Muhimmanci Fasaha na Matar Daidaita
Muhimmin Maitarwa na Maitarwa
Idan an sanya abubuwa daidai da sauran shugaban magana, za su iya bayyana tashin adadin da dama. Don in fahimta dalilai masu yawan takamakawa, ya kamata a yi tasiri game da cewa maitarwa mai tarwa ita ce take tsara irin magana. Wannan fahimtar ta ita bari ne da gano maitarwar maitarwa mai tarwa.
Maitarwar maitarwa mai tarwa, wanda ake kira maitarwar maitarwa don zama lafiya, ita ce muhimmiyar siffofi a cikin electromagnetics. Ya ba wasu alatun da za su iya amfani da su don inganta da kuma kula hanyoyi da take tabbatar da kungiyar loop da shugaban magana mai tarwa. Maitarwar maitarwa wa kungiyar loop, wanda ya samu area A da kuma shugaban magana I, ya kirkiro da:
Ko kuma area ya kirkiro da vector, wanda ya bar da maitarwar maitarwa a zama vector quantity da kuma abubuwan da suka haɗa su suna da ƙarin hagu.
Hagu na maitarwar maitarwa shine perpendicular zuwa plane na kungiyar. Zan iya samun wannan hagu ta haka da amfani da rubutu na hagu na daki—Idan kake kuka rubutu na daki maka a nan kafin kuke kuna shugaban magana, thumb akan kake ya nuna hagu na maitarwar maitarwa. Wannan ta bayyana a Figure 1.
Maitarwar maitarwa na kungiyar shine da kuma shugaban magana da ke jin kungiyar da kuma area da ke samu. Ba zan iya haɗa da shape na kungiyar ba.
Torqu da Maitarwar Maitarwa
Nemi Figure 2, wanda ya bayyana kungiyar da shugaban magana a nan da aka sanya a shugaban magana mai tarwa.
A nan da aka bayyana:
I shine shugaban magana.
B shine vector na shugaban magana.
u shine maitarwar maitarwa.
θ shine angle bayan vector na maitarwar maitarwa da vector na shugaban magana.
Saboda forces da ke jin kungiyar a kofin kungiyar suna haɗa su, net force da ke jin kungiyar ya zama zero. Amma, kungiyar ya samu magnetic torque. Tsawon wannan torque da ke jin kungiyar shine:
Daga Equation 2, za a iya duba cewa torqu (t) shine da nasarar da maitarwar maitarwa. Saboda maitarwar maitarwa take yi aiki daidai da magnet; idan kake sanya a shugaban magana mai tarwa, zan iya samu torque. Wannan torque ya taka aiki daidai da kungiyar har zuwa stable equilibrium position.
Stable equilibrium ana samu a lokacin da shugaban magana ya zama perpendicular zuwa plane na kungiyar (i.e.,θ=0^o). Idan kungiyar ya zama kusa a kan wannan hagu, za a iya kammala kungiyar har zuwa equilibrium state. Torque ya zama zero kuma a lokacin da θ=180^o. Amma, a wannan lokaci, kungiyar ya zama a unstable equilibrium. Kusan kasa na kungiyar daga θ=180^o za a iya kammala kungiyar har zuwa θ=0^o.
Yadda Maitarwar Maitarwa Yana Da Muhimmiyar?
Abubuwa da dama suna iya amfani da interaction bayan kungiyar da shugaban magana. Misali, torqu da ke jin a motor electric shine daidai da interaction bayan shugaban magana na motoci da conductors da shugaban magana. A nan da wannan interaction ya faru, potential energy ya faru a lokacin da conductors ya kusa.
Ita ce interaction bayan maitarwar maitarwa da shugaban magana mai tarwa wanda ya faru potential energy a cikin system na maitarwa. Angle bayan abubuwan da suka haɗa su shine take faru amount of energy (U) da ke samu a cikin system, kamar yadda aka bayyana a nan:
A nan da aka bayyana stored energy values bayan configurations da dama:
Idan θ=0^o, system ya zama a stable equilibrium state, da kuma stored energy ya zama minimum, U=-uB.
Idan θ=90^o, stored energy ya zama U=0.
Idan θ=180^o, stored energy ya zama maximum value, U=uB. Wannan state ya zama unstable equilibrium position.
Fahimtar Net Maitarwar Maitarwa Ta Hanyar Model Atomic
Don in fahimta yadda abubuwa mai maitarwa suna faru shugaban magana, ya kamata a gano quantum mechanics. Amma, saboda wannan topic ya kasance a nan da aka rubuta, muna iya amfani da concept na maitarwar maitarwa da model atomic classical don in samu valuable insights game da yadda abubuwan da suka haɗa su suna haɗa da shugaban magana mai tarwa.
Wannan model ya bayyana electron a nan da yake orbiting nucleus na atom da kuma yake spinning around its own axis, kamar yadda aka bayyana a Figure 3.
Net Maitarwar Maitarwa na Electrons, Atoms, da Abubuwan
Orbital motion na electron zan iya haɗa da tiny current-carrying loop. Saboda haka, ya faru maitarwar maitarwa (denoted as (u1 )a nan). Duk da haka, spin na electron ya faru maitarwar maitarwa (u2). Net maitarwar maitarwa na electron shine vector sum bayan abubuwan da suka haɗa su.
Atom na net maitarwar maitarwa shine vector sum bayan maitarwar maitarwa bayan electrons. Protons na atom suna da maitarwar maitarwa, amma effect overall suna daɗe da electrons.
Net maitarwar maitarwa na abubuwan shine da kuma vector sum bayan maitarwar maitarwa bayan atoms.
Magnetization Vector
Magnetic properties na material shine da kuma maitarwar maitarwa bayan particles. Kamar yadda aka rubuta a nan, maitarwar maitarwa suna haɗa da tiny magnets. Idan material ya samu a shugaban magana mai tarwa, atomic maitarwar maitarwa a cikin material suna haɗa da applied field da kuma suka samu torque. Wannan torque ya taka aiki da kungiyar maitarwar maitarwa har zuwa ƙarin hagu.
Magnetic state na substance ya haɗa da abubuwan da suka haɗa su: number of atomic maitarwar maitarwa a cikin material da kuma degree of their alignment. Idan maitarwar maitarwa generated by microscopic current loops suna haɗa su random, za su iya haɗa su cancel each other out, da kuma samun negligible net magnetic field. Don in bayyana magnetic state na substance, muna iya adda magnetization vector. An kirkiro da wannan shine total maitarwar maitarwa per unit volume na substance:
indamar V shine volume na material.
Idan material ya samu a shugaban magana mai tarwa, maitarwar maitarwa suna haɗa su align, da kuma samun increase in the magnitude of the magnetization vector. Characteristics na magnetization vector suna haɗa su da classification na material as paramagnetic, ferromagnetic, or diamagnetic.
Paramagnetic and ferromagnetic materials shine da atoms with permanent maitarwar maitarwa. Duk da haka, atomic maitarwar maitarwa a cikin diamagnetic materials ba su permanent ba.
Finding the Total Magnetic Field: Permeability and Susceptibility
Idan muna sanya material a cikin shugaban magana. Total shugaban magana a cikin material shine da biyu sources:
Externally applied shugaban magana (B0).
Magnetization na material a response to external field (Bm).
Total shugaban magana a cikin material shine sum bayan biyu components:
B0 shine produced by a current-carrying conductor; Bm shine produced by the magnetic substance. It can be shown that Bm is proportional to the magnetization vector:
indamar μ0 shine constant called permeability of free space. Therefore, we have:
The magnetization vector is also related to external field by the following equation:
indamar Greek letter χ shine proportionality factor known as magnetic susceptibility. Value na χ depends on the type of material.
Combining the last two equations, we have:
Significance of the Equation and Relative Permeability
Wannan equation shine intuitive interpretation: it indicates that the total shugaban magana a cikin material shine equivalent to externally applied shugaban magana multiplied by the factor 1+x. Wannan factor, referred to as relative permeability, shine crucial parameter for characterizing how a material responds to a shugaban magana. The relative permeability is commonly denoted by ur.
Magnetic Susceptibility of Different Materials
Figure 4 depicts the magnetic behavior of three distinct types of materials when they are placed in a uniform magnetic field. The interior area of the material is represented by a yellow rectangle.
Magnetic Susceptibility of Different Materials
In Figure 4(a), the magnetic field lines inside the material are more widely spaced compared to those outside. This indicates that the total magnetic field inside a diamagnetic material is slightly weaker than the externally applied field. For diamagnetic materials, the magnetic susceptibility (X) is a small negative value. For instance, at 300 K, copper has a magnetic susceptibility of –9.8 × 10⁻⁶. As a result, the material partially repels the magnetic field from its interior.
Figure 4(b) demonstrates the response of a paramagnetic material. Here, the magnetic field lines inside the material are more closely packed than those of the external field. This implies that the total magnetic field inside the material is slightly stronger than the external field. For paramagnetic materials, X is a small positive value. For example, at 300 K, the magnetic susceptibility of lithium is 2.1 × 10⁻⁵.
Finally, in Figure 4(c), the ferromagnetic material distorts the magnetic field lines, causing them to pass through the material. The material becomes magnetized, significantly boosting the magnetic field inside. For ferromagnetic materials, X has a positive value ranging from 1,000 to 100,000. Due to their high magnetic susceptibility, these materials generate a magnetic field that is much stronger than the externally applied one.
It's important to note that for ferromagnetic materials, X is not a constant. Consequently, the magnetization (M) is not a linear function of the externally applied magnetic field (B0).
Wrapping Up
Magnetic materials are crucial in a wide variety of applications, including transformers, motors, and data storage devices. The magnetic state of a substance depends on the number of atomic magnetic moments in the material and how well they align in the presence of an external magnetic field. As briefly discussed, we can classify magnetic materials into three types based on these criteria: paramagnetic, diamagnetic, and ferromagnetic. We will explore these categories in more detail in a future article.
