Minda yemagetsi - matambudziko nemhinduro

Minda yemagetsi - matambudziko nemhinduro

1. Poindi A iri pakati pemachaji maviri. Machaji ese ari maviri ane hukuru hwakafanana asi chiratidzo chakatarisana uye akaparadzaniswa nedaro re a. Hukuru hwesimba remagetsi panzvimbo A i36 N/C. Kana poindi A ichifamba ne 1/2a pedyo nechimwe chezvose zviri zviviri mhosva, hukuru hwei hwe munda wemagetsi padanho A?

Zvinozivikanwa:

murandu 1 (q)₁) = +Q

murandu 2 (q)₂) = -Q

Daro riri pakati pekuchaja 1 nepoindi A (r_1A) = ½ a

Daro riri pakati pekuchaja 2 nepoindi A (r_2A) = ½ a

Hukuru hwemunda wemagetsi panzvimbo A (E_A) = 36 NC^-1

Kuda: Hukuru hwemunda wemagetsi

Solution:

Step 1.

Munda wemagetsi unogadzirwa nekuchaja +Q panguva A :

Chaji yekuyedza iri positive uye chaji yekutanga iri positive kuitira kuti divi remagetsi rienderane nechaji yechipiri.

Chaja yemagetsi inogadzirwa nechaja -Q panguva A :

Chaji yekuyedza iri positive uye chaji yechipiri iri negative zvekuti divi remagetsi rinonongedzera kuchaji yechipiri.

Mhedzisiro yemunda wemagetsi panzvimbo A:

Step 2.

Kana poindi A ikaswededzwa pedyo nechaji 1 saka:

Daro riri pakati pekuchaja 1 nepoindi A (r)_1A) = ¼ a

Daro riri pakati pekuchaja 2 nepoindi A (r_2A) = ¾ a

Munda wemagetsi unogadzirwa nechaji +Q panguva A :

Chaji yekuyedza iri positive uye chaji yekutanga iri positive kuitira kuti divi remagetsi rienderane nechaji yechipiri.

Munda wemagetsi unogadzirwa nechaji -Q panzvimbo A :

Chaji yekuyedza iri positive uye chaji yechipiri iri negative zvekuti divi remagetsi rinonongedzera kuchaji yechipiri.

Mhedzisiro yemunda wemagetsi panzvimbo A:

2. Mari mbiri q_A = 1 μC uye q_B = 4 μC dzakaparadzaniswa nedaro re4 cm (k = 9 x 10⁹ N m² C^-2). Chii chiri kukura kwesimba remagetsi pakati pe q?_A uye q_B.

Zvinozivikanwa:

Mari A (q)_A) = 1 μC = 1 x 10^-6 C

Muripo B (q)_B) = 4 μC = 4 x 10^-6 C

k = 9 x 10⁹ N m² C^-2

Daro riri pakati pemari A neB (r)_AB) = 4 cm = 0.04 metres

Daro riri pakati pechaja A nenzvimbo yepakati (r_A) = 0.02 mamitas

Daro riri pakati pechaji B nenzvimbo yepakati (r_B) = 0.02 mamitas

Anozivikanwa: Hukuru hwemunda wemagetsi

Solution:

Munda wemagetsi unogadzirwa nechaji A panzvimbo yepakati:

Chaji yekuyedza iri positive uye chaji A iri positive kuitira kuti divi remagetsi rionekwe pachaji B.

Munda wemagetsi unogadzirwa nechaji B panzvimbo yepakati:

Chaji yekuyedza ine simba uye chaji B ine simba zvekuti divi remagetsi rinonongedzera kuchaji A.

Mhedzisiro yemunda wemagetsi uri pakati penzvimbo:

E_A uye E_B vane divi rakasiyana.

E = E_B - E_A = 9 x gumi^{7 -} 2.25 X 10⁷ = 6.75 x gumi⁷ NC^-1

3. Zvichienderana nemufananidzo uri pazasi, poindi P iri kupi zvekuti hukuru hwemunda wemagetsi papoindi P = 0? (k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

mhinduro

Kana poindi P iri kuruboshwe rwe Q₁; munda wemagetsi unogadzirwa ne Q₁ panzvimbo P panongedzwa kuruboshwe (kure kure Q₁) uye simba remagetsi rinogadzirwa ne Q₂ panzvimbo P inonongedzera kurudyi (nongedzera kurudyi Q₁). Kutungamira kwemunda wemagetsi kwakatarisana zvekuti munda wemagetsi uri panzvimbo P = 0.

Zvinozivikanwa:

Q₁ = +9 μC = +9 x 10^-6 C

Q₂ = -4 μC = -4 x 10^-6 C

k = 9 x 10⁹ Nm²C^-2

Daro riri pakati pekuchaja 1 nekuchaja 2 = 3 cm

Distance between Q₁ uye poindi P (r_1P) = a

Distance between Q₂ uye point P (r)_2P) = 3 + a

Zvaidiwa: Nzvimbo yepoindi P

Solution:

Nzvimbo P iri kuruboshwe rwe Q₁.

Munda wemagetsi unogadzirwa ne Q₁ panguva P :

Mari yekuyedza iri positive uye Q₁ zvakanaka zvekuti divi remagetsi riri kuruboshwe.

Munda wemagetsi unogadzirwa ne Q₂ panguva P :

Mari yekuyedza iri positive uye Q₂ iri negative zvekuti divi remagetsi riri kurudyi.

Mhedzisiro yemunda wemagetsi panzvimbo A:

Shandisa fomura yequadratic kuti uwane:

Distance between Q₂ uye point P (r)_2P) = 3 + a = 3 – 1.8 = 1.2 cm kana 3 + a = 3 – 9 = -6 cm.

Distance between Q₁ uye point P (r)_1P) = a = -9 cm kana -1.8 cm.

Point P iri pa 1.2 masendimita kurudyi rwe Q₂.

4. Mari yekuchaja q₃ iri pa5 cm kurudyi rwe q₂, sezvakaratidzwa mumufananidzo uri pazasi. Chii chiri kukura kwesimba remagetsi pachaji q₃ (1 µC = 10^-6 C).

Solution:

Muripo q₃ zvakanaka zvekuti divi remagetsi riri pachaji q₃ kunongedzera kune minus charge q₂ (E₂) uye kure nekuwedzera muripo q₁ (E₁). Mugumisiro wemunda wemagetsi ihuwandu hwemunda wemagetsi E₁ uye E₂.

Zvinozivikanwa:

Muripo q₁ = 5 µC = 5 x 10^-6 Coulomb

Muripo q₂ = 5 µC = -5 x 10^-6 Coulomb

Daro pakati pemari q₁ uye muripo q₃ (r₁) = 15 cm = 0.15 m = 15 x 10^-2 mamita

Daro pakati pemari q₂ uye muripo q₃ (r₂) = 5 cm = 0.05 m = 5 x 10^-2 mamita

k = 9 x 10⁹ N m² C^-2

Zvaidiwa: Munda wemagetsi uri kuchajiwa q₃

Solution:

Munda wemagetsi 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 = 0.2 x gumi⁷ N / C.

Munda wemagetsi 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 = 1.8 x gumi⁷ N / C.

Mhedzisiro yemunda wemagetsi:

Mhedzisiro yemunda wemagetsi uri kuchajiwa q₃ :

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

Kutungamira kwesimba remagetsi kunongedzera kuruboshwe (kwakafanana nekwaE₂).

5. Machaji maviri akaparadzaniswa sezvakaratidzwa mumufananidzo uri pazasi. Chii chinonzi simba remagetsi panzvimbo P (k = 9 x 10)⁹ N m² C^-2)

mhinduro

Zvinozivikanwa:

Muripo q_A = +2.5 C

Muripo q_B = -2 C

Daro pakati pemari q_A uye poindi P (r)_A) = 5 m

Daro pakati pemari q_B uye poindi P (r)_B) = 2 m

k = 9 x 10⁹ N m² C^-2

Zvaidiwa: hukuru hwemunda wemagetsi panzvimbo P.

Solution:

Munda wemagetsi 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 = 0.9 x gumi⁹ N / C.

Munda wemagetsi B:

E_B = kq_B /r_B²

E_B = (9 x 10⁹)(2) / (2)²

E_B = (18 x 10⁹/ 4

E_B = 4.5 x gumi⁹ N / C.

Mhedzisiro yemunda wemagetsi:

Mhedzisiro yemunda wemagetsi panzvimbo P:

E = E_B – EA = (4.5 – 0.9) x 10⁹ = 3.6 x gumi⁹ N / C.

Kuenda kuruboshwe (kwakafanana nekwaE)_B).

6. Mhosva mbiri Q₁ = -40 µC uye Q₂ = +5 µC sezvakaratidzwa mumufananidzo uri pazasi (k = 9 x 10⁹ Nm².C^-2 uye 1 µC = 10^-6 C). Chii chiri kukura kwesimba remagetsi panzvimbo P?

Zvinozivikanwa:

Muripo q₁ = -40 µC = -40 x 10^-6 C

Muripo q₂ = +5 µC = +5 x 10^-6 C

Kureba pakati pe q₁ uye poindi P (r)₁) = 40 cm = 0.4 m = 4 x 10^-1 m

Kureba pakati pe q₂ uye poindi P (r)₂) = 10 cm = 0.1 = 1 x 10^-1 m

k = 9 x 10⁹ N m² C^-2

Zvaidiwa: hukuru hwemunda wemagetsi panzvimbo P.

Solution:

Munda wemagetsi 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 = 22.5 x gumi⁵ N / C.

Munda wemagetsi 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 = 45 x gumi⁵ N / C.

Mhedzisiro yemunda wemagetsi:

Mhedzisiro yemunda wemagetsi panzvimbo P:

E = E₂ – E1 = (45 – 22.5) x 10⁵ = 22.5 x gumi⁵ N / C.

E = 2.25 x 10⁶ N / C.

Kwakanangana nemagetsi kunongedzera kurudyi (kwakafanana nekwaE₂).

7. Mapoinzi maviri ekuchaja sezvakaratidzwa pamufananidzo uri pazasi.

Nzvimbo P iri kupi zvekuti hukuru hwemunda wemagetsi panhamba P = 0. k = 9.10⁹ Nm².C^-2, 1 µC = 10^-6 C.

Zvinozivikanwa:

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

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

Kureba pakati pe q₁ uye q₂ (r₁₂) = 1 cm

k = zana⁹ Nm².C^-2

Zvaidiwa: Nzvimbo yepoindi P

Solution:

E₁ = hukuru hwesimba remagetsi rinogadzirwa ne q₁ panzvimbo P

Kutungamira kwe E₁ to q₁ nekuti q₁ hazvina kunaka.

E₂ = hukuru hwesimba remagetsi rinogadzirwa ne q₂ panzvimbo P

Kutungamira kwe E₂ kure kure q₂ nekuti q₂ ari positive.

Munda wemagetsi panzvimbo = 0.

Shandisa fomura yequadratic:

Kureba pakati peP naQ₂ = x = 0.5 cm.

Poindi P iri pa 0.5 cm kurudyi q₂ kana 0.25 cm kuruboshwe q₁.

8. Zvichienderana nemufananidzo uri pazasi, kana hukuru hwemunda wemagetsi panzvimbo P = k Q/x², wobva x = ….

Zvinozivikanwa:

E_P = k Q / x²

Zvaidiwa: x

Solution:

E₂ = Hukuru hwesimba remagetsi panzvimbo P nechaji +32Q

r₂ =Kureba pakati pekuchaja +32Q nepoindi P = a + x

Shandisa fomura yequadratic:

1. Chii chinonzi munda wemagetsi?
   • mhinduro: Munda wemagetsi inzvimbo yakatenderedza chinhu chakachajwa uko masimba emagetsi anogona kuonekwa nezvimwe zvinhu zvakachajwa. Munda wemagetsi, zvichireva kuti une hukuru uye gwara panzvimbo imwe neimwe.
2. Simba remunda wemagetsi rinoonekwa sei?
   • mhinduro: Simba kana hukuru hwemunda wemagetsi $E$ pane imwe nguva inotsanangurwa sesimba $F$ vakasangana nemhosva yekuongororwa zvakanaka q₀​ yakaiswa panzvimbo iyoyo, yakakamurwa nehukuru hwechaji yekuedza pachayo: E=​F/q₀​.
3. Simba remagetsi rinosiyana sei nekuda kwekuchaja kwepoindi zvichienderana nedaro?
   • mhinduro: Munda wemagetsi $E$ nekuda kwekubhadhariswa kwepoindi $Q$ inoenderana nechikamu chedaro $r$ kubva pakupomerwa. Hukama hwacho hunopihwa na E=kQ/r², apo $k$ ndiyo nguva dzose yaCoulomb.
4. Ndeipi nzira yemagetsi iri kumberi nekuda kwekuchaja kwakanaka?
   • mhinduro: Munda wemagetsi unobva pakuchaja kwakanaka kunobuda nepakati kubva pakuchaja. Kana paine chaja isina kunaka, munda wacho unobuda nepakati, uchienda kune chaja.
5. Ungaratidza sei minda yemagetsi nemifananidzo?
   • mhinduro: Minda yemagetsi inogona kuratidzwa nemifananidzo uchishandisa mitsetse yemunda (kana mitsetse yesimba). Kutungamira kwemunda chero kupi zvako kwakabatana nemutsetse wemunda panzvimbo iyoyo, uye huwandu hwemitsetse hunoratidza hukuru hwemunda.
6. Chii chinoitika kumunda wemagetsi uri mukati memuchina wemagetsi uri muchiyero chemagetsi?
   • mhinduro: Mukati memuchina wemagetsi uri muchiyero chemagetsi, munda wemagetsi hauna kukwana. Izvi zvinodaro nekuti chero munda wekunze unokonzera maerekitironi akasununguka ari muchina wemagetsi kuti aenderane patsva, zvichibvisa munda wekunze uri mukati.
7. Mitsetse yemagetsi inoshanda sei pedyo nemucheto wakapinza wemuchina wekufambisa magetsi?
   • mhinduro: Pedyo nemucheto wakapinza kana muromo wakapinza wemuchina wekufambisa magetsi, mitsetse yemagetsi inonyanya kusimba, zvichiita kuti pave nemagetsi akasimba munzvimbo iyoyo. Iyi ndiyo hwaro hwekushanda kwemidziyo yakaita setsvimbo yemheni.
8. Nheyo dze superposition dzinoshanda sei kuminda yemagetsi?
   • mhinduro: Munda wemagetsi unokonzerwa nekuchaja kwakawanda panguva imwe chete ingori vhekita yeminda yemagetsi inokonzerwa nekuchaja kwega kwega. Izvi zvinozivikanwa sepfungwa ye superposition.
9. Basa rinoitwa nechinhu chekunze rinoenderana sei nemagetsi pakufambisa chaji mukati memunda?
   • mhinduro: Basa racho $W$ zvinoitwa nemumiriri wekunze pakufambisa chaji $q$ kubva pane imwe nzvimbo kuenda kune imwe mumunda wemagetsi zvakaenzana ne negative yekuchinja kwesimba remagetsi, izvo zviri $W=q\times \Delta V$, apo $\Delta V$ ndiko kuchinja kwesimba remagetsi.

10. Mitsetse yemagetsi inogona kuyambukana here?

    • mhinduro: Kwete, mitsetse yemagetsi haigone kuyambukana. Kana zvikadaro, zvinoreva kuti panzvimbo inoungana magetsi, pane mativi maviri akasiyana emagetsi, izvo zvisingaite.