Magawo amagetsi - mavuto ndi mayankho

Magawo amagetsi - mavuto ndi mayankho

1. Point A ili pakati pa ma charge awiri. Ma charge onsewa ali ndi kukula kofanana koma chizindikiro chotsutsana ndipo amalekanitsidwa ndi mtunda wa a. Kukula kwa mphamvu yamagetsi pamalo A ndi 36 N/C. Ngati point A isuntha 1/2a pafupi ndi imodzi mwa zonse ziwiri Milandu, kodi kukula kwa munda wamagetsi pa mfundo A?

Zodziwika:

kulipiritsa 1 (q)₁) = +Q

kulipiritsa 2 (q)₂) = -Q

Mtunda pakati pa cholipiritsa 1 ndi mfundo A (r_1A) = ½ a

Mtunda pakati pa cholipiritsa 2 ndi mfundo A (r_2A) = ½ a

Kukula kwa mphamvu yamagetsi pa mfundo A (E_A) = 36 NC^-1

SE basi: Kukula kwa mphamvu yamagetsi

Yankho:

Khwerero 1.

Mphamvu yamagetsi imapangidwa ndi chaji +Q panthawi A :

Choyimitsa choyesera ndi chabwino ndipo choyimitsa 1 ndi chabwino kotero kuti komwe magetsi akupita ku choyimitsa 2.

Chaji yamagetsi imapangidwa ndi chaji -Q panthawi A :

Choyimitsa choyesera ndi chabwino ndipo choyimitsa chachiwiri ndi choipa kotero kuti komwe magetsi akupita ku choyimitsa chachiwiri.

Zotsatira za mphamvu yamagetsi pa mfundo A:

Khwerero 2.

Ngati mfundo A yasunthidwa pafupi ndi chaji 1 ndiye kuti:

Mtunda pakati pa cholipiritsa 1 ndi mfundo A (r_1A) = ¼ a

Mtunda pakati pa cholipiritsa 2 ndi mfundo A (r_2A) = ¾ a

Mphamvu yamagetsi imapangidwa ndi chaji +Q panthawi A :

Choyimitsa choyesera ndi chabwino ndipo choyimitsa 1 ndi chabwino kotero kuti komwe magetsi akupita ku choyimitsa 2.

Mphamvu yamagetsi imapangidwa ndi chaji -Q pa mfundo A :

Choyimitsa choyesera ndi chabwino ndipo choyimitsa chachiwiri ndi choipa kotero kuti komwe magetsi akupita ku choyimitsa chachiwiri.

Zotsatira za mphamvu yamagetsi pa mfundo A:

2. Zolipiritsa ziwiri q_A = 1 μC ndi q_B = 4 μC zimalekanitsidwa ndi mtunda wa 4 cm (k = 9 x 10⁹ N m² C^-2Kodi mphamvu ya magetsi pakati pa q ndi yotani?_A ndi q_B.

Zodziwika:

Ndalama A (q)_A) = 1 μC = 1 x 10^-6 C

Cholipiritsa B (q)_B) = 4 μC = 4 x 10^-6 C

k = 9 x 10⁹ N m² C^-2

Mtunda pakati pa zolipiritsa A ndi B (r)_AB) = 4 cm = 0.04 mamita

Mtunda pakati pa choyimitsa A ndi malo apakati (r_A) = mamita 0.02s

Mtunda pakati pa choyimitsa B ndi malo apakati (r_B) = mamita 0.02s

Zodziwika: Kukula kwa mphamvu yamagetsi

Yankho:

Mphamvu yamagetsi yopangidwa ndi chaji A pakati pa malo:

Choyimitsa choyesera ndi chabwino ndipo choyimitsa A ndi chabwino kotero kuti komwe magetsi akupita ku choyimitsa B.

Mphamvu yamagetsi yopangidwa ndi chaji B pamalo apakati:

Choyimitsa choyesera ndi chabwino ndipo choyimitsa B ndi chabwino kotero kuti komwe magetsi akupita ku choyimitsa A.

Zotsatira za mphamvu yamagetsi pakati pa malo:

E_A ndi E_B khalani ndi mbali yosiyana.

E = E_B - E_A = 9x10 pa^{7 -} 2.25 × 10⁷ = 6.75x10 pa⁷ NC^-1

3. Malinga ndi chithunzi chomwe chili pansipa, mfundo P ili kuti kukula kwa mphamvu yamagetsi pa mfundo P = 0? (k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

Anakonza

Ngati mfundo P ili kumanzere kwa Q₁; mphamvu yamagetsi yopangidwa ndi Q₁ pamalo P malo kumanzere (kutali Q₁) ndi mphamvu yamagetsi yopangidwa ndi Q₂ pamalo P akuloza kumanja (kuloza ku Q₁). Njira ya magetsi ili moyang'anizana kotero kuti magetsi ali pamalo a P = 0.

Zodziwika:

Q₁ = +9 μC = +9 x 10^-6 C

Q₂ = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Mtunda pakati pa chaji 1 ndi chaji 2 = 3 cm

Mtunda pakati Q₁ ndi mfundo P (r_1P) = a

Mtunda pakati Q₂ ndi mfundo P (r)_2P) = 3 + a

Akufuna: Malo a mfundo P

Yankho:

Point P yomwe ili kumanzere kwa Q₁.

Malo amagetsi opangidwa ndi Q₁ panthawi P:

Ndalama zoyeserera ndi zabwino ndipo Q₁ ndi yabwino kotero kuti njira ya magetsi ili kumanzere.

Malo amagetsi opangidwa ndi Q₂ panthawi P :

Ndalama zoyeserera ndi zabwino ndipo Q₂ ndi yoipa kotero kuti njira ya magetsi ili kumanja.

Zotsatira za mphamvu yamagetsi pa mfundo A:

Gwiritsani ntchito njira ya quadratic kuti mupeze:

Mtunda pakati Q₂ ndi mfundo P (r)_2P) = 3 + a = 3 – 1.8 = 1.2 cm kapena 3 + a = 3 – 9 = -6 cm.

Mtunda pakati Q₁ ndi mfundo P (r)_1P) = a = -9 cm kapena -1.8 cm.

Point P ili pa 1.2 masentimita kumanja kwa Q₂.

4. Kulipiritsa q₃ ili pa 5 cm kumanja kwa q₂, monga momwe chithunzi chili pansipa chikusonyezera. Kodi mphamvu ya magetsi yomwe ikuperekedwa ndi yaikulu bwanji q?₃ (1 µC = 10^-6 C).

Yankho:

Ndalama q₃ ndi zabwino kotero kuti njira ya magetsi yomwe ikuyendetsedwa ndi q₃ mfundo za chotsitsa cha q₂ (E₂) ndipo kutali ndi ndalama zowonjezera q₁ (E₁Zotsatira za mphamvu yamagetsi ndi kuchuluka kwa mphamvu yamagetsi E₁ ndi E₂.

Zodziwika:

Ndalama q₁ = 5 µC = 5 x 10^-6 Coulomb

Ndalama q₂ = 5 µC = -5 x 10^-6 Coulomb

Mtunda pakati pa zolipiritsa q₁ ndi kulipira q₃ (r₁) = 15 cm = 0.15 m = 15 x 10^-2 meters

Mtunda pakati pa zolipiritsa q₂ ndi kulipira q₃ (r₂) = 5 cm = 0.05 m = 5 x 10^-2 meters

k = 9 x 10⁹ N m² C^-2

Akufuna: Munda wamagetsi womwe uli pachaji q₃

Yankho:

Munda wamagetsi 1:

E₁ = kq₁ /r₁²

E₁ = (9 x 10⁹)(5 x 10^-6) / (15 x 10^-2)²

E₁ = (45 x 10³) / (225 x 10^-4)

E₁ = 0.2x10 pa⁷ N / C

Munda wamagetsi 2:

E₂ = kq₂ /r₂²

E₂ = (9 x 10⁹)(5 x 10^-6) / (5 x 10^-2)²

E₂ = (45 x 10³) / (25 x 10^-4)

E₂ = 1.8x10 pa⁷ N / C

Zotsatira za gawo lamagetsi:

Zotsatira za mphamvu yamagetsi pa q₃ :

E = E₂ - E₁ = (1.8 x 10⁷) – (0.2 x 10⁷) = 1.6 x 10⁷ N / C

Njira ya magetsi ikuloza kumanzere (njira yomweyi monga E₂).

5. Ma charge awiri alekanitsidwa monga momwe chithunzi chili pansipa chikusonyezera. Kodi gawo lamagetsi pa mfundo P ndi chiyani (k = 9 x 10)⁹ N m² C^-2)

Anakonza

Zodziwika:

Ndalama q_A = +2.5 C

Ndalama q_B = -2 C

Mtunda pakati pa zolipiritsa q_A ndi mfundo P (r_A) = 5 m

Mtunda pakati pa zolipiritsa q_B ndi mfundo P (r_B) = 2 m

k = 9 x 10⁹ N m² C^-2

Akufuna: kukula kwa mphamvu yamagetsi pamalo a P.

Yankho:

Munda wamagetsi A:

E_A = kq_A /r_A²

E_A = (9 x 10⁹)(2.5) / (5)²

E_A = (22.5 x 10⁹/ 25

E_A = 0.9x10 pa⁹ N / C

Munda wamagetsi B:

E_B = kq_B /r_B²

E_B = (9 x 10⁹)(2) / (2)²

E_B = (18 x 10⁹/ 4

E_B = 4.5x10 pa⁹ N / C

Zotsatira za gawo lamagetsi:

Zotsatira za mphamvu yamagetsi pa mfundo P:

E = E_B – EA = (4.5 – 0.9) x 10⁹ = 3.6x10 pa⁹ N / C

Njira yopita kumanzere (njira yomweyi monga E_B).

6. Machaji awiri Q₁ = -40 µC ndi Q₂ = +5 µC monga momwe zasonyezedwera pachithunzi pansipa (k = 9 x 10⁹ Nm².C^-2 ndipo 1 µC = 10^-6 C). Kodi mphamvu ya magetsi pa mfundo P ndi yotani?

Zodziwika:

Ndalama q₁ = -40 µC = -40 x 10^-6 C

Ndalama q₂ = +5 µC = +5 x 10^-6 C

Mtunda pakati pa q₁ ndi mfundo P (r₁) = 40 cm = 0.4 m = 4 x 10^-1 m

Mtunda pakati pa q₂ ndi mfundo P (r₂) = 10 cm = 0.1 = 1 x 10^-1 m

k = 9 x 10⁹ N m² C^-2

Akufuna: kukula kwa mphamvu yamagetsi pamalo a P.

Yankho:

Munda wamagetsi 1:

E₁ = kq₁ /r₁²

E₁ = (9 x 10⁹)(40 x 10^-6) / (4 x 10^-1)²

E₁ = (360 x 10³) / (16 x 10^-2)

E₁ = 22.5x10 pa⁵ N / C

Munda wamagetsi 2:

E₂ = kq₂ /r₂²

E₂ = (9 x 10⁹)(5 x 10^-6) / (1 x 10^-1)²

E₂ = (45 x 10³) / 1 x 10^-2

E₂ = 45x10 pa⁵ N / C

Zotsatira za gawo lamagetsi:

Zotsatira za mphamvu yamagetsi pa mfundo P:

E = E₂ – E1 = (45 – 22.5) x 10⁵ = 22.5x10 pa⁵ N / C

E = 2.25 x 10⁶ N / C

Njira ya magetsi ikuloza kumanja (njira yomweyi monga E)₂).

7. Ma point charge awiri monga momwe zasonyezedwera pachithunzi chili pansipa.

Kodi mfundo P ili kuti kotero kuti kukula kwa mphamvu yamagetsi pa mfundo P = 0. k = 9.10⁹ Nm².C^-2, 1 µC = 10^-6 C.

Zodziwika:

Cholipiritsa 1 (q)₁) = -9 µC = -9.10^-6 Coulomb

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

Mtunda pakati pa q₁ ndi q₂ (r₁₂) = 1 cm

k = 9.10 ndi⁹ Nm².C^-2

Akufuna: Malo a mfundo P

Yankho:

E₁ = kukula kwa mphamvu yamagetsi yopangidwa ndi q₁ pa mfundo P

Malangizo a E₁ ku q₁ chifukwa q₁ ndi negative.

E₂ = kukula kwa mphamvu yamagetsi yopangidwa ndi q₂ pa mfundo P

Malangizo a E₂ kutali q₂ chifukwa q₂ ndi zabwino.

Munda wamagetsi pamalopo = 0.

Gwiritsani ntchito njira ya quadratic:

Mtunda pakati pa P ndi q₂ = x = 0.5 cm.

Mfundo P ili pa 0.5 cm kumanja q₂ kapena 0.25 cm kumanzere q₁.

8. Malinga ndi chithunzi chomwe chili pansipa, ngati kukula kwa mphamvu yamagetsi pa mfundo P = k Q/x², kenako x = ….

Zodziwika:

E_P = k Q / x²

Akufuna: x

Yankho:

E₂ = Kukula kwa mphamvu yamagetsi pamalo P potengera mphamvu +32Q

r₂ = Mtunda pakati pa mphamvu +32Q ndi mfundo P = a + x

Gwiritsani ntchito njira ya quadratic:

1. Kodi munda wamagetsi ndi chiyani?
   • yankho: Munda wamagetsi ndi dera lozungulira chinthu chodzazidwa ndi magetsi komwe mphamvu zamagetsi zimatha kuwonedwa ndi zinthu zina zodzazidwa ndi magetsi. Ndi munda wa vector, zomwe zikutanthauza kuti uli ndi kukula ndi njira pamalo aliwonse.
2. Kodi mphamvu ya magetsi imatsimikiziridwa bwanji?
   • yankho: Mphamvu kapena kukula kwa munda wamagetsi $E$ pa mfundo inayake imafotokozedwa ngati mphamvu $F$ adakumana ndi chindapusa chabwino cha mayeso q₀​ pamalopo, kugawidwa ndi kukula kwa mtengo woyeserera wokha: E=​F/q₀​.
3. Kodi mphamvu yamagetsi chifukwa cha kulipidwa kwa mfundo imasiyana bwanji ndi mtunda?
   • yankho: Malo amagetsi $E$ chifukwa cha ndalama zolipirira $Q$ ndi yofanana kwambiri ndi sikweya ya mtunda $r$ kuchokera ku mlandu. Ubalewu waperekedwa ndi E=kQ/r², kumene $k$ ndi nthawi zonse ya Coulomb.
4. Kodi mphamvu yamagetsi ikupita kuti chifukwa cha mphamvu yabwino?
   • yankho: Mphamvu yamagetsi chifukwa cha mphamvu yabwino yomwe imachokera kunja kuchokera pa mphamvu. Pa mphamvu yoipa, mphamvu yamagetsi imalowera mkati, kupita ku mphamvu.
5. Kodi mungawonetse bwanji malo amagetsi pogwiritsa ntchito zithunzi?
   • yankho: Minda yamagetsi ikhoza kuimiridwa pogwiritsa ntchito mizere yamunda (kapena mizere yamphamvu). Kulunjika kwa munda nthawi iliyonse kumakhala kofanana ndi mzere wamunda pamalopo, ndipo kuchuluka kwa mizere kumasonyeza kukula kwa mundawo.
6. Kodi chimachitika ndi chiyani ku mphamvu yamagetsi mkati mwa kondakitala mu electrostatic equilibrium?
   • yankho: Mkati mwa kondakitala mu electrostatic equilibrium, mphamvu yamagetsi ndi zero. Izi zili choncho chifukwa mphamvu yakunja iliyonse imapangitsa ma elekitironi aulere mu kondakitala kugawanso, zomwe zimapangitsa kuti mphamvu yakunja mkati ichotsedwe.
7. Kodi mizere yamagetsi imayenda bwanji pafupi ndi m'mphepete wakuthwa wa kondakitala?
   • yankho: Pafupi ndi m'mphepete wakuthwa kapena nsonga yolunjika ya kondakitala, mizere yamagetsi imakhala yolimba kwambiri, zomwe zimapangitsa kuti magetsi akhale olimba kwambiri m'derali. Ichi ndiye maziko a magwiridwe antchito a zida monga ndodo yamagetsi.
8. Kodi mfundo za superposition zimagwira ntchito bwanji pamagetsi?
   • yankho: Munda wamagetsi chifukwa cha ma chaji angapo pamalo amodzi ndi chiwerengero cha vekitala cha minda yamagetsi chifukwa cha ma chaji aliwonse. Izi zimadziwika kuti mfundo ya superposition.
9. Kodi ntchito yochitidwa ndi wothandizira wakunja imakhudzana bwanji ndi gawo lamagetsi posuntha chojambulira mkati mwa gawolo?
   • yankho: Ntchitoyo $W$ chochitidwa ndi wothandizira wakunja potumiza ndalama $q$ kuchokera pamalo amodzi kupita kwina mu gawo lamagetsi ndikofanana ndi negative ya kusintha kwa mphamvu yamagetsi, zomwe ndi $W=q\times \Delta V$, kumene $\Delta V$ ndi kusintha kwa mphamvu yamagetsi.

10. Kodi mizere yamagetsi ingadutsenane?

    • yankho: Ayi, mizere yamagetsi singadutse limodzi. Ngati itadutsana, zikutanthauza kuti pamalo olumikizirana, pali njira ziwiri zosiyana za magetsi, zomwe sizingatheke.