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 ne1/2a pedyo neimwe yemachaji ese ari maviri , hukuru hwesimba remagetsi panzvimbo A hwakaita sei?

Zvinozivikanwa:

Mutengo 1 (q ₁ ) = +Q

Mutengo wechipiri (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 hwesimba remagetsi panzvimbo A (E _A ) = 36 NC ^-1

Zvinodiwa: Hukuru hwesimba remagetsi

Solution:

Danho rekutanga.

Munda wemagetsi unogadzirwa nechaji +Q panzvimbo A :

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

Chaja yemagetsi inogadzirwa nechaja -Q panzvimbo 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:

Nhambwe iri 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 panzvimbo 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. Machaji maviri q _A = 1 μC uye q _B = 4 μC akaparadzaniswa nedaro re 4 cm (k = 9 x 10 ⁹ N m ² C ⁻² ). Chii chiri kukura kwesimba remagetsi pakati pe q _A na q _B.

Zvinozivikanwa:

Chaja A (q _A ) = 1 μC = 1 x 10 ⁻⁶ C

Chaja B (q _B ) = 4 μC = 4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ N m ² C ⁻²

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

Kureba pakati pekuchaja A nenzvimbo yepakati (r _A ) = 0.02 metres s

Daro riri pakati pechaji B nenzvimbo yepakati (r _B ) = 0.02 metres s

Inozivikanwa: 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 naE _B vane divi rakasiyana.

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

3. Zvichienderana nemufananidzo uri pazasi, poindi P iri kupi zvekuti hukuru hwemunda wemagetsi panzvimbo P = 0? (k = 9 x 10 ⁹ Nm ² C ^{−2 ,} 1 μC = 10 ⁻⁶ C)

mhinduro

Kana poindi P iri kuruboshwe rweMubvunzo 1 _; munda wemagetsi unogadzirwa neMubvunzo 1 _papoindi P unonongedzera kuruboshwe ( kure neMubvunzo 1 ₎ uye munda wemagetsi unogadzirwa neMubvunzo 2 _papoindi P unonongedzera kurudyi (nongedzera kuMubvunzo 1 ₎ . Kutungamira kwemunda wemagetsi kwakatarisana zvekuti munda wemagetsi papoindi P = 0.

Zvinozivikanwa:

Mubvunzo ₁ = +9 μC = +9 x 10 ⁻⁶ C

Mubvunzo ₂ = -4 μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Daro riri pakati pekuchaja 1 nekuchaja 2 = 3 cm

Daro riri pakati peQ ₁ nepoindi P (r _1P ) = a

Daro riri pakati peQ ₂ nepoindi P (r _2P ) = 3 + a

Zvinodiwa: Nzvimbo yepoindi P

Solution:

Poindi P iri kuruboshwe rweQ1_.

Munda wemagetsi wakagadzirwa neQ 1 _panzvimbo P :

Chaji yekuyedza iri positive uye Q ₁ iri positive zvekuti divi remagetsi riri kuruboshwe.

Munda wemagetsi _wakagadzirwa neQ2 panzvimbo P :

Chaji yekuyedza iri positive uye Q2 _iri negative kuitira kuti divi remagetsi riri kurudyi.

Mhedzisiro yemunda wemagetsi panzvimbo A:

Shandisa fomura yequadratic kuti uwane:

Daro riri pakati peQ ₂ nepoindi P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm kana 3 + a = 3 – 9 = -6 cm.

Kureba pakati peQ ₁ nepoindi P (r _1P ) = a = -9 cm kana -1.8 cm.

Poindi P iri pa 1.2 cm kurudyi rwe Q ₂.

4. Chaja q ₃ iri pa5 cm kurudyi rweq ₂ , sezvakaratidzwa mumufananidzo uri pazasi. Chii chiri kukura kwesimba remagetsi pachaja q ₃ (1 µC = 10 ^-6 C).

Solution:

Chaji q ₃ yakanaka zvekuti divi remagetsi ari kuchaja q ₃ rinonongedzera ku minus charge q ₂ (E ₂ ) uye kure neplus charge q ₁ (E ₁ ). Mhedzisiro yemagetsi ihuwandu hwemagetsi ari kuchaja E ₁ na E ₂.

Zvinozivikanwa:

Chaji q ₁ = 5 µC = 5 x 10 ^-6 Coulomb

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

Daro riri pakati pekuchaja q ₁ nekuchaja q ₃ (r ₁ ) = 15 cm = 0.15 m = 15 x 10 ^-2 mamita

Daro riri pakati pekuchaja q ₂ nekuchaja q ₃ (r ₂ ) = 5 cm = 0.05 m = 5 x 10 ^-2 mamita

k = 9 x 10 ⁹ N m ² C ^-2

Zvinodiwa: Munda wemagetsi uri kuchajiwa q ₃

Solution:

Munda wemagetsi 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

Munda wemagetsi 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

Mhedzisiro yemunda wemagetsi:

Mhedzisiro yemunda wemagetsi uri pachaji q ₃ :

E = E ₂ – E ₁ = (1.8 x 10 ⁷ ) – (0.2 x 10 ⁷ ) = 1.6 x 10 ⁷ 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 m ² C ^-2 )

mhinduro

Zvinozivikanwa:

Mari q _A = +2.5 C

Mari q _B = -2 C

Daro riri pakati pekuchaja q _A nepoindi P (r _A ) = 5 m

Daro riri pakati pekuchaja q _B nepoindi P (r _B ) = 2 m

k = 9 x 10 ⁹ N m ² C ^-2

Zvinodiwa: hukuru hwesimba remagetsi panzvimbo P.

Solution:

Munda wemagetsi 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

Munda wemagetsi 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

Mhedzisiro yemunda wemagetsi:

Mhedzisiro yemunda wemagetsi panzvimbo P:

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

Kuenda kuruboshwe (kwakafanana nekwaE _B ).

6. Machaji maviri Q ₁ = -40 µC uye Q ₂ = +5 µC sezvakaratidzwa mumufananidzo uri pazasi (k = 9 x 10 ⁹ Nm ² .C ^-2 uye 1 µC = 10 ^-6 C). Chii chiri kukura kwesimba remagetsi panzvimbo P?

Zvinozivikanwa:

Chaji q ₁ = -40 µC = -40 x 10 ^-6 C

Chaji q ₂ = +5 µC = +5 x 10 ^-6 C

Daro riri pakati peq ₁ nepoindi P (r ₁ ) = 40 cm = 0.4 m = 4 x 10 ^-1 m

Daro riri pakati peq ₂ nepoindi P (r ₂ ) = 10 cm = 0.1 = 1 x 10 ^-1 m

k = 9 x 10 ⁹ N m ² C ^-2

Zvinodiwa: hukuru hwesimba remagetsi panzvimbo P.

Solution:

Munda wemagetsi 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

Munda wemagetsi 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

Mhedzisiro yemunda wemagetsi:

Mhedzisiro yemunda wemagetsi panzvimbo 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

Kunongedzwa kwesimba remagetsi kunongedzera kurudyi (kwakafanana nekwaE2 ₎.

7. Mapoinzi maviri ekuchaja sezvakaratidzwa pamufananidzo uri pazasi.

Nzvimbo P iri kupi zvekuti hukuru hwemunda wemagetsi panzvimbo P = 0. k = 9.10 ⁹ Nm ² .C ^-2 , 1 µC = 10 ^-6 C.

Zvinozivikanwa:

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

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

Kureba pakati peq ₁ neq ₂ (r ₁₂ ) = 1 cm

k = 9.10 ⁹ Nm ² .C ^-2

Zvinodiwa: Nzvimbo yepoindi P

Solution:

E ₁ = hukuru hwesimba remagetsi rinogadzirwa neq ₁ panzvimbo P

Kutungamira kweE 1 _kusvika kuq 1 _nekuti q 1 _haina kunaka.

E ₂ = hukuru hwesimba remagetsi rinogadzirwa neq ₂ panzvimbo P

Kuenda kwaE2 kuri kure neq2 nekuti _{q2 yakanaka} ._​

Munda wemagetsi panzvimbo = 0.

Shandisa fomura yequadratic:

Daro riri pakati peP neq ₂ = x = 0.5 cm.

Poindi P iri pa 0.5 cm kurudyi q ₂ kana 0.25 cm kuruboshwe q ₁.

8. Zvichienderana nemufananidzo uri pazasi, kana hukuru hwemunda wemagetsi panzvimbo P = k Q/x ² , ipapo x = ….

Zvinozivikanwa:

EP = k Q / _x ²

Aida: x

Solution:

E ₂ = Hukuru hwesimba remagetsi panzvimbo P nekuchaja +32Q

r ₂ = Daro pakati pekuchaja +32Q uye poindi 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.