Me kuke so ku bude sauki da take da rayuwa a matsayin mai sauƙi na musamman da take da rayuwa?

Shi'arri na faruwa (Electromagnetic Field) yana cikin muhimmanci ga shi'arri na tsakiyar zafi (Electric Field) da kuma shi'arri na faruwar magana (Magnetic Field), wadanda suka yi hankali a kan tushen Maxwell. Don samun shi'arri na faruwa zuwa shi'arri na tsakiyar zafi kawai da shi'arri na faruwar magana, muna bukata a fahimtar yadda wannan shi'arri suke haɗa da yake da kuma yadda ake iya samun shi masu inganci a kan al'amuran da suka fi dace.

1. Fafin Tsarin Muhimmancin Shi'arri na Faruwa

Shi'arri na faruwa yana cikin siffofin vector na hudu mita (four-dimensional) wadanda ana ke shi'arri na tsakiyar zafi da kuma shi'arri na faruwar magana. A cikin yanayin relativity, za a iya tabbatar da shi'arri na tsakiyar zafi da kuma shi'arri na faruwar magana su ne 'yan abubuwan tensor field. Amma a cikin yanayin ba sa relativity, muna iya tabbatar da shi'arri na biyu masu inganci.

2. Koyarar Shi'arri na Tsakiyar Zafi Da Shi'arri Na Faruwar Magana

Don koyarar shi'arri na tsakiyar zafi da shi'arri na faruwar magana a cikin shi'arri na faruwa, muna iya yi karatu a kan abubuwan masu nau'o'i:

Shi'arri Na Tsakiyar Zafi

Shi'arri na tsakiyar zafi E yana bazu saboda kungiyar tsakiyoyin zafi. Yana iya bayyana a kan:

Tushen da ya dace a nan darin Maxwell (Gauss's law):

∇⋅E=ρ/ϵ0

• ρ ita ce kungiyar tsakiyoyin zafi, da kuma ϵ0 ita ce permittivity of free space.

• Tushen da ya dace a nan noma darin Maxwell (Faraday's law of induction):

∇×E=−∂B/∂t

wannan yana nuna cewa rawa a kan shi'arri na tsakiyar zafi yana haɗa da rawa a kan lokacin shi'arri na faruwar magana.

Shi'arri Na Faruwar Magana

Shi'arri na faruwar magana B yana bazu saboda tsakiyoyin zafi masu ido ko kuma tsakiyoyin zafi. Bayanan ita ce:

Tushen da ya dace a nan labaran darin Maxwell:∇⋅B=0, wanda yana nuna cewa monopoles na faruwar magana babba ba su ne.

Tushen da ya dace a nan uku darin Maxwell

∇×B=μ0J+μ0ϵ0 ∂E/∂t

J ita ce kungiyar tsakiyoyin zafi, da kuma μ0 ita ce permeability of free space.

3. Karatu Masu Inganci Shi'arri Na Tsakiyar Zafi Da Shi'arri Na Faruwar Magana A Cikin Al'amuran Da Suka Fi Dace

A cikin al'amuran da suka fi dace, za a iya samun shi'arri na faruwa zuwa shi'arri na tsakiyar zafi kawai ko kuma shi'arri na faruwar magana kawai:

Shi'arri Na Tsakiyar Zafi Kawai

Idan ba a gama shi'arri na faruwar magana masu ido (i.e.,∂B/∂t =0), shi'arri na tsakiyar zafi yana bazu shi'arri na tsakiyar zafi kawai.

Misalai, a cikin electrostatics, shi'arri na tsakiyar zafi yana bazu saboda kungiyar tsakiyoyin zafi masu inganci.

Shi'arri Na Faruwar Magana Kawai

Idan ba a gama shi'arri na tsakiyar zafi masu ido (i.e.,∂E/∂t=0), shi'arri na faruwar magana yana bazu shi'arri na faruwar magana kawai.

Misalai, a cikin shi'arri na faruwar magana da tsakiyoyin zafi masu ido, shi'arri na faruwar magana yana bazu saboda tsakiyoyin zafi masu inganci.

4. Abubuwan Mai Rarraba

A cikin al'amuran da ake amfani, muna iya halarta tushen Maxwell don samun muhimmancin shi'arri na faruwa. Don shi'arri na tsakiyar zafi da shi'arri na faruwar magana masu inganci, muna iya rubuta abubuwan mai rarraba:

Abubuwan Mai Rarraba Ta Shi'arri Na Tsakiyar Zafi

Idan B yana bazu static, then∇×E=0, wanda yana nuna cewa shi'arri na tsakiyar zafi yana da shiga da kuma zai iya bayyana a kan potential V scalar: E=−∇V.

Abubuwan Mai Rarraba Ta Shi'arri Na Faruwar Magana (Abubuwan Mai Rarraba Ta Shi'arri Na Faruwar Magana)

Idan E yana bazu static, then∇×B=μ0 J, wanda yana nuna cewa shi'arri na faruwar magana zai iya hasashen ta a kan Ampère's circuital law.

Bayanai

Shi'arri na faruwa zai iya samun shi'arri na tsakiyar zafi da shi'arri na faruwar magana, kuma shi'arri na tsakiyar zafi da shi'arri na faruwar magana masu inganci su ne misalai a cikin al'amuran da suka fi dace. A cikin tushen Maxwell, muna iya karatu rayuwar shi'arri na faruwa da kuma samun shi zuwa shi'arri na tsakiyar zafi kawai ko kuma shi'arri na faruwar magana kawai idan yana da kyau. Wannan samun shi yana da muhimmanci a cikin fahimtar da kuma halartar masu al'amuran shi'arri na faruwa a cikin al'amuran da ake amfani.

Idan kana son tambaya ko kuma kana buƙata cikakken bayanai, kara min ni!