Tambayoyi Misali Game da Ƙarfin Wutar Lantarki Mai Sakamako
Wutar lantarki wani nau'i ne na makamashi wanda yake da matuƙar muhimmanci ga rayuwarmu ta yau da kullum. Ɗaya daga cikin muhimman ra'ayoyi a fannin kimiyyar lantarki shine ƙarfin Coulomb, wanda ke bayyana hulɗar da ke tsakanin cajin lantarki. Fahimtar ƙarfin lantarki da ke haifar da hakan yana da matuƙar muhimmanci a aikace-aikace da yawa, tun daga fasahar lantarki zuwa fahimtar abubuwan da ke faruwa a sararin samaniya. Ga cikakken bayani game da misalan matsaloli da kuma yadda za a tantance ƙarfin lantarki da ke haifar da hakan.
Gabatarwa ga Manufar Coulomb Force
Kafin mu shiga cikin matsalar misali, bari mu sake duba dokar Coulomb. Dokar Coulomb ta bayyana cewa ƙarfin lantarki tsakanin cajin maki biyu yana daidai da samfurin girmansu kuma yana daidai da murabba'in nisan da ke tsakaninsu. A lissafi, ana iya bayyana ƙarfin Coulomb \( F \) kamar haka:
\[ F = k_e \frac{|q_1 q_2|}{r^2} \]
Ina:
– \( F \) shine girman ƙarfin lantarki.
– \( k_e \) shine madaidaicin Coulomb, \( k_e \approx 8,99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).
– \( q_1 \) da \( q_2 \) su ne girman cajin.
– \( r \) shine nisan da ke tsakanin caji.
Tambayoyi da Tattaunawa Samfura
Tambaya ta 1: Caji Biyu a Layi Madaidaiciya
Cajin maki biyu \( q_1 = 4 \mu C \) da \( q_2 = -3 \mu C \) suna nan a nisan 3 cm daga juna. Lissafa girma da alkiblar ƙarfin Coulomb tsakanin waɗannan cajin guda biyu.
Tattaunawa:
Mataki na farko shine a canza caji da nisa zuwa raka'o'in SI:
– \( q_1 = sau 4 10^{-6} C \)
– \( q_2 = -3 \sau 10^{-6} C \)
– \( r = sau 3 10^{-2} m \)
Amfani da lissafin dokar Coulomb:
\[ F = k_e \frac{|q_1 q_2|}{r^2} \]
Maye gurbin dabi'un da aka sani:
\[ F = (8,99 \sau 10^9) \frac{(sau 4 \sau 10^{-6})(sau 3 \sau 10^{-6})}{(sau 3 \sau 10^{-2})^2} \]
Lissafa girman ƙarfin:
\[ F = (8,99 \sau 10^9) \frac{12 \sau 10^{-12}}{9 \sau 10^{-4}} \]
\[ F = (8,99 \sau 10^9) \sau (1,33 \sau 10^{-8}) \]
\[ F = 1,197 \sau 10^2 \]
\[ F = 119,7 \, N \]
Alkiblar ƙarfi: Tunda \( q_1 \) yana da kyau kuma \( q_2 \) yana da korau, ƙarfin yana da kyau. Don haka, ƙarfin da ke kan \( q_1 \) yana fuskantar \( q_2 \) kuma akasin haka.
Tambaya ta 2: Caji Uku a cikin Alwatika Mai Daidaito
An sanya caji uku, kowanne \( q = 2 \mu C \), a kan kusurwar alwatika mai daidaito tare da gefuna tsawon santimita 5. A ƙididdige ƙarfin da ya haifar da aiki akan kowane caji.
Tattaunawa:
Canza caji da nisa zuwa raka'o'in SI:
– \( q = sau 2 10^{-6} C \)
– \( r = sau 5 10^{-2} m \)
Ƙarfi tsakanin laifuka biyu:
\[ F = k_e \frac{q^2}{r^2} \]
Maye gurbin dabi'un da aka sani:
\[ F = (8,99 \sau 10^9) \frac{(sau 2 \sau 10^{-6})^2}{(sau 5 \sau 10^{-2})^2} \]
\[ F = (8,99 \sau 10^9) \frac{4 \sau 10^{-12}}{25 \sau 10^{-4}} \]
\[ F = (8,99 \sau 10^9) \sau (1,6 \sau 10^{-10}) \]
\[ F = 1,4384 N \]
Wannan ƙarfin yana aiki akan kowace caji biyu a cikin alwatika. Domin nemo ƙarfin da ke aiki akan kowace caji, yana da mahimmanci a bincika ƙarfin da ke aiki akan kowace caji guda biyu a cikin alwatika mai lanƙwasa da kuma karkata.
A ce cajin da ke \( A \) ya karɓi ƙarfi daga \( B \) da \( C \):
– Ƙarfin daga \( B \) zuwa \( A \) shine \( F_{AB} = 1,4384 \, N \).
– Ƙarfin daga \(C \) zuwa \(A \) shine \(F_{AC} = 1,4384 \, N \).
Tunda waɗannan ƙarfin biyu suna samar da kusurwar 60° tare da juna (saboda alwatika mai daidaitawa), zamu iya amfani da nazarin sassan vector don nemo sakamakon.
Sassan ƙarfi a kan axis na x da axis na y:
\[ F_{Ax} = F_{AB} \cos 30^\circ + F_{AC} \cos 30^\circ \]
\[ F_{Ay} = F_{AB} \sin 30^\circ – F_{AC} \sin 30^\circ \]
Duk da haka, tunda duka ƙarfin suna da daidaito kuma daidai suke a ɓangarorin biyu, za a soke dukkan sassan y kuma yadda ya kamata, ƙarfin kwance yana shafar cajin \(A \) ne kawai.
\[
F_{Ax} = 2F_{AB} \cos 30^\cir \\
= 2(1,4384 \ N \cdot \ 0,866) \\
= 2 \cdot 1.2467 \\
= 2.4934N
]
Don haka ƙarfin wutar lantarki da ke kan ɗayan cajin shine ( F = 2.4934 N.
Kammalawa
Tantance ƙarfin lantarki da ke fitowa daga tsarin cajin maki yana buƙatar cikakken fahimtar dokar Coulomb da kuma ikon wargaza ƙarfin vector zuwa sassanta. A cikin yanayi mafi rikitarwa tare da caji uku ko fiye, nazarin vector sau da yawa kayan aiki ne mai mahimmanci don samun sakamako masu kyau. Ta hanyar matsalolin aiki kamar waɗannan, za mu iya fahimtar da kuma amfani da ra'ayoyin kimiyyar lissafi yadda ya kamata.
