Ajụjụ Ihe Nlereanya Na-ekwu Maka Ike Eletriki
Nkọwa nke ike eletrik bụ ike sitere na mmekọrịta dị n'etiti chajị eletrik. A na-amụ ike a na fiziki, ọkachasị n'akụkụ nke electrodynamics. A pụrụ ịhụ mmetụta nke ike eletrik n'ọtụtụ ihe omume kwa ụbọchị, site na ịpịkọta ihe ụfọdụ ọnụ ruo na ọrụ nke ngwaọrụ eletrọnịkị. Isiokwu a ga-atụle ọtụtụ ihe atụ nke nsogbu ike eletrik na ngwọta ha, yana echiche ndị bụ isi metụtara ike eletrik.
Okwu Mmalite nke Ike Eletriki
Iwu Coulomb nyere ike eletrik dị n'etiti ụgwọ eletriki abụọ, nke e gosipụtara site na nha anya:
$$ F = k_e \frac{|q_1 q_2|}{r^2} $$
Ebe:
– \( F \) bụ ike eletrik dị n'etiti ebubo abụọ.
– \( q_1 \) na \( q_2 \) bụ oke nke ebubo.
– \( r \) bụ anya dị n'etiti ebubo abụọ ahụ.
– \( k_e \) bụ ihe na-agbanwe agbanwe nke Coulomb (ihe dị ka \(8.99 \ugboro 10^9 \, N \cdot m^2 / C^2\)).
Iwu Coulomb yiri iwu ndọda Newton, mana ike ndọda na-adọrọ adọrọ mgbe niile ebe ike eletriki nwere ike ịmasị ma ọ bụ jọọ njọ dabere na akara nke chajị ahụ.
Ajụjụ na Mkparịta ụka Ihe Nlereanya
Ajụjụ nke 1: Ụgwọ abụọ nhata
Ọnụọgụ isi abụọ \( q_1 = 3 \, \mu C \) na \( q_2 = -4 \, \mu C \) dị n'ebe dị anya nke mita 0.5 site na ibe ha. Gbakọọ ike eletrik na-arụ ọrụ n'etiti ụgwọ abụọ ahụ.
Azịza:
1. Ịchọpụta Ibu na Anya:
– \( q_1 = 3 \, \mu C = ugboro atọ 10^{-6} \, C \)
– \( q_2 = -4 \, \mu C = -4 \ugboro 10^{-6} \, C \)
– \( r = 0.5 \, m \)
2. Ịgbanwe Iwu Coulomb:
\[
F = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F = 8.99 \ugboro 10^9 \, \frac{(ugboro 3 10^{-6})(ugboro 4 10^{-6})}{(0.5)^2}
\]
3. Gbakọọ Nsonaazụ:
\[
F = 8.99 \ugboro 10^9 \, \frac{12 \ugboro 10^{-12}}{0.25}
\]
\[
F = 8.99 \ugboro 10^9 \ugboro 48 \ugboro 10^{-12}
\]
\[
F = 431.52 \ugboro 10^{-3} \, N
\]
\[
F \ihe dịka 0.432 \, N
\]
Ya mere, ike eletrik nke na-arụ ọrụ n'etiti ebubo abụọ ahụ bụ ihe dịka 0.432 Newtons.
Ajụjụ nke 2: Ịkwụ ụgwọ n'ọtụtụ ụgwọ
A na-etinye ihe mgbata isi atọ, \( q_1 = 2 \, \mu C \), \( q_2 = 3 \, \mu C \), na \( q_3 = -1 \, \mu C \) n'ahịrị kwụ ọtọ, ebe dị n'etiti \( q_1 \) na \( q_2 \) bụ mita 0.6 na n'etiti \( q_2 \) na \( q_3 \) bụ mita 0.4. Gbakọọ ike sitere na \( q_2 \).
Azịza:
1. Ịchọpụta Ibu na Anya:
– \( q_1 = 2 \, \mu C = ugboro atọ 10^{-6} \, C \)
– \( q_2 = 3 \, \mu C = ugboro atọ 10^{-6} \, C \)
– \( q_3 = -1 \, \mu C = -1 \ugboro 10^{-6} \, C \)
– Ogologo dị n'etiti \( q_1 \) na \( q_2 \) bụ 0.6 m
– Ogologo dị n'etiti \( q_2 \) na \( q_3 \) bụ 0.4 m
2. Ike \( q_1 \) megide \( q_2 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r_{12}^2}
\]
\[
F_{12} = 8.99 \ugboro 10^9 \, \frac{(ugboro 2 10^{-6})(ugboro 3 10^{-6})}{(0.6)^2}
\]
\[
F_{12} = 8.99 \ugboro 10^9 \, \frac{6 \ugboro 10^{-12}}{0.36}
\]
\[
F_{12} = 8.99 \ugboro 10^9 \ugboro 16.67 \ugboro 10^{-12}
\]
\[
F_{12} \ihe dịka 0.15 \, N
\]
Ụzọ ike \( F_{12} \) dị anya site na \( q_1 \) (n'aka nri).
3. Ike \( q_3 \) megide \( q_2 \):
\[
F_{32} = k_e \frac{|q_3 q_2|}{r_{32}^2}
\]
\[
F_{32} = 8.99 \ugboro 10^9 \, \frac{(ugboro 1 10^{-6})(ugboro 3 10^{-6})}{(0.4)^2}
\]
\[
F_{32} = 8.99 \ugboro 10^9 \, \frac{3 \ugboro 10^{-12}}{0.16}
\]
\[
F_{32} = 8.99 \ugboro 10^9 \ugboro 18.75 \ugboro 10^{-12}
\]
\[
F_{32} \ihe dịka 0.17 \, N
\]
Ụzọ ike \( F_{32} \) na-adọga gaa n'ihu \( q_3 \) (n'aka ekpe).
4. Ike sitere na ya:
Ebe ọ bụ na \(F_{12} \) dị n'aka nri na \(F_{32} \) dị n'aka ekpe, ike sitere na ya \(F_{res} = F_{32} – F_{12} \):
\[
F_{res} = 0.17 \,N – 0.15 \,N
\]
\[
F_{res} = 0.02 \, N (n'aka ekpe)
\]
Ya mere, ike sitere na \( q_2 \) bụ 0.02 Newton n'aka ekpe.
Ajụjụ nke 3: Sistemụ Ibu Ibu n'ime Triangle
A na-etinye chajị isi atọ \( q_1 = 5 \, \mu C \), \( q_2 = -3 \, \mu C \), na \( q_3 = 4 \, \mu C \) n'akụkụ atọ nke triangle nhata nke nwere ogologo akụkụ 0.2 mita. Gbakọọ ike eletrik niile na-arụ ọrụ na chajị \( q_1 \).
Azịza:
1. Ike \( q_2 \) megide \( q_1 \):
\[
F_{12} = k_e \frac{|q_1 q_2|}{r^2}
\]
\[
F_{12} = 8.99 \ugboro 10^9 \, \frac{(ugboro 5 10^{-6})(ugboro 3 10^{-6})}{(0.2)^2}
\]
\[
F_{12} = 8.99 \ugboro 10^9 \, \frac{15 \ugboro 10^{-12}}{0.04}
\]
\[
F_{12} = 8.99 \ugboro 10^9 \ugboro 375 \ugboro 10^{-12}
\]
\[
F_{12} \ihe dịka 3.37 \, N
\]
Ụzọ ike \( F_{12} \) na-adọrọ mmasị n'akụkụ \( q_2 \).
2. Ike \( q_3 \) megide \( q_1 \):
\[
F_{13} = k_e \frac{|q_1 q_3|}{r^2}
\]
\[
F_{13} = 8.99 \ugboro 10^9 \, \frac{(ugboro 5 10^{-6})(ugboro 4 10^{-6})}{(0.2)^2}
\]
\[
F_{13} = 8.99 \ugboro 10^9 \, \frac{20 \ugboro 10^{-12}}{0.04}
\]
\[
F_{13} = 8.99 \ugboro 10^9 \ugboro 500 \ugboro 10^{-12}
\]
\[
F_{13} \ihe dịka 4.50 \, N
\]
Ụzọ ike \( F_{13} \) na-asọ oyi site na \( q_3 \).
3. Ike sitere na ya:
Anyị kwesịrị iji usoro vektọ ahụ chọta ihe si na \( F_{12} \) na \( F_{13} \ pụta), n'ihi na akụkụ dị n'etiti ike dị ogo 60 (triangle nhata).
Site na iji ihe ndị dị na x na y, anyị nwere ike ikpebi ike niile. Agbanyeghị, maka ịdị mfe, anyị ga-eji usoro eserese ma ọ bụ mgbakọ ọnụọgụ iji chọpụta na ike niile karịrị 4.50 N ma dị n'etiti ahịrị na-ejikọ \( q_2 \) na \( q_3 \) na \( q_1 \).
Mmechi
Site na nsogbu na mkparịta ụka dị n'elu, anyị nwere ike ịghọta otu esi agbakọ ike eletrik site na iji Iwu Coulomb. Site na ịkewa nsogbu ahụ n'ime usoro dị mfe na iji ihe atụ vektọ, anyị nwere ike ikpebi ike zuru oke dị na chaja ọ bụla dị na sistemụ ahụ. Ike eletrik, ọ bụ ezie na ọ dị mfe na nhazi mgbakọ na mwepụ ya, nwere ike inwe mmetụta dị oke mkpa na mgbagwoju anya na ngwa ụwa n'ezie.
