Ajụjụ Ihe Nlereanya Na-atụle Iwu Coulomb
Iwu Coulomb bụ isi ihe dị mkpa na fiziki nke na-akọwa ike dị n'etiti chajị eletriki abụọ. A mụrụ iwu a n'ime obere ubi nke electrostatics, ọ na-akọwa otu chajị eletriki si adọta ma ọ bụ na-achụpụ ibe ha. Onye ọkà mmụta sayensị French bụ Charles-Augustin de Coulomb bu ụzọ tụpụta iwu a na narị afọ nke 18. Isiokwu a ga-atụle Iwu Coulomb site n'inyocha ihe atụ na ngwọta ha, si otú a na-enyere ndị na-agụ akwụkwọ aka ịghọta ojiji bara uru nke ụkpụrụ a dị mkpa.
Ntọala nke echiche: Gịnị bụ Iwu Coulomb?
Iwu Coulomb kwuru na oke ike electrostatic \( F \) dị n'etiti chajị isi abụọ \( q_1 \) na \( q_2 \) dabara kpọmkwem na ngwaahịa nke oke chajị abụọ ahụ ma na-agbanwe agbanwe na square nke anya \( r \) dị n'etiti ha. N'ụzọ mgbakọ na mwepụ, enwere ike ịkọwa usoro maka Iwu Coulomb dị ka:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Ebe:
– \( F \) bụ oke nke ike electrostatic
– \( k_e \) bụ mgbanwe nke Coulomb (\( 8.9875 \ugboro 10^9 \, N \cdot m^2 \cdot C^{-2} \))
– \( q_1 \) na \( q_2 \) bụ nha nke chajị eletriki
– \( r \) bụ anya dị n'etiti ebubo abụọ ahụ
Ajụjụ Ihe Nlereanya nke 1
Ajụjụ:
E nwere ihe mgbata isi abụọ: \( q_1 = 2 \u003 10^{-6} \, C \) na \( q_2 = -3 \u003 10^{-6} \, C \). Ha dị mita 0,05 n'ebe dị iche. Gbakọọ oke ike electrostatic nke na-arụ ọrụ n'etiti chajị abụọ ahụ.
Mkparịta ụka:
Nzọụkwụ mbụ bụ idegharị usoro maka Iwu Coulomb:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Ugbu a, anyị na-eji usoro a dochie ụkpụrụ ndị a maara:
\[ k_e = 8.9875 \ugboro 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = ugboro abụọ 10^{-6} \, C \]
\[ q_2 = -3 \ugboro 10^{-6} \, C \]
\[ r = 0,05 \, m \]
Anyị na-etinye ụkpụrụ ndị a n'ime usoro ahụ:
\[ F = 8.9875 \ugboro 10^9 \, \frac{|2 \ugboro 10^{-6} \cdot -3 \ugboro 10^{-6}|}{(0,05)^2} \]
\[ F = 8.9875 \ugboro 10^9 \, \frac{6 \ugboro 10^{-12}}{0,0025} \]
\[ F = 8.9875 \ugboro 10^9 \, \frac{6 \ugboro 10^{-12}}{2,5 \ugboro 10^{-3}} \]
\[ F = 8.9875 \ugboro 10^9 \, \ugboro 2,4 \ugboro 10^{-9} \]
\[ F = 21.57 \, N \]
Ebe ọ bụ na chajị \( q_2 \) adịghị mma, ike electrostatic nke na-arụ ọrụ bụ ike na-adọrọ adọrọ, n'ihi na chajị dị mma na nke na-adịghị mma na-adọta ibe ha.
Ajụjụ Ihe Nlereanya nke 2
Ajụjụ:
A na-ekewapụ chaja eletriki abụọ \( q_1 = 5 \u003 10^{-9} \, C \) na \( q_2 = 10 \u003 10^{-9} \, C \) site na anya nke mita 0,1. Gbakọọ oke ike electrostatic na-arụ ọrụ na \( q_1 \).
Mkparịta ụka:
Jiri usoro Iwu Coulomb ọzọ:
\[ F = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
Dochie ụkpụrụ ndị a maara:
\[ k_e = 8.9875 \ugboro 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = ugboro abụọ 10^{-9} \, C \]
\[ q_2 = ugboro abụọ 10^{-9} \, C \]
\[ r = 0,1 \, m \]
\[ F = 8.9875 \ugboro 10^9 \, \frac{(ugboro 5 10^{-9}) (ugboro 10 10^{-9})}{(0,1)^2} \]
\[ F = 8.9875 \ugboro 10^9 \, \frac{50 \ugboro 10^{-18}}{0,01} \]
\[ F = 8.9875 \ugboro 10^9 \, \ugboro 5 \ugboro 10^{-15} \]
\[ F = 44.9375 \, N \]
Ike nke na-arụ ọrụ bụ ike na-asọ oyi, n'ihi na ma chajị \( q_1 \) na \( q_2 \) nwere otu akara ahụ, ya bụ, ihe dị mma.
Ajụjụ Ihe Nlereanya nke 3
Ajụjụ:
Ọnụọgụ isi atọ dị n'ahịrị kwụ ọtọ. Ọnụọgụ mbụ bụ \( q_1 = 2 \mu C \), ọnụọgụ nke abụọ bụ \( q_2 = -1 \mu C \), ọnụọgụ nke atọ bụkwa \( q_3 = 3 \mu C \). Anya dị n'etiti \( q_1 \) na \( q_2 \) bụ 0,1 m, ebe anya dị n'etiti \( q_2 \) na \( q_3 \) bụ 0,2 m. Gbakọọ nha na ntụziaka nke ike electrostatic zuru oke na-arụ ọrụ na \( q_2 \).
Mkparịta ụka:
Nke mbụ, anyị na-agbakọ ike electrostatic dị n'etiti \( q_1 \) na \( q_2 \):
\[ F_{12} = k_e \frac{|q_1 \cdot q_2|}{r^2} \]
\[ k_e = 8.9875 \ugboro 10^9 \, N \cdot m^2 \cdot C^{-2} \]
\[ q_1 = ugboro abụọ 10^{-6} \, C \]
\[ q_2 = -1 \ugboro 10^{-6} \, C \]
\[ r = 0,1 \, m \]
\[ F_{12} = 8.9875 \ugboro 10^9 \, \frac{(ugboro 2 10^{-6}) (-1 \ugboro 10^{-6})}{(0,1)^2} \]
\[ F_{12} = 8.9875 \ugboro 10^9 \, \frac{2 \ugboro 10^{-12}}{0,01} \]
\[ F_{12} = 8.9875 \ugboro 10^9 \, \ugboro 2 \ugboro 10^{-10} \]
\[ F_{12} = 1.7975 \, N \]
Ebe ọ bụ na \( q_1 \) dị mma ma \( q_2 \) bụ ihe na-adịghị mma, ike \( F_{12} \) bụ ike na-adọrọ adọrọ nke na-eduga n'ebe \( q_1 \) nọ.
Nke abụọ, anyị na-agbakọ ike electrostatic dị n'etiti \( q_2 \) na \( q_3 \):
\[ F_{23} = k_e \frac{|q_2 \cdot q_3|}{r^2} \]
\[ q_2 = -1 \ugboro 10^{-6} \, C \]
\[ q_3 = ugboro abụọ 10^{-6} \, C \]
\[ r = 0,2 \, m \]
\[ F_{23} = 8.9875 \ugboro 10^9 \, \frac{(-1 \ugboro 10^{-6}) (ugboro 3 10^{-6})}{(0,2)^2} \]
\[ F_{23} = 8.9875 \ugboro 10^9 \, \frac{3 \ugboro 10^{-12}}{0,04} \]
\[ F_{23} = 8.9875 \ugboro 10^9 \, \ugboro 7.5 \ugboro 10^{-11} \]
\[ F_{23} = 0.67406 \, N \]
Ebe ọ bụ na \( q_2 \) bụ ihe na-adịghị mma na \( q_3 \) bụ ihe dị mma, ike \( F_{23} \) bụ ike na-adọrọ adọrọ nke na-eduga n'ebe \( q_3 \) nọ.
N'ikpeazụ, anyị na-ejikọta ike abụọ ahụ iji chọta ihe ikpeazụ:
Ike zuru oke na \( q_2 \):
\[ F_{\text{total}} = F_{12} – F_{23} \]
\[ F_{\text{ngụkọta}} = 1.7975 \, N – 0.67406\, N \]
\[ F_{\text{ngụkọta}} = 1.12344 \, N \]
Ụzọ nke ike zuru oke dị n'ihu \( q_1 \) n'ihi na ike \( F_{12} \) karịrị \( F_{23} \).
Mmechi
Iwu Coulomb na-enye nghọta dị mkpa gbasara mmekọrịta dị n'etiti chaja eletrik, ma nke na-adọrọ adọrọ ma nke na-asọ oyi. Ihe atụ ndị a tụlere na-egosi ojiji nke iwu a n'ịgbakọ ike electrostatic site n'ịtụle oke nke chaja na anya dị n'etiti ha. Nghọta zuru oke nke Iwu Coulomb nwere ike inyere anyị aka ịghọta ụdị ihe dị iche iche na-eme na eletriki na magnetik nke na-eme gburugburu anyị.
