Me kana da zan iya ce a mafi girman magana a kan farkon mafi yawan ƙwarewa mai magana da mafi yawan kwarewa mai tsari? A nan ana iya cewa abin da ke magana da mafi yawan ƙwarewa na magana ne suka haɗa da mafi yawan kwarewa mai tsari a matsayin hanyoyin ƙwarewa. Amma a nan ana iya cewa abin da ke magana da mafi yawan kwarewa mai tsari ba suka haɗa da mafi yawan ƙwarewa na magana. Wannan yana nuna cewa mafi yawan ƙwarewa na magana tana da muhimmanci a kan hanyoyin ƙwarewa da kuma mafi yawan kwarewa mai tsari.

Karamin Musamman da Karamin Bura a Kananan Fashin Yawan Musamman da Karamin Bura

Karamin musamman da karamin bura suna cikin abubuwa mafi yawa a kananen fashi, kuma suna da muhimmanci a kananan fashin da suke samar da tattalin gwamnati. Tana da wannan bayanin mai sarrafa game da fashin da keke suke samar da:

1. Takaitaccen da Ta'azirin Gida

Karamin Musamman: Karamin musamman yana nufin karamin yawan musamman, ya kunfiya ko kai. Daga raka-raka na Coulomb, yawan musamman da aka fito da karamin musamman yake rage da darajar da duka (1/r2) kuma yana nuna radially outward (ko inward) daga (ko zuwa) karamin.

Karamin Bura: Karamin bura yana nufin karamin yawan bura, maimakon hakan, ba a tabbatar da karamin bura a tsakanin. An gudanar da duk fashin bura a kananan dippolin (zuba da karamin mai yawa da karamin mai bakwai). Idan karamin bura suna cikin al'adun, za su fito da yawan bura masu sahihiwa da wani babban karamin musamman, amma wannan ta hanyar tushen zai ce.

2. Tattalin Kwamfuta

Karamin Musamman

Tartibar Yawan Musamman: Yawan musamman E da aka fito da karamin musamman yana da sfera mai kyau kuma ta yi amfani da raka-raka na Coulomb:

idance $\mathrm{<br>}$q ita ce karamin, ϵ0 ita ce vacuum permittivity, $\mathrm{<br>}$r ita ce hanyar da dacewa da karamin zuwa wurin labari, da r^ ita ce radial unit vector.

• Tartibar Potential na Musamman: Potential na musamman V da aka fito da karamin musamman yake rage linearly da hanyar:

Karamin Bura (Hypothetical)

• Tartibar Yawan Bura: Idan karamin bura suna cikin al'adun, za su fito da yawan bura mai sfera mai kyau B, ta yi amfani da shaida da raka-raka na Coulomb:

  

• idance   $\mathrm{<span\; style="font-family:\; arial,\; helvetica,\; sans-serif;\; font-size:\; 16px;">g\; ita\; ce\; karamin\; bura, </span>\; }$μ0 ita ce vacuum permeability,   $\mathrm{<br>\; }$r ita ce hanyar da dacewa da karamin bura zuwa wurin labari, da r^ ita ce radial unit vector.

• Tartibar Potential na Bura: Potential na bura ϕm yana rage linearly da hanyar:

  

3. Muhimmin Tsarin Linyawar Yawan

• Linyawar Yawan Musamman: Linyawar yawan musamman da aka fito da karamin musamman suna nuna daga karamin mai yawa (ko zuwa karamin mai bakwai) kuma suna nuna zuwa tsakiyar jaha. Wannan linyawar suna nuna divergence, idan yawan musamman yana nuna radiates outward.

• Linyawar Yawan Bura: Linyawar yawan bura da aka fito da karamin bura suna nuna daga karamin bura (ko zuwa shi) kuma suna nuna zuwa tsakiyar jaha. Wannan linyawar suna nuna divergence, idan yawan bura yana nuna radiates outward.

4. Multipole Expansions Masu Yawan

• Electric Multipoles: Da karamin musamman, akwai electric dipoles, quadrupoles, etc. Electric dipole yana nufin karamin da suka bi da yawan musamman, kuma tartibar yawan da aka fito da shi yana da muhimmanci da symmetry da decay characteristics masu yawan.

• Magnetic Multipoles: Fashin bura a halayen yana nuna magnetic dipoles, misali bar magnets ko current loops. Tartibar yawan da aka fito da magnetic dipole yana da muhimmanci da electric dipole, amma a halayen, ana iya magana ne magnetic dipoles ba da multipole masu yawan.

5. Yawan Maxwell's Equations

• Karamin Musamman: A cikin Maxwell's equations, charge density ρ yana nuna a Gauss's law for electricity:

• Wannan yana nuna cewa presence of an electric monopole yana nuna divergence a yawan musamman.

• Karamin Bura: A cikin Maxwell's equations, ba a nuna magnetic charge density ρm, saboda haka Gauss's law for magnetism yana nuna:

Wannan yana nuna cewa a cikin classical electromagnetism, ba a tabbatar da karamin bura. Amma idan karamin bura suna cikin al'adun, wannan equation yana nuna:

Wannan yana nuna cewa karamin bura suna cikin al'adun.

6. Quantum Effects

• Karamin Musamman: Karamin musamman suna cikin al'adun, kuma yawan da suke fito da suke nuna quantum electrodynamics (QED).

• Karamin Bura: Ba a tabbatar da karamin bura, amma suna nuna muhimmanci a cikin quantum mechanics. Misali, Dirac ya bayar cewa presence of magnetic monopoles yana nuna quantization of both electric and magnetic charges kuma yana nuna phase of the wave function of charged particles.

Summary

• Karamin Musamman: Ana tabbatar da su, suke fito da yawan musamman mai sfera mai kyau da rage da square of the distance.

• Karamin Bura: Hypothetical, theoretically should produce a similar spherically symmetric magnetic field that decays with the square of the distance.

Farkon mafi yawa yana nuna cewa karamin musamman suna cikin al'adun, amma karamin bura suna nuna hypothesis mai tsari.