Filayen lantarki - matsaloli da mafita

Filayen lantarki - matsaloli da mafita

1. Maki A yana tsakiyar caji biyu. Dukansu caji suna da girma iri ɗaya amma alama ce ta akasin haka kuma an raba su da nisan a. Girman filin lantarki a maki A shine 36 N/C. Idan maki A ya motsa 1/2a kusa da ɗaya daga cikin caji biyu , menene girman filin lantarki a maki A?

An sani:

Caji 1 (q ₁ ) = +Q

Caji 2 (q ₂ ) = -Q

Nisa tsakanin caji 1 da maki A (r _1A ) = ½ a

Nisa tsakanin caji 2 da maki A (r _2A ) = ½ a

Girman filin lantarki a wurin A (E _A ) = 36 NC ^-1

Ana so: Girman filin lantarki

Magani:

Mataki na 1.

Ana samar da filin lantarki ta hanyar caji +Q a wurin A :

Cajin gwaji yana da kyau kuma cajin 1 yana da kyau don haka alkiblar filin lantarki tana nuna caji 2.

Cajin wutar lantarki da aka samar ta hanyar caji -Q a aya ta A :

Cajin gwaji yana da kyau kuma cajin 2 yana da rashin kyau don haka alkiblar filin lantarki tana nuna caji 2.

Sakamakon filin lantarki a wuri na A:

Mataki 2.

Idan aka matsar da maki A kusa da caji 1 to:

Nisa tsakanin caji 1 da maki A (r _1A ) = ¼ a

Nisa tsakanin caji 2 da maki A (r _2A ) = ¾ a

Filin wutar lantarki da aka samar ta hanyar caji +Q a aya ta A :

Cajin gwaji yana da kyau kuma cajin 1 yana da kyau don haka alkiblar filin lantarki tana nuna caji 2.

Filin wutar lantarki da aka samar ta hanyar caji -Q a aya ta A :

Cajin gwaji yana da kyau kuma cajin 2 yana da rashin kyau don haka alkiblar filin lantarki tana nuna caji 2.

Sakamakon filin lantarki a wuri na A:

2. Caji biyu q _A = 1 μC da q _B = 4 μC an raba su da nisan 4 cm (k = 9 x 10 ⁹ N m ² C ⁻² ). Menene girman filin lantarki a tsakiya tsakanin q _A da q _B.

An sani:

Cajin A (qA ₎ = 1 μC = 1 x 10 ⁻⁶ C

Cajin B (qB ₎ = 4 μC = 4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ N m ² C ⁻²

Nisa tsakanin caji A da B (r _AB ) = 4 cm = mita 0.04

Nisa tsakanin caji A da wurin tsakiya (rA ₎ = mita 0.02 a s

Nisa tsakanin caji B da wurin tsakiya (r _B ) = mita 0.02 a s

Sananne: Girman filin lantarki

Magani:

Filin wutar lantarki da aka samar ta hanyar caji A a tsakiyar wurin:

Cajin gwaji yana da kyau kuma cajin A yana da kyau don haka alkiblar filin lantarki tana nuna cajin B.

Filin wutar lantarki da aka samar ta hanyar caji B a tsakiyar wurin:

Cajin gwaji yana da kyau kuma cajin B yana da kyau don haka alkiblar filin lantarki tana nuna cajin A.

Sakamakon filin lantarki a tsakiyar wurin:

E _A da E _B suna da akasin alkibla.

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

3. Bisa ga hoton da ke ƙasa, inda aka sanya wurin P don girman filin lantarki a wurin P = 0? (k = 9 x 10 ⁹ Nm ² C ^{−2 ,} 1 μC = 10 ⁻⁶ C)

Magani

_{Idan maki} P yana gefen hagu na Q1 ; filin lantarki da Q1 ya samar _a gefen P yana nuna hagu ( daga Q1 ₎ kuma filin lantarki da Q2 ya samar a gefen P yana nuna dama (nuna Q1 ₎ . Alkiblar filin lantarkin ta kasance akasin _haka don filin lantarkin da ke gefen P = 0.

An sani:

Q1 = +9 _μC = +9 x 10 ⁻⁶ C

Q2 = -4 _μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Nisa tsakanin caji 1 da caji 2 = 3 cm

Nisa tsakanin Q ₁ da maki P (r _1P ) = a

Nisa tsakanin Q ₂ da maki P (r _2P ) = 3 + a

Ana so: Matsayin maki P

Magani:

Ma'ana ta P tana gefen hagu na Q1_.

Filin wutar lantarki da Q1 _ya samar a aya ta P:

Cajin gwaji yana da kyau kuma Q1 _yana da kyau don haka alkiblar filin lantarki tana zuwa hagu.

Filin wutar lantarki da Q2 _ya samar a wuri na P :

Cajin gwaji yana da kyau kuma Q2 _yana da rashin tabbas don haka alkiblar filin lantarki tana zuwa dama.

Sakamakon filin lantarki a wuri na A:

Yi amfani da dabarar quadratic don nemo:

Nisa tsakanin Q ₂ da maki P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm ko 3 + a = 3 – 9 = -6 cm.

Nisa tsakanin Q ₁ da maki P (r _1P ) = a = -9 cm ko -1.8 cm.

Maki na P yana a 1.2 cm a gefen dama na Q2_.

4. Cajin q ₃ yana a 5 cm dama na q ₂ , kamar yadda aka nuna a cikin hoton da ke ƙasa. Menene girman filin lantarki a caji q ₃ (1 µC = 10 ^-6 C).

Magani:

Cajin q ₃ yana da kyau ta yadda alkiblar filin lantarki a caji q ₃ ke nuna cajin da aka rage q ₂ (E ₂ ) kuma nesa da cajin da aka ƙara q ₁ (E ₁ ). Sakamakon filin lantarki shine jimlar filayen lantarki E ₁ da E ₂.

An sani:

Cajin q ₁ = 5 µC = 5 x 10 ^-6 Coulomb

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

Nisa tsakanin caji q ₁ da caji q ₃ (r ₁ ) = 15 cm = 0.15 m = mita 15 x 10 ^-2

Nisa tsakanin caji q ₂ da caji q ₃ (r ₂ ) = 5 cm = 0.05 m = mita 5 x 10 ^-2

k = 9 x 10 ⁹ N m ² C ^-2

Ana nema: Filin wutar lantarki da ke caji q ₃

Magani:

Filin lantarki na 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

Filin lantarki na 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

Sakamakon filin lantarki:

Sakamakon filin lantarki da ke caji _q3 :

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

Alkiblar filin lantarki tana nuni zuwa ga hagu (daidai da alkiblar E ₂ ).

5. An raba caji biyu kamar yadda aka nuna a cikin hoton da ke ƙasa. Menene filin lantarki a wurin P (k = 9 x 10 ⁹ N m ² C ^-2 )

Magani

An sani:

Cajin q _A = +2.5 C

Cajin q _B = -2 C

Nisa tsakanin caji q _A da maki P (r _A ) = 5 m

Nisa tsakanin caji q _B da maki P (r _B ) = 2 m

k = 9 x 10 ⁹ N m ² C ^-2

Ana so: girman filin lantarki a wurin P.

Magani:

Filin lantarki 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

Filin lantarki na 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

Sakamakon filin lantarki:

Sakamakon filin lantarki a wurin P:

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

Alkiblar zuwa hagu (daidai da alkiblar E _B ).

6. Caji biyu Q ₁ = -40 µC da Q ₂ = +5 µC kamar yadda aka nuna a cikin hoton da ke ƙasa (k = 9 x 10 ⁹ Nm ² .C ^-2 da 1 µC = 10 ^-6 C),. Menene girman filin lantarki a wurin P.

An sani:

Cajin q ₁ = -40 µC = -40 x 10 ^-6 C

Cajin q ₂ = +5 µC = +5 x 10 ^-6 C

Nisa tsakanin q ₁ da maki P (r ₁ ) = 40 cm = 0.4 m = 4 x 10 ^-1 m

Nisa tsakanin q ₂ da maki P (r ₂ ) = 10 cm = 0.1 = 1 x 10 ^-1 m

k = 9 x 10 ⁹ N m ² C ^-2

Ana so: girman filin lantarki a wurin P.

Magani:

Filin lantarki na 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

Filin lantarki na 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

Sakamakon filin lantarki:

Sakamakon filin lantarki a wurin 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

Alkiblar filin lantarki tana nuni zuwa dama (daidai da alkiblar E ₂ ).

7. Cajin maki biyu kamar yadda aka nuna a cikin hoton da ke ƙasa.

Ina aka samo wurin P ta yadda girman filin lantarki a wurin P = 0. k = 9.10 ⁹ Nm ² .C ^-2 , 1 µC = 10 ^-6 C.

An sani:

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

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

Nisa tsakanin q ₁ da q ₂ (r ₁₂ ) = 1 cm

k = 9.10 ⁹ Nm ² .C ^-2

Ana so: Matsayin maki P

Magani:

E ₁ = girman filin lantarki da q ₁ ya samar a wuri na P

Alkiblar E ₁ zuwa q ₁ saboda q ₁ ba ta da kyau.

E ₂ = girman filin lantarki da q ₂ ya samar a wuri na P

Alkiblar E ₂ ba ta da q ₂ saboda q ₂ yana da kyau.

Filin lantarki a wurin = 0.

Yi amfani da dabarar quadratic:

Nisa tsakanin P da q ₂ = x = 0.5 cm.

Maki na P yana a 0.5 cm zuwa dama q ₂ ko 0.25 cm zuwa hagu q ₁.

8. Bisa ga hoton da ke ƙasa, idan girman filin lantarki a wurin P = k Q/x ² , to x = ….

An sani:

EP = k Q / _x ²

Ana so : x

Magani:

E ₂ = Girman filin lantarki a wurin P ta hanyar caji +32Q

r ₂ = Nisa tsakanin caji +32Q da maki P = a + x

Yi amfani da dabarar quadratic:

1. Menene filin lantarki?
   • Amsa: Filin lantarki yanki ne da ke kewaye da wani abu mai caji inda wasu abubuwa masu caji za su iya fuskantar ƙarfin lantarki. Filin vector ne, ma'ana yana da girma da alkibla a kowane wuri.
2. Ta yaya ake tantance ƙarfin filin lantarki?
   • Amsa: Ƙarfi ko girman filin lantarki $E$ a wani lokaci ana ayyana shi a matsayin ƙarfi $F$ an fuskanci cajin gwaji mai kyau q₀​ an sanya shi a wannan lokacin, an raba shi da girman cajin gwajin da kansa: E=​F/q₀​.
3. Ta yaya filin lantarki saboda cajin maki ya bambanta da nisa?
   • Amsa: Filin lantarki $E$ saboda cajin maki $Q$ daidai yake da murabba'in nisa $r$ daga cajin. An bayar da dangantakar ta hanyar E=kQ/r², inda $k$ shine tushen Coulomb na dindindin.
4. Menene alkiblar filin lantarki saboda cajin da ke da kyau?
   • Amsa: Filin lantarki saboda caji mai kyau yana nuna waje daga cajin. Ga caji mai kyau, filin yana nuna ciki, zuwa ga cajin.
5. Ta yaya za ku iya wakiltar filayen lantarki ta hanyar zane-zane?
   • Amsa: Ana iya nuna filayen lantarki ta hanyar zane ta amfani da layukan filin (ko layukan ƙarfi). Alkiblar filin a kowane lokaci tana daidai da layin filin a wannan lokacin, kuma yawan layukan yana nuna girman filin.
6. Me ke faruwa da filin lantarki a cikin na'urar lantarki a cikin ma'aunin lantarki?
   • Amsa: A cikin na'urar lantarki a cikin ma'aunin lantarki, filin lantarki sifili ne. Wannan saboda duk wani filin waje yana sa electrons kyauta a cikin na'urar lantarki su sake rarrabawa, yana soke filin waje da ke ciki.
7. Ta yaya layukan filin lantarki ke aiki kusa da gefen jagora mai kaifi?
   • Amsa: Kusa da gefen mai kaifi ko kuma gefen jagora, layukan filin lantarki sun fi yawa, wanda ke haifar da ƙarfin filin lantarki a wannan yankin. Wannan shine tushen aikin na'urori kamar sandar walƙiya.
8. Ta yaya ƙa'idodin superposition ke aiki a filayen lantarki?
   • Amsa: Filin lantarki da ke faruwa sakamakon caji da yawa a wani wuri shine kawai jimlar filayen lantarki da ke faruwa sakamakon kowane caji. Wannan ana kiransa da ƙa'idar superposition.
9. Ta yaya aikin da wakili na waje ke yi yake da alaƙa da filin lantarki yayin motsa caji a cikin filin?
   • Amsa: Aikin $W$ wani wakili na waje ya yi shi wajen ɗaukar caji $q$ daga wani wuri zuwa wani a cikin filin lantarki daidai yake da mummunan canjin makamashin wutar lantarki, wanda shine $W=q\times \Delta V$, inda $\Delta V$ shine canjin ƙarfin wutar lantarki.

10. Shin layukan filin lantarki za su iya haɗuwa da juna?

    • Amsa: A'a, layukan filin lantarki ba za su iya ratsa juna ba. Idan sun yi, hakan yana nufin cewa a wurin haɗuwa, akwai hanyoyi biyu daban-daban na filin lantarki, wanda ba zai yiwu ba.