Amasimu kagesi - izinkinga nezixazululo

Amasimu kagesi - izinkinga nezixazululo

1. Iphuzu A litholakala phakathi kwamashaji amabili. Womabili amashaji anobukhulu obufanayo kodwa uphawu oluphambene futhi ahlukaniswe yibanga elingu-a. Ubukhulu bensimu kagesi endaweni A bungu-36 N/C. Uma iphuzu A lihamba ngo-1/2a eduze nenye yamashaji womabili , buyini ubukhulu bensimu kagesi endaweni A?

Kwaziwa:

Ishaja 1 (q ₁ ) = +Q

Ishaja 2 (q ₂ ) = -Q

Ibanga eliphakathi kokushaja 1 nephuzu A (r _1A ) = ½ a

Ibanga eliphakathi kokushaja 2 nephuzu A (r _2A ) = ½ a

Ubukhulu bensimu kagesi endaweni A (E _A ) = 36 NC ^-1

Okufunwayo: Ubukhulu bensimu kagesi

Isixazululo:

Isinyathelo 1.

Insimu kagesi ikhiqizwa ngokushaja +Q endaweni A :

Ishaja yokuhlola ilungile kanti ishaja 1 ilungile ukuze isiqondiso sensimu kagesi sibheke ekushajeni 2.

Ishaja kagesi ekhiqizwa yishaja -Q endaweni A :

Ishaja yokuhlola ilungile kanti ishaja 2 imbi ukuze isiqondiso sensimu kagesi sibheke ekushajeni 2.

Umphumela wensimu kagesi endaweni A:

Isinyathelo 2.

Uma iphuzu A lisondela ekushajeni 1 khona-ke:

Ibanga eliphakathi kokushaja 1 nephuzu A (r _1A ) = ¼ a

Ibanga eliphakathi kokushaja 2 kanye nephuzu A (r _2A ) = ¾ a

Insimu kagesi ekhiqizwa yi-charge +Q endaweni A :

Ishaja yokuhlola ilungile kanti ishaja 1 ilungile ukuze isiqondiso sensimu kagesi sibheke ekushajeni 2.

Insimu kagesi ekhiqizwa yi-charge -Q endaweni A :

Ishaja yokuhlola ilungile kanti ishaja 2 imbi ukuze isiqondiso sensimu kagesi sibheke ekushajeni 2.

Umphumela wensimu kagesi endaweni A:

2. Amashaja amabili q _A = 1 μC kanye q _B = 4 μC ahlukaniswe ngebanga elingu-4 cm (k = 9 x 10 ⁹ N m ² C ^{−2 ). Ubukhulu bensimu kagesi phakathi kuka-q} _A no-q _B buyini.

Kwaziwa:

Ishaja A (q _A ) = 1 μC = 1 x 10 ⁻⁶ C

Ishaja B (q _B ) = 4 μC = 4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ N m ² C ⁻²

Ibanga phakathi kwezindleko A kanye no-B (r _AB ) = 4 cm = 0.04 amamitha

Ibanga phakathi kweshaja A nendawo ephakathi (r _A ) = 0.02 amamitha s

Ibanga phakathi kweshaja B nendawo ephakathi (r _B ) = 0.02 amamitha s

Okuyaziwayo: Ubukhulu bensimu kagesi

Isixazululo:

Insimu kagesi ekhiqizwa yi-charge A endaweni ephakathi nendawo:

Ishaja yokuhlola ilungile kanti ishaja u-A ilungile ukuze isiqondiso sensimu kagesi sibheke ekushajeni u-B.

Insimu kagesi ekhiqizwa yishaja B endaweni ephakathi nendawo:

Ishaja yokuhlola ilungile kanti ishaja B ilungile ukuze isiqondiso sensimu kagesi sibheke ekushajeni u-A.

Umphumela wensimu kagesi endaweni ephakathi:

I-E _A ne-E _B zinezindlela eziphambene.

E = E _B – E _A = 9 x 10 ^{7 –} 2.25 x 10 ⁷ = 6.75 x 10 ⁷ NC ^-1

3. Ngokusho komfanekiso ongezansi, iphuzu P likuphi ukuze ubukhulu bensimu kagesi endaweni P = 0? (k = 9 x 10 ⁹ Nm ² C ^{−2 ,} 1 μC = 10 ⁻⁶ C)

Isixazululo

Uma iphuzu P litholakala kwesobunxele se -Q ₁ ; insimu kagesi ekhiqizwe yi -Q ₁ ephuzwini P ikhomba kwesobunxele ( kude ne -Q ₁ ) kanye nensimu kagesi ekhiqizwe yi -Q ₂ ephuzwini P ikhomba kwesokudla (khomba ku- Q ₁ ). Isiqondiso sensimu kagesi siphambene ukuze insimu kagesi ephuzwini P = 0.

Kwaziwa:

Q ₁ = +9 μC = +9 x 10 ⁻⁶ C

Q ₂ = -4 μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Ibanga phakathi kokushaja 1 nokushaja 2 = 3 cm

Ibanga phakathi kuka -Q ₁ nephuzu P (r _1P ) = a

Ibanga phakathi kuka- Q ₂ nephuzu P (r _2P ) = 3 + a

Okufunwayo: Isikhundla sephuzu P

Isixazululo:

Iphuzu P litholakala kwesobunxele se- Q ₁.

Insimu kagesi ekhiqizwe yi -Q ₁ endaweni P:

Ishaja yokuhlola ilungile kanti u-Q ₁ ulungile ukuze isiqondiso sensimu kagesi siye ngakwesobunxele.

Insimu kagesi ekhiqizwe yi _- Q2 endaweni ethi P :

Ishaja yokuhlola ilungile kanti u-Q ₂ ulungile ukuze isiqondiso sensimu kagesi sibe ngakwesokudla.

Umphumela wensimu kagesi endaweni A:

Sebenzisa ifomula ye-quadratic ukuthola i-:

Ibanga phakathi kwe -Q ₂ nephuzu P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm noma 3 + a = 3 – 9 = -6 cm.

Ibanga phakathi kwe -Q ₁ nephuzu P (r _1P ) = a = -9 cm noma -1.8 cm.

Iphuzu P litholakala ku -1.2 cm kwesokudla se- Q ₂.

4. Ishaja q ₃ etholakala ku-5 cm kwesokudla se-q ₂ , njengoba kuboniswe esithombeni esingezansi. Ubukhulu bensimu kagesi ekushajeni q ₃ buyini (1 µC = 10 ^-6 C).

Isixazululo:

Ishaja q ₃ ilungile ukuze isiqondiso sensimu kagesi ekushajeni q ₃ sibhekisele kushaja encane q ₂ (E ₂ ) futhi sisuke kushaja yokuhlanganisa q ₁ (E ₁ ). Umphumela wensimu kagesi yisamba sezinkundla zikagesi E ₁ no-E ₂.

Kwaziwa:

Ishaja q ₁ = 5 µC = 5 x 10 ^-6 Coulomb

Ishaja q ₂ = 5 µC = -5 x 10 ^{-6 Ama} -Coulomb

Ibanga phakathi kokushaja q ₁ kanye nokushaja q ₃ (r ₁ ) = 15 cm = 0.15 m = 15 x 10 ^-2 amamitha

Ibanga phakathi kokushaja q ₂ kanye nokushaja q ₃ (r ₂ ) = 5 cm = 0.05 m = 5 x 10 ^-2 amamitha

k = 9 x 10 ⁹ N m ² C ^-2

Okufunwayo: Insimu kagesi eshajayo q ₃

Isixazululo:

Insimu kagesi 1:

E ₁ = kq ₁ / r ₁ ²

E ₁ = (9 x 10 ⁹ )(5 x 10 ^-6 ) / (15 x 10 ^-2 ) ²

E ₁ = (45 x 10 ³ ) / (225 x 10 ^-4 )

E ₁ = 0.2 x 10 ⁷ N/C

Insimu kagesi 2:

E ₂ = kq ₂ / r ₂ ²

E ₂ = (9 x 10 ⁹ )(5 x 10 ^-6 ) / (5 x 10 ^-2 ) ²

E ₂ = (45 x 10 ³ ) / (25 x 10 ^-4 )

E ₂ = 1.8 x 10 ⁷ N/C

Umphumela wensimu kagesi:

Umphumela wensimu kagesi eshajayo q ₃ :

E = E ₂ – E ₁ = (1.8 x 10 ⁷ ) – (0.2 x 10 ⁷ ) = 1.6 x 10 ⁷ N/C

Isiqondiso sensimu kagesi sikhomba ngakwesobunxele (isiqondiso esifanayo nesika-E2 ₎.

5. Kuhlukaniswe amashaja amabili njengoba kuboniswe esithombeni esingezansi. Iyini insimu kagesi endaweni P (k = 9 x 10 ⁹ N m ² C ^-2 )

Isixazululo

Kwaziwa:

Ishaja q _A = +2.5 C

Ishaja q _B = -2 C

Ibanga phakathi kokushaja q _A kanye nephuzu P (r _A ) = 5 m

Ibanga phakathi kokushaja q _B kanye nephuzu P (r _B ) = 2 m

k = 9 x 10 ⁹ N m ² C ^-2

Okufunwayo: ubukhulu bensimu kagesi endaweni ethi P.

Isixazululo:

Insimu kagesi A:

E _A = kq _A / r _A ²

E _A = (9 x 10 ⁹ )(2.5) / (5) ²

E _A = (22.5 x 10 ⁹ ) / 25

I-EA = 0.9 x 10 ^{9 N} _/ C

Insimu kagesi B:

E _B = kq _B / r _B ²

E _B = (9 x 10 ⁹ )(2) / (2) ²

E _B = (18 x 10 ⁹ ) / 4

I-E _B = 4.5 x 10 ⁹ N/C

Umphumela wensimu kagesi:

Umphumela wensimu kagesi endaweni P:

E = E _B – EA = (4.5 – 0.9) x 10 ⁹ = 3.6 x 10 ⁹ N/C

Isiqondiso esiya kwesobunxele (isiqondiso esifanayo nesika-E _B ).

6. Amashaja amabili Q ₁ = -40 µC kanye Q ₂ = +5 µC njengoba kuboniswe esithombeni esingezansi (k = 9 x 10 ⁹ Nm ² .C ^-2 kanye no-1 µC = 10 ^-6 C). Ubukhulu bensimu kagesi endaweni P buyini.

Kwaziwa:

Ishaja q ₁ = -40 µC = -40 x 10 ^-6 C

Ishaja q ₂ = +5 µC = +5 x 10 ^-6 C

Ibanga phakathi kwe-q ₁ nephuzu P (r ₁ ) = 40 cm = 0.4 m = 4 x 10 ^-1 m

Ibanga phakathi kuka-q ₂ nephuzu P (r ₂ ) = 10 cm = 0.1 = 1 x 10 ^-1 m

k = 9 x 10 ⁹ N m ² C ^-2

Okufunwayo: ubukhulu bensimu kagesi endaweni ethi P.

Isixazululo:

Insimu kagesi 1:

E ₁ = kq ₁ / r ₁ ²

E ₁ = (9 x 10 ⁹ )(40 x 10 ^-6 ) / (4 x 10 ^-1 ) ²

E ₁ = (360 x 10 ³ ) / (16 x 10 ^-2 )

E ₁ = 22.5 x 10 ⁵ N/C

Insimu kagesi 2:

E ₂ = kq ₂ / r ₂ ²

E ₂ = (9 x 10 ⁹ )(5 x 10 ^-6 ) / (1 x 10 ^-1 ) ²

E ₂ = (45 x 10 ³ ) / 1 x 10 ^-2

E ₂ = 45 x 10 ⁵ N/C

Umphumela wensimu kagesi:

Umphumela wensimu kagesi endaweni P:

E = E ₂ – E1 = (45 – 22.5) x 10 ⁵ = 22.5 x 10 ⁵ N/C

E = 2.25 x 10 ⁶ N/C

Isiqondiso sensimu kagesi sikhomba ngakwesokudla (isiqondiso esifanayo nesika-E2 ₎.

7. Amacala amabili njengoba kuboniswe esithombeni esingezansi.

Iphi iphuzu P ukuze ubukhulu bensimu kagesi endaweni P = 0. k = 9.10 ⁹ Nm ² .C ^-2 , 1 µC = 10 ^-6 C.

Kwaziwa:

Ishaja 1 (q ₁ ) = -9 µC = -9.10 ^{-6 Ama} -Coulomb

Ishaja 2 (q ₂ ) = 1 µC = 1.10 ^-6 Coulomb

Ibanga phakathi kuka-q ₁ no-q ₂ (r ₁₂ ) = 1 cm

k = 9.10 ⁹ Nm ² .C ^-2

Okufunwayo: Isikhundla sephuzu P

Isixazululo:

E ₁ = ubukhulu bensimu kagesi ekhiqizwa yi-q ₁ endaweni P

Isiqondiso sika- E ₁ kuya ku -q ₁ ngoba u-q ₁ ungemuhle.

E ₂ = ubukhulu bensimu kagesi ekhiqizwa yi-q ₂ endaweni P

Indlela u-E ₂ aqondani ngayo no-q ₂ ngoba u-q ₂ ulungile.

Insimu kagesi endaweni = 0.

Sebenzisa ifomula ye-quadratic:

Ibanga eliphakathi kuka-P no-q ₂ = x = 0.5 cm.

Iphuzu P litholakala ku-0.5 cm ngakwesokudla q ₂ noma 0.25 cm ngakwesokunxele q ₁.

8. Ngokusho kwesibalo esingezansi, uma ubukhulu bensimu kagesi endaweni ethi P = k Q/x ² , khona-ke x = ….

Kwaziwa:

I-EP = k Q / _x ²

Kufunwa: x

Isixazululo:

E ₂ = Ubukhulu bensimu kagesi endaweni P ngokushaja +32Q

r ₂ = Ibanga phakathi kokushaja +32Q kanye nephuzu P = a + x

Sebenzisa ifomula ye-quadratic:

1. Iyini insimu kagesi?
   • Impendulo: Insimu kagesi yindawo ezungeze into eshajiwe lapho amandla kagesi angabonwa khona ezinye izinto ezishajiwe. Iyinsimu yevektha, okusho ukuthi inobukhulu kanye nesiqondiso kuzo zonke izindawo.
2. Amandla ensimu kagesi anqunywa kanjani?
   • Impendulo: Amandla noma ubukhulu bensimu kagesi $E$ endaweni ethile kuchazwa njengamandla $F$ ubhekene necala lokuhlolwa elihle q₀​ ibekwe kulelo phuzu, ihlukaniswe ngobukhulu beshaja yokuhlola uqobo: E=​F/q₀​.
3. Insimu kagesi ngenxa yokushaja kwephuzu ihluka kanjani ngokwebanga?
   • Impendulo: Insimu kagesi $E$ ngenxa yokushaja iphuzu $Q$ ilingana ngokuphambene nesikwele sebanga $r$ kusukela ekubekweni icala. Ubudlelwano bunikezwa ngu E=kQ/r², lapho $k$ kuyinto engaguquki kaCoulomb.
4. Iyiphi indlela insimu kagesi eqondiswa ngayo ngenxa yokushaja okuhle?
   • Impendulo: Insimu kagesi ngenxa yokushaja okuhle okuvela ngaphandle kusuka ekushajeni. Uma kushaja okubi, insimu ikhomba ngaphakathi, ibheke ekushajeni.
5. Ungazimela kanjani izinkundla zikagesi ngemidwebo?
   • Impendulo: Amasimu kagesi angamelwa ngemidwebo kusetshenziswa imigqa yensimu (noma imigqa yamandla). Isiqondiso sensimu kunoma iyiphi indawo sithinta umugqa wensimu kuleyo ndawo, futhi ubuningi bemigqa bubonisa ubukhulu bensimu.
6. Kwenzekani ensimini kagesi ngaphakathi komqhubi ku-electrostatic equilibrium?
   • Impendulo: Ngaphakathi komqhubi olinganiselayo ngogesi, insimu kagesi ingu-zero. Lokhu kungenxa yokuthi noma iyiphi insimu yangaphandle ibangela ukuthi ama-electron akhululekile kumqhubi aphinde asabalale, okukhansela insimu yangaphandle engaphakathi.
7. Imigqa kagesi isebenza kanjani eduze konqenqema olubukhali lomqhubi?
   • Impendulo: Eduze komphetho obukhali noma inhloko ecijile yomqhubi, imigqa yensimu kagesi igxile kakhulu, okuholela ensimini kagesi enamandla kuleyo ndawo. Lesi yisisekelo sokusebenza kwamadivayisi afana nenduku yombani.
8. Izimiso ze-superposition zisebenza kanjani ezinkundleni zikagesi?
   • Impendulo: Insimu kagesi ngenxa yokushaja okuningi endaweni ethile imane nje iyisamba se-vector samasimu kagesi ngenxa yokushaja ngakunye. Lokhu kwaziwa ngokuthi isimiso se-superposition.
9. Umsebenzi owenziwa yi-ejenti yangaphandle uhlobene kanjani nensimu kagesi lapho kuhanjiswa ishaja ngaphakathi kwensimu?
   • Impendulo: Umsebenzi $W$ kwenziwa yi-ejenti yangaphandle ekuhambiseni inkokhelo $q$ kusuka endaweni eyodwa kuya kwenye ensimini kagesi kufana ne-negative yokushintsha kwamandla kagesi, okuyi- $W=q\times \Delta V$, lapho $\Delta V$ ushintsho emandleni kagesi.

10. Ingabe imigqa kagesi ingake yeqane?

    • Impendulo: Cha, imigqa yensimu kagesi ayikwazi ukuwelana. Uma beyenza, kungasho ukuthi endaweni lapho kuhlangana khona imigwaqo, kunezindlela ezimbili ezahlukene zensimu kagesi, okuyinto engenakwenzeka.