Mienzaniso yeMibvunzo Inokurukura Simba Pakufambisa Mari
Pendauluan
Fizikisi kudzidza nezvezviitiko zvechisikigo, kusanganisira masimba anoshanda pazvinhu. Imwe nyaya inonakidza inowanzo kurukurwa isimba rinofambisa mafambiro, kunyanya muminda yemagetsi nemagineti. Simba rinofambisa mafambiro mumunda wemagetsi kana magineti rinozivikanwa seLorentz force. Chinyorwa chino chichakurukura mienzaniso yakati wandei yezvinetso uye hurukuro yavo maererano nesimba rinofambisa mafambiro.
Simba reLorentz
Simba reLorentz musanganiswa wesimba remagetsi nesimba remagineti rinoshanda pakuchaja kuri kufamba mumunda wemagetsi nemumunda wemagineti. Pamasvomhu, simba reLorentz (F) rinogona kuratidzwa ne equation:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \nguva \mathbf{B}) \]
Di mana:
- \( \ mathbf{F} \) isimba reLorentz
– \( q \) ndiyo muripo
– \( \mathbf{E} \) ndiyo nzvimbo yemagetsi
– \( \mathbf{v} \) ndiko kumhanya kwekuchaja
– \( \mathbf{B} \) ndiyo simba remagineti
Nekuenzanisa uku, tinogona kuongorora masimba anoshanda pachaji inofamba mumunda wemagetsi uye munda wemagineti.
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Simba Rinobhadhariswa Mumunda Wemagetsi
Mubvunzo:
Chaji yakanaka \( q = 2 \times 10^{-6} \, C \) iri mumunda wemagetsi wakaenzana \( E = 5 \times 10^4 \, N/C \) yakananga kurudyi. Verenga simba riri kushanda pachaji.
Kukurukurirana:
Kana paine chaji mumunda wemagetsi pasina simba remagineti, simba reLorentz rinoumbwa chete nechikamu chesimba remagetsi:
\[ \mathbf{F} = q \mathbf{E} \]
Ne \( q = 2 \times 10^{-6} \, C \) uye \( \mathbf{E} = 5 \times 10^4 \, N/C \):
\[ \mathbf{F} = (2 \kawa 10^{-6} \, C) \kawa (5 \kawa 10^4 \, N/C) \]
\[ \mathbf{F} = 0.1 \, N \]
Kutungamira kwesimba \( \mathbf{F} \) kuri munzira imwecheteyo nemagetsi nekuti chaji yacho yakanaka. Saka, simba rinoshanda pachaji iri 0.1 N kurudyi.
Mubvunzo 2: Simba Pakuchaja Mumunda Wemagineti
Mubvunzo:
Chaji isina kunaka \( q = -3 \times 10^{-6} \, C \) inofamba nekumhanya \( \mathbf{v} = 2 \times 10^3 \, m/s \) pamwe chete nex-axis mumunda wemagineti wakaenzana \( \mathbf{B} = 0.5 \, T \) wakanangana nez-axis. Verenga simba rinoshanda pachaji.
Kukurukurirana:
Kana chaji ichifamba mumunda wemagineti pasina simba remagetsi, simba reLorentz rinoumbwa chete nezvikamu zvesimba remagineti:
\[ \mathbf{F} = q (\mathbf{v} \nguva \mathbf{B}) \]
Ne \( q = -3 \times 10^{-6} \, C \), \( \mathbf{v} = 2 \times 10^3 \, m/s \) munzira ye x, uye \( \mathbf{B} = 0.5 \, T \) munzira ye z:
Kuverenga \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 2 \kawa 10^3 \, m/s \, \hat{i} \]
\[ \mathbf{B} = 0.5 \, T \, \hat{k} \]
\[ \mathbf{v} \nguva \mathbf{B} = (2 \nguva 10^3 \, m/s \, \hat{i}) \nguva (0.5 \, T \, \hat{k}) \]
\[ \mathbf{v} \nguva \mathbf{B} = 2 \nguva 10^3 \, m/s \nguva 0.5 \, T \, \hat{i} \nguva \hat{k} \]
\[ \hat{i} \times \hat{k} = -\hat{j} \]
\[ \mathbf{v} \times \mathbf{B} = – (1 \times 10^3 \, T \cdot m/s) \, \hat{j} \]
Saka, simba remagineti:
\[ \mathbf{F} = q \mathbf{v} \nguva \mathbf{B} \]
\[ \mathbf{F} = (-3 \kawa 10^{-6} C) \kawa ( -10^3 \, T \cdot m/s \, \hat{j}) \]
\[ \mathbf{F} = 3 \nguva 10^{-3} \, N \, \hat{j} \]
\[ \mathbf{F} = 0.003 \, N \, \hat{j} \]
Kutungamira kwesimba \( \mathbf{F} \) kuri kudivi re y-axis rakanaka. Saka, simba rinoshanda pachaji iri 0.003 N zvichikwira (mudivi re y-axis rakanaka).
Mubvunzo 3: Simba Rinochajwa Mumagetsi Nemagetsi
Mubvunzo:
Chaji yakanaka \( q = 1.5 \times 10^{-6} \, C \) inofamba nekumhanya \( \mathbf{v} = 4 \times 10^3 \, m/s \) munzira ye y mumunda wemagetsi \( \mathbf{E} = 3 \times 10^4 \, N/C \) munzira ye x, uye simba remagineti \( \mathbf{B} = 0.2 \, T \) munzira ye z. Verenga simba re net rinoshanda pachaji.
Kukurukurirana:
Simba rose reLorentz:
\[ \mathbf{F} = q (\mathbf{E} + \mathbf{v} \nguva \mathbf{B}) \]
Kutanga, verenga \( \mathbf{v} \times \mathbf{B} \):
\[ \mathbf{v} = 4 \kawa 10^3 \, m/s \, \hat{j} \]
\[ \mathbf{B} = 0.2 \, T \, \hat{k} \]
\[ \mathbf{v} \nguva \mathbf{B} = (4 \nguva 10^3 \, m/s \, \hat{j}) \nguva (0.2 \, T \, \hat{k}) \]
\[ \mathbf{v} \nguva \mathbf{B} = 4 \nguva 10^3 \, m/s \nguva 0.2 \, T \, \hat{j} \nguva \hat{k} \]
\[ \hat{j} \times \hat{k} = \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = (0.8 \times 10^3 \, T \cdot m/s) \, \hat{i} \]
\[ \mathbf{v} \times \mathbf{B} = 800 \, T \cdot m/s \, \hat{i} \]
Zvadaro, simba remagetsi:
\[ q \mathbf{E} = (1.5 \kawa 10^{-6} \, C) \kawa (3 \kawa 10^4 \, N/C \, \hat{i}) \]
\[ q \mathbf{E} = 0.045 \, N \, \hat{i} \]
Simba remagineti:
\[ q (\mathbf{v} \times \mathbf{B}) = (1.5 \times 10^{-6} \, C) \times (800 \, T \cdot m/s \, \hat{i}) \]
\[ q (\ mathbf{v} \nguva \mathbf{B}) = 0.0012 \, N \, \hat{i} \]
Manyorerwo ese:
\[ \mathbf{F} = q \mathbf{E} + q (\mathbf{v} \nguva \mathbf{B}) \]
\[ \mathbf{F} = 0.045 \, N \, \heti{i} + 0.0012 \, N \, \hat{i} \]
\[ \ mathbf{F} = 0.0462 \, N \, \hat{i} \]
Saka, simba rose rinoshanda pachaji i0.0462 N kurudyi (positive x-axis).
Mhedziso
Simba remagetsi rinofamba mumagetsi nemagineti rinoenderana zvikuru negwara uye hukuru hwemunda wega wega pamwe nekumhanya uye rudzi rwemagetsi. Kuburikidza nemuenzaniso wemibvunzo nehurukuro iri pamusoro apa, zvinotarisirwa kuti vaverengi vanzwisise zviri nani mashandisirwo emutemo wesimba reLorentz mumamiriro akasiyana-siyana. Kunzwisisa uku hakungokoshi chete mudzidziso asiwo mukushandiswa kunoshanda muminda yetekinoroji nesainzi senge mukugadzirwa kwemamota emagetsi, kunzwisisa chiitiko cheaurora, uye basa rezvikamu muzvikwiriso zvinomhanyisa mafambiro emagetsi.
