Goobaha korontada - dhibaatooyinka iyo xalalka

Goobaha korontada - dhibaatooyinka iyo xalalka

1. Barta A waxay ku taal bartamaha u dhaxaysa laba dallacaad. Labada dallacaadba waxay leeyihiin cabbir isku mid ah laakiin calaamad ka soo horjeeda waxaana kala fogeeya masaafada a. Cabbirka goobta korantada ee barta A waa 36 N/C. Haddii barta A ay u dhaqaaqdo 1/2a meel u dhow mid ka mid ah labada dallacaad , waa maxay baaxadda goobta korontada ee barta A?

La yaqaan:

Kharash 1 (q ₁ ) = +Q

Kharash 2 (q ₂ ) = -Q

Masaafada u dhaxaysa kharashka 1 iyo dhibicda A (r _1A ) = ½ a

Masaafada u dhaxaysa kharashka 2 iyo dhibicda A (r _2A ) = ½ a

Baaxadda goobta korantada ee barta A (E _A ) = 36 NC ^-1

La Doonayo: Baaxadda goobta korantada

Xalka:

Tallaabada 1aad.

Goobta korantada waxaa lagu soo saaraa dallac + Q barta A :

Dalacaadda tijaabada waa togan tahay, dalacaadda 1aadna waa togan tahay si jihada goobta korontada ay u muujiso dalacaadda 2.

Dareeraha korontada ee uu soo saaro dallacaadda -Q barta A :

Dalacaadda tijaabada waa togan tahay, dalacaadda 2-na waa taban tahay si jihada goobta korontada ay u muujiso dalacaadda 2.

Natiijada garoonka korantada ee barta A:

Tallaabada 2.

Haddii dhibicda A loo raro meel u dhow dallacaadda 1 markaas:

Masaafada u dhaxaysa kharashka 1 iyo dhibicda A (r _1A ) = ¼ a

Masaafada u dhaxaysa kharashka 2 iyo dhibicda A (r _2A ) = ¾ a

Goobta korantada ee ay soo saarto dallacaadda + Q barta A :

Dalacaadda tijaabada waa togan tahay, dalacaadda 1aadna waa togan tahay si jihada goobta korontada ay u muujiso dalacaadda 2.

Goobta korantada ee ay soo saarto charge -Q barta A :

Dalacaadda tijaabada waa togan tahay, dalacaadda 2-na waa taban tahay si jihada goobta korontada ay u muujiso dalacaadda 2.

Natiijada garoonka korantada ee barta A:

2. Laba dallacaad q _A = 1 μC iyo q _B = 4 μC waxaa kala fogaada masaafada 4 cm (k = 9 x 10 ⁹ N m ² C ⁻² ). Waa maxay baaxadda goobta korantada ee bartamaha u dhaxaysa q _A iyo q _B.

La yaqaan:

Dalac A (q _A ) = 1 μC = 1 x 10 ⁻⁶ C

Dalac B (q _B ) = 4 μC = 4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ N m ² C ⁻²

Masaafada u dhaxaysa khidmadaha A iyo B (r _AB ) = 4 cm = 0.04 mitir

Masaafada u dhaxaysa dallacaadda A iyo barta dhexe (r _A ) = 0.02 mitir s

Masaafada u dhaxaysa dallacaadda B iyo barta dhexe (r _B ) = 0.02 mitir s

La yaqaan: Cabbirka goobta korantada

Xalka:

Goobta korantada ee lagu soo saaro dallacaadda A barta dhexe:

Dalacaadda tijaabada waa togan tahay, dalacaadda A-na waa togan tahay si jihada goobta korantada ay u tilmaamto dalacaadda B.

Goobta korantada ee ay soo saarto dallacaadda B barta dhexe:

Dalacaadda tijaabada waa togan tahay, dalacaadda B-na waa togan tahay si jihada goobta korantada ay u tilmaamto dalacaadda A.

Natiijada ka dhalatay goobta korantada ee barta dhexe:

E _A iyo E _B waxay leeyihiin jiho liddi ku ah.

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

3. Sida ku cad sawirka hoose, meesha ay ku taal barta P si baaxadda goobta korontada ee barta P ay u noqoto 0? (k = 9 x 10 ⁹ Nm ² C ^{−2 ,} 1 μC = 10 ⁻⁶ C)

Solution

Haddii dhibicda P ay ku taal bidixda Q ₁ ; goobta korontada ee uu soo saaro Q ₁ ee dhibicda P waxay tilmaamaysaa bidixda ( ka fog Q ₁ ) goobta korontada ee uu soo saaro Q ₂ ee dhibicda P waxay tilmaamaysaa midig (tilmaan Q ₁ ). Jihada goobta korontada waa ka soo horjeed si goobta korontada ee dhibicda P = 0.

La yaqaan:

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

Masaafada u dhaxaysa dallacaadda 1 iyo dallacaadda 2 = 3 cm

Masaafada u dhaxaysa Q ₁ iyo barta P (r _1P ) = a

Masaafada u dhaxaysa Q ₂ iyo barta P (r _2P ) = 3 + a

La Doonayo: Booska dhibicda P

Xalka:

Barta P waxay ku taal bidixda Q ₁.

Goobta korantada ee ay soo saarto _Q1 barta P :

Dareeraha tijaabada waa togan yahay Q1 _-na waa togan yahay si jihada goobta korontada ay u socoto dhanka bidix.

Goobta korantada ee ay soo _saarto Q2 barta P :

Dakhli tijaabo ah waa togan yahay Q2 _-na waa taban yahay si jihada goobta korontada ay u socoto dhanka midig.

Natiijada garoonka korantada ee barta A:

Adeegso qaacidada labajibbaaran si aad u hesho:

Masaafada u dhaxaysa Q ₂ iyo barta P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm ama 3 + a = 3 – 9 = -6 cm.

Masaafada u dhaxaysa Q ₁ iyo barta P (r _1P ) = a = -9 cm ama -1.8 cm.

Barta P waxay ku taal 1.2 cm dhanka midig ee Q ₂.

4. Dalacaadda q ₃ waxay ku taal 5 cm dhanka midig ee q ₂ , sida ku cad jaantuska hoose. Waa maxay baaxadda goobta korantada ee dalacaadda q ₃ (1 µC = 10 ^-6 C).

Xalka:

Dakhli q ₃ waa mid togan si jihada goobta korontada ee ku jirta dakhli q ₃ ay u tilmaamto dallacaadda laga jaray q ₂ (E ₂ ) oo ay uga fogaato dallacaadda lagu daray q ₁ (E ₁ ). Natiijada goobta korontada waa wadarta goobaha korontada E ₁ iyo E ₂.

La yaqaan:

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

Dalacaadda q ₂ = 5 µC = -5 x 10 ^-6 Coulombs

Masaafada u dhaxaysa dallacaadda q ₁ iyo dallacaadda q ₃ (r ₁ ) = 15 cm = 0.15 m = 15 x 10 ^-2 mitir

Masaafada u dhaxaysa dallacaadda q ₂ iyo dallacaadda q ₃ (r ₂ ) = 5 cm = 0.05 m = 5 x 10 ^-2 mitir

k = 9 x 10 ⁹ N m ² C ^-2

La Raadinayo: Goobta korontada ee ku xiran q ₃

Xalka:

Goobta korantada 1aad:

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

Goobta korantada 2aad:

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

Natiijada goobta korantada:

Natiijada ka dhalatay goobta korontada ee ku xiran q ₃ :

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

Jihada goobta korontada waxay u jeeddaa dhanka bidix (jihada la mid ah E ₂ ).

5. Laba dallacaad ayaa loo kala saaray sida ku cad jaantuska hoose. Waa maxay goobta korantada ee barta P (k = 9 x 10 ⁹ N m ² C ^-2 )

Solution

La yaqaan:

Dakhli q _A = +2.5 C

Dakhli q _B = -2 C

Masaafada u dhaxaysa dallacaadda q _A iyo barta P (r _A ) = 5 m

Masaafada u dhaxaysa dallacaadda q _B iyo barta P (r _B ) = 2 m

k = 9 x 10 ⁹ N m ² C ^-2

La rabay: baaxadda goobta korantada ee barta P.

Xalka:

Goobta korantada 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

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

Goobta korantada B:

E _B = kq _B / r _B ²

E _B = (9 x 10 ⁹ )(2) / (2) ²

E _B = (18 x 10 ⁹ ) / 4

E _B = 4.5 x 10 ⁹ N/C

Natiijada goobta korantada:

Natiijada goobta korantada ee barta P:

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

Jihada bidix u socota (jihada E _B ).

6. Laba dallacaad Q ₁ = -40 µC iyo Q ₂ = +5 µC sida ku cad jaantuska hoose (k = 9 x 10 ⁹ Nm ² .C ^-2 iyo 1 µC = 10 ^-6 C),. Waa maxay baaxadda goobta korantada ee barta P.

La yaqaan:

Dalacaadda q ₁ = -40 µC = -40 x 10 ^-6 C

Dalacaadda q ₂ = +5 µC = +5 x 10 ^-6 C

Masaafada u dhaxaysa q ₁ iyo barta P (r ₁ ) = 40 cm = 0.4 m = 4 x 10 ^-1 m

Masaafada u dhaxaysa q ₂ iyo barta P (r ₂ ) = 10 cm = 0.1 = 1 x 10 ^-1 m

k = 9 x 10 ⁹ N m ² C ^-2

La rabay: baaxadda goobta korantada ee barta P.

Xalka:

Goobta korantada 1aad:

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

Goobta korantada 2aad:

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

Natiijada goobta korantada:

Natiijada garoonka korantada ee barta 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

Jihada garoonka korontada waxay u jeeddaa dhanka midig (jihada la mid ah E ₂ ).

7. Laba dhibcood oo lagu dallaco sida ku cad sawirka hoose.

Xaggee bay ku taal barta P si baaxadda goobta korantada ee barta P = 0. k = 9.10 ⁹ Nm ² .C ^-2 , 1 µC = 10 ^-6 C.

La yaqaan:

Dakhli 1 (q ₁ ) = -9 µC = -9.10 ^-6 Coulombs

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

Masaafada u dhaxaysa q ₁ iyo q ₂ (r ₁₂ ) = 1 cm

k = 9.10 ⁹ Nm ² .C ^-2

La Doonayo: Booska dhibicda P

Xalka:

E ₁ = baaxadda goobta korantada ee uu soo saaro q ₁ barta P

Jihada E ₁ ilaa q ₁ sababtoo ah q ₁ waa taban.

E ₂ = baaxadda goobta korantada ee uu soo saaro q ₂ barta P

Jihada E ₂ way ka fog tahay q ₂ sababtoo ah q ₂ waa togan.

Goobta korantada ee barta = 0.

Isticmaal qaacidada labajibbaaran:

Masaafada u dhaxaysa P iyo q ₂ = x = 0.5 cm.

Barta P waxay ku taal 0.5 cm dhanka midig q ₂ ama 0.25 cm dhanka bidix q ₁.

8. Sida ku cad sawirka hoose, haddii baaxadda goobta korantada ee barta P = k Q/x ² , markaas x = ….

La yaqaan:

EP = k Q / _x ²

La rabay : x

Xalka:

E ₂ = Cabbirka goobta korantada ee barta P iyadoo la adeegsanayo dallacaadda +32Q

r ₂ = Masaafada u dhaxaysa dallacaadda +32Q iyo dhibicda P = a + x

Isticmaal qaacidada labajibbaaran:

1. Waa maxay garoon koronto?
   • Jawaab: Goob koronto waa gobol ku wareegsan shay la dallacay halkaas oo xoogagga korontada ay la kulmi karaan walxaha kale ee la dallacay. Waa goob vector ah, taasoo la micno ah inay leedahay baaxad iyo jihaba dhinac kasta.
2. Sidee loo go'aamiyaa xoogga gaaska korontada?
   • Jawaab: Xoogga ama baaxadda garoon koronto $E$ meel waxaa lagu qeexaa xoog $F$ khibrad tijaabo oo togan leh q₀​ la dhigay markaas, iyadoo loo qaybinayo baaxadda kharashka tijaabada lafteeda: E=​F/q₀​.
3. Sidee bay garoonka korontada ee ay sababto kharashka dhibcaha u kala duwan yihiin masaafada?
   • Jawaab: Goobta korontada $E$ sabab u ah lacag dhibic ah $Q$ waa mid liddi ku ah labajibbaaranaha masaafada $r$ laga bilaabo dacwadda. Xiriirka waxaa bixiya E=kQ​/r², halkaas oo $k$ waa joogtada Coulomb.
4. Waa maxay jihada garoonka korontada sababtoo ah dallac togan?
   • Jawaab: Goobta korontada ee ay sababto dallac togan waxay si radial ah uga soo baxaysaa dallacaadda. Dallac taban, goobtu waxay si radial ah ugu soo jeeddaa dallacaadda.
5. Sidee ayaad si garaaf ahaan ah ugu matali kartaa goobaha korontada?
   • Jawaab: Goobaha korontada waxaa lagu matali karaa garaaf ahaan iyadoo la adeegsanayo khadadka goobta (ama khadadka xoogga). Jihada goobta meel kasta waxay la jaanqaadaysaa xariiqda goobta ee meeshaas, cufnaanta xariiqyaduna waxay tilmaamaysaa baaxadda goobta.
6. Maxaa ku dhacaya goobta korantada ee ku jirta koontaroolka marka la eego dheelitirka elektaroonigga ah?
   • Jawaab: Gudaha koontaroolka ee dheelitirka elektrostatic-ka, goobta korontadu waa eber. Tani waa sababta oo ah goob kasta oo dibadda ah waxay sababtaa in elektaroono bilaash ah oo ku jira koontaroolka ay dib u qaybiyaan, taasoo joojinaysa goobta dibadda ee gudaha.
7. Sidee bay khadadka goobta korontada u dhaqmaan meel u dhow gees fiiqan oo ka mid ah koontaroolaha?
   • Jawaab: Meel u dhow cidhif fiiqan ama cidhif fiiqan oo ka mid ah koronto-dhaliyaha, khadadka goobta korontada ayaa aad u xoog badan, taasoo horseedaysa garoon koronto oo xooggan oo gobolkaas ah. Tani waa saldhigga hawlgalka aaladaha sida usha hillaaca.
8. Sidee mabaadi'da kor u qaadista loogu dabaqayaa goobaha korontada?
   • Jawaab: Goobta korontada ee ay sababaan dallacaadyo badan oo hal dhibic ah waa wadarta guud ee goobaha korontada ee ka dhasha dallacaad kasta oo shaqsiyeed. Tan waxaa loo yaqaan mabda'a sare u qaadista.
9. Sidee shaqada uu qabto wakiil dibadeed waxay la xiriirtaa goobta korontada marka uu kharash ku dhex wareegayo goobta?
   • JawaabShaqada $W$ waxaa sameeya wakiil dibadeed marka uu wareejinayo lacag $q$ laga bilaabo hal dhibic ilaa mid kale oo ku jirta goobta korontada waxay la mid tahay taban isbeddelka tamarta korontada ee iman karta, taas oo ah $W=q\times \Delta V$, halkaas oo $\Delta V$ waa isbeddelka awoodda korantada.

10. Xariiqyada garoonka korontada ma is dhaafi karaan?

    • Jawaab: Maya, khadadka korontada iskuma gudbi karaan. Haddii ay sidaas sameeyaan, waxay tilmaamaysaa in meesha isgoyska, ay jiraan laba jiho oo kala duwan oo ka mid ah goobta korontada, taas oo aan suurtogal ahayn.