be36f72c1ece2525d0dd9bc17324e7ba) | ![{displaystyle mathbf {B} ^ {extsf {G}} = mathbf {H} ^ {extsf {G}} + 4pi mathbf {M} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4649924147965e6e832c7ac10f174e12cf0f5b92) |
![{displaystyle mathbf {M} ^ {extsf {SI}} = chi _ {ext {m}} ^ {extsf {SI}} mathbf {H} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/da339e9942aeebd3236cb4475289b336b63753aa) | ![{displaystyle mathbf {M} ^ {extsf {LH}} = chi _ {ext {m}} ^ {extsf {LH}} mathbf {H} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ecc9c8a2751801b335fa60dd273ce116d3d4aa3) | ![{displaystyle mathbf {M} ^ {extsf {G}} = chi _ {ext {m}} ^ {extsf {G}} mathbf {H} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a01e1f03f3863f233691698c7ccf54988450a1bd) |
![{displaystyle mathbf {B} ^ {extsf {SI}} = mu ^ {extsf {SI}} mathbf {H} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c17f2b343d442a18806d191f6974c9443132daa3) | ![{displaystyle mathbf {B} ^ {extsf {LH}} = mu ^ {extsf {LH}} mathbf {H} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f575f0ab6813c1c4c231c633f5ccb9766869548) | ![{displaystyle mathbf {B} ^ {extsf {G}} = mu ^ {extsf {G}} mathbf {H} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f44bc67e4f6c21c66cc0287f3b54b22f16574fd4) |
![{displaystyle mu ^ {extsf {SI}} / mu _ {0} = 1 + chi _ {ext {m}} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91ed4d331e6e93e2d272784351d0da034f667685) | ![{displaystyle mu ^ {extsf {LH}} = 1 + chi _ {ext {m}} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/428f41c114835d33245a9336c08bfbc09b6e3b91) | ![{displaystyle mu ^ {extsf {G}} = 1 + 4pi chi _ {ext {m}} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/631b80eedb753d9b8588d0151f08aeac7e989dfb) |
qayerda
Miqdorlar
,
va
o'lchovsiz va ularning soni bir xil qiymatga ega. Aksincha, magnit sezuvchanlik
barcha tizimlarda o'lchovsiz, ammo mavjud turli xil raqamli qiymatlar xuddi shu material uchun:
![{displaystyle chi _ {ext {m}} ^ {extsf {SI}} = chi _ {ext {m}} ^ {extsf {LH}} = 4pi chi _ {ext {m}} ^ {extsf {G}} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/88fda5b76a8a8527f4e3ab7cc75137c44b2b6fd2)
Vektorli va skalyar potentsiallar
Elektr va magnit maydonlarni vektor potentsiali bo'yicha yozish mumkin A va skalar potentsiali
:
Ism | SI miqdori | Lorents-Heaviside miqdorlari | Gauss miqdori |
---|
Elektr maydoni (statik) | ![{displaystyle mathbf {E} ^ {extsf {SI}} = - abla phi ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5eb9314af919782fdfd641eeedcacfc5a933c7a) | ![{displaystyle mathbf {E} ^ {extsf {LH}} = - abla phi ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5260ebe1c9cf2ad3b596663b5b0fc73604017908) | ![{displaystyle mathbf {E} ^ {extsf {G}} = - abla phi ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf98b8a82f83a396f44e0e1cb2fccd49334632e) |
Elektr maydoni (umumiy) | ![{displaystyle mathbf {E} ^ {extsf {SI}} = - abla phi ^ {extsf {SI}} - {frac {qisman mathbf {A} ^ {extsf {SI}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c178b3c0c01fff7b25cac700308a1a83142a3d5d) | ![{displaystyle mathbf {E} ^ {extsf {LH}} = - abla phi ^ {extsf {LH}} - {frac {1} {c}} {frac {qisman mathbf {A} ^ {extsf {LH}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/465f44a8eee9f59008a3af418930bcc98347ce0b) | ![{displaystyle mathbf {E} ^ {extsf {G}} = - abla phi ^ {extsf {G}} - {frac {1} {c}} {frac {qisman mathbf {A} ^ {extsf {G}}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b689a2da48e2f695a432986f57a90c5896ada3da) |
Magnit B maydon | ![{displaystyle mathbf {B} ^ {extsf {SI}} = abla imes mathbf {A} ^ {extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71de77db8b0789312f03aa918a6564c54a267363) | ![{displaystyle mathbf {B} ^ {extsf {LH}} = abla imes mathbf {A} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3827959a774a3177952d8bc827dbcb22d1cbbca6) | ![{displaystyle mathbf {B} ^ {extsf {G}} = abla imes mathbf {A} ^ {extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9870ac126f718bdc436a5644cf029e413ea2d190) |
Tizimlar orasidagi iboralar va formulalarni tarjima qilish
Har qanday ifodani yoki formulani SI, Lorents-Heaviside yoki Gauss tizimlari o'rtasida aylantirish uchun quyidagi jadvalda keltirilgan mos keladigan miqdorlarni to'g'ridan-to'g'ri tenglashtirish va shu bilan almashtirish mumkin. Bu Maksvell tenglamalari kabi yuqoridagi ro'yxatda keltirilgan har qanday aniq formulalarni ko'paytiradi.
Masalan, tenglamadan boshlang
![{displaystyle abla cdot mathbf {E} ^ {extsf {SI}} = ho ^ {extsf {SI}} / epsilon _ {0},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d46127742dc649d173133ae467dc486d99bb9be)
va jadvaldagi tenglamalar
![{displaystyle {sqrt {epsilon _ {0}}} mathbf {E} ^ {extsf {SI}} = mathbf {E} ^ {extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a19ce4255e776c7dfb3a96e36513a584e5b76373)
![{displaystyle {frac {1} {sqrt {epsilon _ {0}}}} ho ^ {extsf {SI}} = ho ^ {extsf {LH}},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/01cc3d45079b3923e98dc694885720c2d88fb8f3)
omilni so'nggi identifikatorlar bo'ylab harakatga keltiradi va o'rnini bosadi, natijada
![{displaystyle abla cdot left({frac {1}{sqrt {epsilon _{0}}}}mathbf {E} ^{ extsf {LH}}ight)=left({sqrt {epsilon _{0}}}ho ^{ extsf {LH}}ight)/epsilon _{0},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/35710a14c2054254f77d28371ed94cc761c08cad)
keyin soddalashtiradi
![{displaystyle abla cdot mathbf {E} ^{ extsf {LH}}=ho ^{ extsf {LH}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/830897a7ef6536c676a391ee1e54746b4f59364e)
Ism | SI birliklari | Lorents-Heaviside birliklari | Gauss birliklari |
---|
elektr maydoni, elektr potentsiali | ![{displaystyle {sqrt {epsilon _{0}}}left(mathbf {E} ^{ extsf {SI}},varphi ^{ extsf {SI}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/19dd408d2e008737b396beb9b297400e4964ce40) | ![{displaystyle left(mathbf {E} ^{ extsf {LH}},varphi ^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bdef527d09fee7bf8ab55b61503188eb8c746be) | ![{displaystyle {frac {1}{sqrt {4pi }}}left(mathbf {E} ^{ extsf {G}},varphi ^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6a86dadc908917d7847004649634620840e1bf7) |
elektr siljish maydoni | ![{displaystyle {frac {1}{sqrt {epsilon _{0}}}}mathbf {D} ^{ extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc28997495e9f7246d7a08c0b08548fcf28483aa) | ![{displaystyle mathbf {D} ^{ extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4bb7786542f3c7e3c79a1cce0073e8eeba740661) | ![{displaystyle {frac {1}{sqrt {4pi }}}mathbf {D} ^{ extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1268ddd012fcc69d2cb95bf3bfadc3958fabfd0) |
elektr zaryadi, elektr zaryadining zichligi, elektr toki, elektr tokining zichligi, qutblanish zichligi, elektr dipol momenti | ![{displaystyle {frac {1}{sqrt {epsilon _{0}}}}left(q^{ extsf {SI}},ho ^{ extsf {SI}},I^{ extsf {SI}},mathbf {J} ^{ extsf {SI}},mathbf {P} ^{ extsf {SI}},mathbf {p} ^{ extsf {SI}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae64b9e897584b7c8bae11815351f00df016f131) | ![{displaystyle left(q^{ extsf {LH}},ho ^{ extsf {LH}},I^{ extsf {LH}},mathbf {J} ^{ extsf {LH}},mathbf {P} ^{ extsf {LH}},mathbf {p} ^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6279da69f17271dc1d23ddf27e568bf8591d683d) | ![{displaystyle {sqrt {4pi }}left(q^{ extsf {G}},ho ^{ extsf {G}},I^{ extsf {G}},mathbf {J} ^{ extsf {G}},mathbf {P} ^{ extsf {G}},mathbf {p} ^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4309fb905c36ca27cd68222dafaecff04a0dd9e8) |
magnit B maydon, magnit oqimi, magnit vektor potentsiali | ![{displaystyle {frac {1}{sqrt {mu _{0}}}}left(mathbf {B} ^{ extsf {SI}},Phi _{ ext{m}}^{ extsf {SI}},mathbf {A} ^{ extsf {SI}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a2cdcae50651b5fab1f7ff0f3c37be495e30953) | ![{displaystyle left(mathbf {B} ^{ extsf {LH}},Phi _{ ext{m}}^{ extsf {LH}},mathbf {A} ^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d04cd0d0b8f0150d4127e067b360acb239a2fa36) | ![{displaystyle {frac {1}{sqrt {4pi }}}left(mathbf {B} ^{ extsf {G}},Phi _{ ext{m}}^{ extsf {G}},mathbf {A} ^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56671ce73f8e295240693e43f9281188f77c6907) |
magnit H maydon | ![{displaystyle {sqrt {mu _{0}}} mathbf {H} ^{ extsf {SI}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/314dd0183f7ffd1eedb83d664bfb4eeb92cd2c77) | ![{displaystyle mathbf {H} ^{ extsf {LH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6627e723c79b35a4c90f362d514a8712f0a2efb7) | ![{displaystyle {frac {1}{sqrt {4pi }}}mathbf {H} ^{ extsf {G}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77fea6db84d277f73ce4853dd511619882dff3bd) |
magnit moment, magnitlanish | ![{displaystyle {sqrt {mu _{0}}}left(mathbf {m} ^{ extsf {SI}},mathbf {M} ^{ extsf {SI}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e241ea4a32492586fc98acebc30006545fa37faa) | ![{displaystyle left(mathbf {m} ^{ extsf {LH}},mathbf {M} ^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8591966f0e3f66a60544f93cc9857f64da45392) | ![{displaystyle {sqrt {4pi }}left(mathbf {m} ^{ extsf {G}},mathbf {M} ^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e74b27ed6e34ccde5e143cff0d98846e79a8329) |
nisbiy o'tkazuvchanlik, nisbiy o'tkazuvchanlik | ![{displaystyle left({frac {epsilon ^{ extsf {SI}}}{epsilon _{0}}},{frac {mu ^{ extsf {SI}}}{mu _{0}}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4b65b56b21e7d81440744ee6f68681dbdaa04998) | ![{displaystyle left(epsilon ^{ extsf {LH}},mu ^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e93759015d1fa214941b96d5acde076d5f12a436) | ![{displaystyle left(epsilon ^{ extsf {G}},mu ^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f345367b6c9178c7e9c8d467208a76b65ca2abf8) |
elektr sezuvchanligi, magnit sezuvchanlik | ![{displaystyle left(chi _{ ext{e}}^{ extsf {SI}},chi _{ ext{m}}^{ extsf {SI}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac28b370156bab2bd2c582eb8d8cfc76452dae17) | ![{displaystyle left(chi _{ ext{e}}^{ extsf {LH}},chi _{ ext{m}}^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a69eb9c3de18fc59b2bd5d89c64825a2215b051) | ![{displaystyle 4pi left(chi _{ ext{e}}^{ extsf {G}},chi _{ ext{m}}^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d15d70a8dd0b5e3c7c2a9d9fc097a38b620d48b) |
o'tkazuvchanlik, o'tkazuvchanlik, sig'im | ![{displaystyle {frac {1}{epsilon _{0}}}left(sigma ^{ extsf {SI}},S^{ extsf {SI}},C^{ extsf {SI}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/472d093db7c0ce51ecf9858b7c2444232719f92f) | ![{displaystyle left(sigma ^{ extsf {LH}},S^{ extsf {LH}},C^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e34278f13dbbc90ceb646bc6f9aa4a3bf689dab1) | ![{displaystyle 4pi left(sigma ^{ extsf {G}},S^{ extsf {G}},C^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a91c3b99c0fa134bb0db8f00d783812dfcfe535b) |
qarshilik, qarshilik, induktivlik | ![{displaystyle epsilon _{0}left(ho ^{ extsf {SI}},R^{ extsf {SI}},L^{ extsf {SI}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1841c2e005b41c8e80db928103044112981675a) | ![{displaystyle left(ho ^{ extsf {LH}},R^{ extsf {LH}},L^{ extsf {LH}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e27ea86aaa4902cefc27259c75cc300283765005) | ![{displaystyle {frac {1}{4pi }}left(ho ^{ extsf {G}},R^{ extsf {G}},L^{ extsf {G}}ight)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79ec1b4dd9e0304c094624a44890d14cdb5ad4c9) |
CGSni tabiiy birliklar bilan almashtirish
Oddiy SI darslik tenglamalarini va to'plamlarini qabul qilganda ε0 = µ0 = v = 1 olish uchun; olmoq tabiiy birliklar, hosil bo'lgan tenglamalar Heaviside-Lorentz formulasi va o'lchamlariga amal qiladi. Konversiya faktorga o'zgartirish kiritishni talab qilmaydi 4π, Gauss tenglamalaridan farqli o'laroq. SIda Kulonning teskari kvadrat qonun tenglamasi F = q1q2/4πε0r2. O'rnatish ε0 = 1 HLU shaklini olish uchun: F = q1q2/4.r2. Gauss shakli mavjud emas 4π maxrajda.
Sozlash orqali v = 1 HLU bilan Maksvell tenglamalari va Lorents tenglamalari SI misoli bilan bir xil bo'ladi ε0 = µ0 = v = 1.
![abla cdot mathbf {E} =ho ,](https://wikimedia.org/api/rest_v1/media/math/render/svg/c255e6042325b636698176c23e4af37082109535)
![abla cdot mathbf {B} =0,](https://wikimedia.org/api/rest_v1/media/math/render/svg/81396a5142e5c5db064c5c5536e2c0ce916991cf)
![abla imes mathbf {E} =-{frac {partial mathbf {B} }{partial t}},](https://wikimedia.org/api/rest_v1/media/math/render/svg/ad0dd018601f4cb9692d453703d4749cd526d512)
![abla imes mathbf {B} ={frac {partial mathbf {E} }{partial t}}+mathbf {J} ,](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a9e708232789d5733157fbf90a05699b5578431)
![{displaystyle mathbf {F} =q(mathbf {E} +mathbf {v} imes mathbf {B} ),}](https://wikimedia.org/api/rest_v1/media/math/render/svg/194391f2030437b46c31d4e52663b3c981619798)
Ushbu tenglamalar SI ishi bilan osonlikcha bog'liq bo'lishi mumkinligi sababli, ratsionalizatsiya qilingan tizimlar zamonaviylashmoqda.
Kvant mexanikasida
Qo'shimcha sozlash ε0 = µ0 = v = ħ = kB = 1 massa, vaqt, energiya, uzunlik va boshqalar uchun qiymat sifatida tanlanishi mumkin bo'lgan bitta o'lchov qiymati bilan parametrlangan tabiiy birlik tizimini hosil qiladi. Masalan, massani tanlash m, boshqalari ushbu doimiylar bilan ko'paytirilib aniqlanadi: orqali uzunlik shkalasi l = ħ / mcva vaqt shkalasi t = ħ / mc2, va boshqalar.
Lorents-Heaviside Planck birliklari
O'rnatish
Lorents-Heaviside hosilini beradi Plank birliklari, yoki ratsionalizatsiya qilingan Plank birliklari. Ommaviy shkala shunday tanlanganki tortishish doimiysi bu
, ga teng Kulon doimiysi. (Qarama-qarshilik bilan, Gauss Plank birliklari o'rnatildi
.)
Lorents-Xevisayddagi fizikaning asosiy tenglamalari Plank birliklari (ratsionalizatsiya qilingan Plank birliklari) | SI shakli | O'lchovsiz shakl |
---|
Massa-energiya ekvivalenti yilda maxsus nisbiylik | ![{E=mc^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a11f6367922a2aec036114de24eaebe50af525cd) | ![{E=m}](https://wikimedia.org/api/rest_v1/media/math/render/svg/caa715510d94516f683f0de37467e5d28277f04f) |
Energiya va momentum munosabati | ![{displaystyle E^{2}=m^{2}c^{4}+p^{2}c^{2};}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a97c3e3a826a6f1dad2bea41da4717b4f0f4ee61) | ![{displaystyle E^{2}=m^{2}+p^{2};}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61d369370fd69851db3bbd8671cf384e50222149) |
Ideal gaz qonuni | ![{displaystyle PV=nRT=Nk_{ ext{B}}T}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5f52f71f8778223065e7fa7e444051e49c316b0) | ![{displaystyle PV=NT}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f8183cef199057206a39ee99a6cb7d8f05f7d70) |
Issiqlik energiyasi zarrachaga per erkinlik darajasi | ![{E={ frac {1}{2}}k_{ ext{B}}T}](https://wikimedia.org/api/rest_v1/media/math/render/svg/124fc0dd81d576d7dbfd09f917ca1d9058a0625d) | ![{E={ frac {1}{2}}T}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7cc095b41195ad825ff5c619ab66f36051e21bb) |
Boltsmannikiga tegishli entropiya formula | ![{S=k_{ ext{B}}ln Omega }](https://wikimedia.org/api/rest_v1/media/math/render/svg/94d69a23adc2e6d8c1719317514ec853780c8852) | ![{S=ln Omega }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7fafc4184734fc665758d7cdd646d144774dbc9b) |
Plank-Eynshteyn munosabatlari uchun burchak chastotasi | ![{E=hbar omega }](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8b3ea50735995ccad5a5a4396ec14c2d6bc284) | ![{E=omega }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9645811f960ccdd6c2616ef43745a698e024449c) |
Plank qonuni uchun qora tan da harorat T | ![I(omega ,T)={frac {hbar omega ^{3}}{4pi ^{3}c^{2}}}~{frac {1}{e^{frac {hbar omega }{k_{ ext{B}}T}}-1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0a14c20397d684cfc2957996581bdb7c00f25b6) | ![I(omega ,T)={frac {omega ^{3}}{4pi ^{3}}}~{frac {1}{e^{omega /T}-1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0c8373f8425e59d0704d0a451ef114b1aa6e412) |
Stefan-Boltsman doimiysi σ belgilangan | ![{displaystyle sigma ={frac {pi ^{2}k_{ ext{B}}^{4}}{60hbar ^{3}c^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eeaa4b08bc677d45862835cd45e82a3da7e6d9e7) | ![{displaystyle sigma ={frac {pi ^{2}}{60}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e003b89fed91d89f3f0e5aac3a5f33f6c8dce944) |
Shredinger tenglamasi | ![{displaystyle -{frac {hbar ^{2}}{2m}}abla ^{2}psi (mathbf {r} ,t)+V(mathbf {r} ,t)psi (mathbf {r} ,t)=ihbar {frac {partial psi (mathbf {r} ,t)}{partial t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9890432edd743362a44e980619d07fe2ad7abca0) | ![{displaystyle -{frac {1}{2m}}abla ^{2}psi (mathbf {r} ,t)+V(mathbf {r} ,t)psi (mathbf {r} ,t)=i{frac {partial psi (mathbf {r} ,t)}{partial t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e346e4f624805c946b3c7a8a591ce0eb45349428) |
Hamiltoniyalik shakli Shredinger tenglamasi | ![{displaystyle Hleft|psi _{t}ightangle =ihbar {frac {partial }{partial t}}left|psi _{t}ightangle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/79478af7e42d28c8d818cc23b8c36b150b67f642) | ![{displaystyle Hleft|psi _{t}ightangle =i{frac {partial }{partial t}}left|psi _{t}ightangle }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f5780e761db09b6ef323f877cc4dd3818b5eee2) |
Ning kovariant shakli Dirak tenglamasi | ![(ihbar gamma ^{mu }partial _{mu }-mc)psi =0](https://wikimedia.org/api/rest_v1/media/math/render/svg/b42be7781f0589908144c218fb1d913a84f0cf51) | ![(igamma ^{mu }partial _{mu }-m)psi =0](https://wikimedia.org/api/rest_v1/media/math/render/svg/bea78573eed462f413d61d972ab1e7f571c3a4ea) |
Unruh harorati | ![{displaystyle T={frac {hbar a}{2pi ck_{B}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a92bcabbce234dd311a692d4cd0cd2c524f5130c) | ![{displaystyle T={frac {a}{2pi }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae945baa917c9b784f6dd5e8e1445246fd299d17) |
Kulon qonuni | ![F={frac {1}{4pi epsilon _{0}}}{frac {q_{1}q_{2}}{r^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8d3a31baacfd989711342eeea94906a1f6d85a15) | ![{displaystyle F={frac {q_{1}q_{2}}{4pi r^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69334812e7eb4fd5589a6924341d78adc7f83cee) |
Maksvell tenglamalari | ![abla cdot mathbf {E} ={frac {1}{epsilon _{0}}}ho](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c3f28af564c085c84e3f134ad9d4eafcc5829d3) ![abla cdot mathbf {B} =0](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c9f988389c33cdf773f3f188e166031f91adedb)
![abla imes mathbf {E} =-{frac {partial mathbf {B} }{partial t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2eb118e22c941e34f5537dbbdcaa3d7ba23603e0)
![abla imes mathbf {B} ={frac {1}{c^{2}}}left({frac {1}{epsilon _{0}}}mathbf {J} +{frac {partial mathbf {E} }{partial t}}ight)](https://wikimedia.org/api/rest_v1/media/math/render/svg/2488e501044dbd47fc06e18572da0fbe13d7b1c2)
| ![{displaystyle abla cdot mathbf {E} =ho }](https://wikimedia.org/api/rest_v1/media/math/render/svg/d39f2b2476e711fc4ce3d0a993b83ce2a3abafd4) ![abla cdot mathbf {B} =0](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c9f988389c33cdf773f3f188e166031f91adedb)
![abla imes mathbf {E} =-{frac {partial mathbf {B} }{partial t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2eb118e22c941e34f5537dbbdcaa3d7ba23603e0)
![{displaystyle abla imes mathbf {B} = mathbf {J} + {frac {qisman mathbf {E}} {qisman t}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/acffcee088129b817ac7ca4656c37377c24a0349)
|
Bio-Savart qonuni | ![{displaystyle Delta B = {frac {mu _ {0} I} {4pi}} {frac {Delta L} {r ^ {2}}} sin heta}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0db0fd7ac7f9befdeb776ba69367636d828ea3e3) | ![{displaystyle Delta B = {frac {I} {4pi}} {frac {Delta L} {r ^ {2}}} sin heta}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a757b1fec65af2ea12db491e0b5091e0f3584e5) |
Bio-Savart qonuni | ![{displaystyle mathbf {B} (mathbf {r}) = {frac {mu _ {0}} {4pi}} int _ {C} {frac {I, d {oldsymbol {ell}} imes mathbf {r '}} {| mathbf {r '} | ^ {3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fbce8f9853a30893fa96653a3dab0b062d7b80fa) | ![{displaystyle mathbf {B} (mathbf {r}) = {frac {1} {4pi}} int _ {C} {frac {I, d {oldsymbol {ell}} imes mathbf {r '}} {| mathbf { r '} | ^ {3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87e2434db35a3ca913c8fd578c4b3c334e46120f) |
Elektr maydonining intensivligi va elektr induksiyasi | ![{displaystyle mathbf {D} = epsilon _ {0} mathbf {E}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f4dc398ca7e3209a6f2aa1aea2b74714702f7ef) | ![{displaystyle mathbf {D} = mathbf {E}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3bfae927f34c7f29623b1a85ea496fd73bb0ef96) |
Magnit maydon intensivligi va magnit induksiya | ![{displaystyle mathbf {B} = mu _ {0} mathbf {H}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d2fd45a5e63db4904cb79193388449e8cb2ccf8) | ![{displaystyle mathbf {B} = mathbf {H}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8881e09bd8dd67ecb207e030d709e092530344b2) |
Nyutonning butun olam tortishish qonuni | ![{displaystyle F = -G {frac {m_ {1} m_ {2}} {r ^ {2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5fe9cd3ed42e32a6332ada6255b9e22d965911b5) | ![{displaystyle F = - {frac {m_ {1} m_ {2}} {4pi r ^ {2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fa45e8fd305c09e67e9819b6035443923a29d6cf) |
Eynshteyn maydon tenglamalari yilda umumiy nisbiylik | ![{G_ {mu u} = 8pi {G ustidan c ^ {4}} T_ {mu u}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75e68495e6578b952a38e53455298f8e0bcc7433) | ![{displaystyle {G_ {mu u} = 2T_ {mu u}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81b791c77a8d1aca4a32974faf1ff8dfaf3f4e5d) |
Shvartschild radiusi | ![{displaystyle r_ {s} = {frac {2GM} {c ^ {2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d03b01348b751e6f4eaff085b3effa9542e2935d) | ![{displaystyle r_ {s} = {frac {M} {2pi}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6895de5d5e52542c416f87f7915cbb2b384ba5a1) |
Xoking harorati qora tuynuk | ![{displaystyle T_ {H} = {frac {hbar c ^ {3}} {8pi GMk_ {B}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b7e3964e928b1dbb9c80b2a370f088078c5531f) | ![{displaystyle T_ {H} = {frac {1} {2M}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1267211c65797194cce2f8d5f32576f7364cfdad) |
Bekenshteyn –Xoking qora tuynuk entropiyasi[4] | ![S_ {ext {BH}} = {frac {A_ {ext {BH}} k_ {ext {B}} c ^ {3}} {4Ghbar}} = {frac {4pi Gk_ {ext {B}} m_ {ext {BH}} ^ {2}} {hbar c}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0d01615f1c3ee57cc39fe201b10d5a635d62b5) | ![{displaystyle S_ {ext {BH}} = pi A_ {ext {BH}} = m_ {ext {BH}} ^ {2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee98584aae64d084255645e0c9efe8b7efcd7a9b) |
Izohlar
Adabiyotlar
Tashqi havolalar
|
---|
Joriy | |
---|
Fon | |
---|
Tarixiy | Metrik | |
---|
Evropa | |
---|
Osiyo | |
---|
Afrika | |
---|
Shimoliy Amerika | |
---|
Janubiy Amerika | |
---|
|
---|
Qadimgi | |
---|
Maqolalar ro'yxati | |
---|
Boshqalar | |
---|