Simba remagetsi - matambudziko nemhinduro

Simba remagetsi - matambudziko nemhinduro

1. Tatu mhosva sezvakaratidzwa mumufananidzo uri pazasiChii chinonzi simba remagetsi akasangana nemhosva B. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

Zvinozivikanwa:

q_A = 10 µC = 10 x 10^-6 C = zana^-5 Coulomb

q_B = 10 µC = 10 x 10^-6 = 10^-5 Coulomb

q_C = 20 µC = 20 x 10^-6 = 2 x gumi^-5 Coulomb

r_AB = 0.1 m = 10^-1 m

r_BC = 0.1 m = 10^-1 m

k = 9 x 10⁹ Nm²C^-2

Zvaidiwa: Simba remagetsi rinoonekwa nechaji B

Solution:

Kune masimba maviri emagetsi anoshandiswa pachaji B, iro simba remagetsi riri pakati pechaji A nechaji B. (F_AB) uye zvakare simba remagetsi riri pakati pemari B neC (F_BC). Simba remagetsi rinoonekwa nechaji B rinobva pasimba F_AB uye simba F_BC.

Simba remagetsi riri pakati pechaja A neB:

murandu A iri positive uye charge B iri positive saka ndiyo nzira yairi kuenda F_AB mapoinzi ekuchaja C.

Simba remagetsi riri pakati pechaja B neC:

Chaji B yakanaka uye chaji C yakanaka saka F_BC mapoinzi ekuchaja A.

Simba remagetsi rinoonekwa nechaji B:

F_B =F_BC - F_AB = 180 – 90 = 90 N.

Hukuru hwesimba remagetsi rinoonekwa nechaji B (F_B) is 90 Newtons. Kutungamira kwe F_B zvakafanana nekwakananga F_BC , mapoinzi ekuchaja A.

2. Simba remagetsi riri pacharge B riri kukura sei uye rinotungamira kupi? (k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

Zvinozivikanwa:

Mari A (q)_A) = +Q

Muripo B (q)_B) = -2Q

Mari C (q)_C) = -Q

Daro riri pakati pemari A neB (r)_AB) = r

Daro riri pakati pemari B neC (r)_BC) = 2r

k = 9 x 10⁹ Nm²C^-2

Zvaidiwa: Hukuru uye kutungamira kwesimba remagetsi riri pachaji B.

Solution:

Simba remagetsi riri pakati pechaja A neB:

Chaji A yakanaka uye chaji B yakanaka saka ndiyo nzira yairi kuenda F_AB mapoinzi ekuchaja A.

Simba remagetsi riri pakati pechaja B nechaja C:

Muripo B is negative uye chaji C iri negative saka ndiyo nzira yakananga F_BC mapoinzi ekuchaja A.

Mauto emagetsi anoshanda pabasa rekutonga B:

F = F_AB +F_BC = 2 k Q²/r² + 0.5 k Q²/r² = 2.5 k Q²/r² = 2.5 k Q² r^-2

Kutungamira kwesimba remagetsi kunongedzera kuchaja A (kuruboshwe).

3. Machaji maviri emagetsi, anoratidzwa mumufananidzo uri pazasi. Chaji panzvimbo A i8 µC uye simba remagetsi rinoshanda pachaji dzese i45 N. Kana chaji A ichifamba kurudyi 1 cm, chii chinonzi simba rinokwezva rinoshanda pachaji dzese. k = 9.10⁹ Nm².C^-2.

Zvinozivikanwa:

Chaja yemagetsi panzvimbo A (q)_A) = 8 µC = 8 x 10^-6 Coulomb

Mabasa emagetsi pamhosva dzese dziri mbiri (F) = 45 Newtons

Daro riri pakati pemari dzese dziri mbiri (r)_AB) = 4 cm = 0.04 mamita = 4 x 10^-2 mamita

Nguva dzose (k) = 9 x 10⁹ Nm².C^-2

Zvaidiwa: Simba remagetsi riri pakati pemachaji ese ari maviri kana chaji A ichienda kurudyi 1 cm.

Solution:

Chaja yemagetsi panzvimbo B :

Kuenzanisa kwesimba remagetsi:

F = k (q)_A)(q)_B) / r²

Fr² = k (q)_A)(q)_B)

q_B = Fr² / k (q_A)

Chaja yemagetsi panzvimbo B :

q_B = (45)(4 x 10^-2)² / (9 x 10⁹)(8 x 10^-6)

q_B = (45)(16 x 10^-4) / 72 x 10³

q_B = (720 x 10^-4) / (72 x 10³)

q_B = 10 x gumi^-7 Coulomb

Simba remagetsi riri pakati pechaja dzemagetsi A naB:

Kana chaji paA ichifamba kurudyi 1 cm zvinoreva kuti daro riri pakati pechaji dzese i3 cm = 0.03 metres = 3 x 10^-2 mita.

F = k (q)_A)(q)_B) / r²

F = (9 x 10⁹)(8 x 10^-6)(10 x 10^-7) / (3 x 10^-2)²

F = (9 x 10⁹)(80 x 10^-13) / (9 x 10^-4)

F = (1 x 10⁹)(80 x 10^-13) / (1 x 10^-4)

F = (80 x 10^-4) / (1 x 10^-4)

F = 80 Newton

4. Machaji maviri emagetsi panzvimbo P neQ akaparadzaniswa nedaro re10 cm, sangana nesimba rinokwezva re8 Newton. Kana chaji Q ichifamba 5 cm kuti ichaji P, saka simba remagetsi chii. (1 µC = 10^-6 C na k = 9 x 10⁹ Nm².C^-2).

Zvinozivikanwa:

Kureba pakati pemari P na Q (r)_PQ) = 10 cm = 0.1 m = 1 x 10^-1 m

Simba remagetsi riri pakati pemari P neQ (F) = 8 N

Chaja yemagetsi Q (q)_Q) = 40 µC = 40 x 10^-6 C

Nguva dzose (k) = 9 x 10⁹ Nm².C^-2

Zvaidiwa: Simba remagetsi riri pakati pemachaji P neQ kana chaji Q ikafambiswa 5 cm kuti ichaji P.

Solution:

Kutanga, verenga chaji yemagetsi P, wobva waverenga simba remagetsi pakati pechaji dzese dziri mbiri, kana chaji yemagetsi Q ikafambiswa ne5 cm kuti ichaji P.

Chaja yemagetsi P :

q_P = Fr² / k (q_Q)

q_P = (8)(1 x 10^-1)² / (9 x 10⁹)(40 x 10^-6)

q_P = (8)(1 x 10^-2) / 360 x 10³

q_P = (8 x 10^-2) / (36 x 10⁴)

q_P = (1 x 10^-2) / (4.5 x 10⁴)

q_P = (1 / 4.5) x 10^-6 Coulomb

Simba remagetsi riri pakati pechaja dzemagetsi P na Q:

Kana chaji panhamba Q ikafambiswa 5 cm kuruboshwe, ipapo daro riri pakati pechaji dzese i5 cm = 0.05 metres = 5 x 10^-2 mamita

F = k (q)_P)(q)_Q) / r²

F = (9 x 10⁹)((1 / 4.5) x 10^-6)(40 x 10^-6) / (5 x 10^-2)²

F = (2 x 10³)(40 x 10^-6) / (25 x 10^-4)

F = (80 x 10^-3) / (25 x 10^-4)

F = 3.2 x 10¹

F = 32 Newton

5. Simba remagetsi rinowanikwa nechaji q_B iri 8 N (1 µC = 10^-6 C na k = 9.10⁹ Nm².C^-2Kana muripo q_B yafamba 4 cm kubva kuA, saka chii chinonzi simba remagetsi rinoonekwa neq?_B.

Zvinozivikanwa:

Daro riri pakati pemari A neB (r)_AB) = 2 cm = 0.02 m = 2 x 10^-2 m

Simba remagetsi riri pakati pemari A neB (F) = 8 N

Chaja yemagetsi A (q)_A) = 2 µC = 2 x 10^-6 C

Nguva dzose (k) = 9 x 10⁹ Nm².C^-2

Zvaidiwa: Simba remagetsi riri pakati pechaja A neB kana daro riri pakati pechaja dzese dziri 4 cm.

Solution:

Kutanga, verenga chaji yemagetsi B, wobva waverenga simba remagetsi pakati pechaji dzese, kana daro rechaji dzese dziri 4 cm = 0.04 metres = 4 x 10^-2 mita.

Chaja yemagetsi pa B :

q_B = Fr² / k (q_A)

q_B = (8)(2 x 10^-2)² / (9 x 10⁹)(2 x 10^-6)

q_B = (8)(4 x 10^-4) / (18 x 10³)

q_B = (32 x 10^-4) / (18 x 10³)

q_B = (32/18) x 10^-7

qB = (16/9) x 10^-7 Coulomb

Simba remagetsi riri pakati pechaja A neB:

F = k (q)_A)(q)_B) / r²

F = (9 x 10⁹)(2 x 10^-6)((16/9) x 10^-7) / (4 x 10^-2)²

F = (18 x 10³)((16/9) x 10^-7) / (16 x 10^-4)

F = (2 x 10³)(16 x 10^-7) / (16 x 10^-4)

F = (2 x 10³)(1 x 10^-7) / (1 x 10^-4)

F = (2 x 10^-4) / (1 x 10^-4)

F = 2 Newton

6. Machaji matatu A, B naC sezvakaratidzwa mumufananidzo uri pazasi. AB = BC = 20 cm uye machaji akafanana (q = 2µC). k = 9.10⁹ Nm².C^-2, 1 µ = 10^-6Chii chiri kukura kwesimba remagetsi panzvimbo B?

Zvinozivikanwa:

Chaja panzvimbo A (q)_A) = 2 µC = 2 x 10^-6 Coulomb

Chaja panzvimbo B (q)_B) = 2 µC = 2 x 10^-6 Coulomb

Chaja panzvimbo C (q)_C) = 2 µC = 2 x 10^-6 Coulomb

Nhambwe kubva paB kusvika paC (r)_BC) = 20 cm = 0.2 mamita = 2 x 10^-1 mamita

Nhambwe kubva paB kusvika paA (r)_BA) = 20 cm = 0.2 mamita = 2 x 10^-1 mamita

k = zana⁹ Nm².C^-2

Zvaidiwa: Hukuru hwesimba remagetsi hunoshanda panzvimbo B

Solution:

Simba remagetsi riri pakati pemachaji panzvimbo B neC:

F_BC = k (q)_B)(q)_C) / r_BC²

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

F_BC = (9 x 10⁹)(4 x 10^-12) / (4 x 10^-2)

F_BC = (36 x 10^-3) / (4 x 10^-2)

F_BC = 9 x gumi^-1

F_BC = 0.9 Newton

Machaji emagetsi panzvimbo B neC akanaka zvekuti simba remagetsi F rinoenda mberi._BC kuruboshwe kure nepoindi C.

Simba remagetsi riri pakati pemachaji panzvimbo B neA:

F_BA = k (q)_B)(q)_A) / r_BA²

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

F_BA = (9 x 10⁹)(4 x 10^-12) / (4 x 10^-2)

F_BA = (36 x 10^-3) / (4 x 10^-2)

F_BA = 9 x gumi^-1

F_BA = 0.9 Newton

Machaji emagetsi panzvimbo B neA akanaka zvekuti simba remagetsi F rinoenda mberi._BA pasi, kure nenzvimbo A.

Mhedzisiro yemasimba emagetsi:

7. Mari nhatu Q₁,Q₂, uye Q₃ sezvakaratidzwa mumufananidzo uri pazasi. Kureba kweAB = kureba kweBC = 30 cm. Anozivikanwa: k = zana⁹ Nm².C^-2 uye 1 µ = 10^-6 zvino mhedzisiro yesimba remagetsi riripo Q₁.

Zvinozivikanwa:

Chaja panzvimbo A (q)_A) = 3 µC = 3 x 10^-6 Coulomb 

Chaja panzvimbo B (q)_B) = -10 µC = -10 x 10^-6 Coulomb

Chaja panzvimbo C (q)_C) = 4 µC = 4 x 10^-6 Coulomb

Nhambwe kubva paB kusvika paC (r)_BC) = 30 cm = 0.3 mamita = 3 x 10^-1 mamita

Nhambwe kubva paB kusvika paC (r)_BA) = 30 cm = 0.3 mamita = 3 x 10^-1 mita s

k = zana⁹ Nm².C^-2

Zvaidiwa: Mhedzisiro yesimba remagetsi panzvimbo B

Solution:

Simba remagetsi riri pakati pemachaji panzvimbo B neC:

F_BC = k (q)_B)(q)_C) / r_BC²

F_BC = (9 x 10⁹)(10 x 10^-6)(4 x 10^-6) / (3 x 10^-1)²

F_BC = (9 x 10⁹)(40 x 10^-12) / (9 x 10^-2)

F_BC = (360 x 10^-3) / (9 x 10^-2)

F_BC = 40 x gumi^-1

F_BC = 4 Newton

Chaja yemagetsi panzvimbo B haina kunaka uye chaja yemagetsi panzvimbo C yakanaka, saka ndiyo nzira yesimba remagetsi F_BC kurudyi, kunongedza C.

Simba remagetsi riri pakati pemachaji panzvimbo B neA:

F_BA = k (q)_B)(q)_A) / r_BA²

F_BA = (9 x 10⁹)(10 x 10^-6)(3 x 10^-6) / (3 x 10^-1)²

F_BA = (9 x 10⁹)(30 x 10^-12) / (9 x 10^-2)

F_BA = (270 x 10^-3) / (9 x 10^-2)

F_BA = 30 x gumi^-1

F_BA = 3 Newton

Chaja yemagetsi panzvimbo B haina kunaka uye chaja yemagetsi panzvimbo A yakanaka, saka ndiyo nzira yesimba remagetsi F_BA kumusoro kusvika panzvimbo A.

Mhedzisiro yesimba remagetsi:

1. Chii chinonzi simba remagetsi? mhinduro: Simba remagetsi isimba guru rinoitika pakati pezvinhu nekuda kwekuchaja kwaro kwemagetsi. Rinogona kukwezva (pakati pekuchaja kwakatarisana) kana kutsamwisa (pakati pekuchaja kwakafanana).
2. Ukuru hwesimba remagetsi riri pakati pemapoinzi maviri hunoonekwa sei? mhinduro: Hukuru hwesimba remagetsi riri pakati pemapoinzi maviri hunopihwa nemutemo waCoulomb. Hunoenderana zvakananga nechibereko chehukuru hwemapoinzi uye hunoenderana nechikamu chedaro riri pakati pawo. F=kx q₁​x q₂​/ r², apo $k$ ndiyo nguva dzose yaCoulomb.
3. Chii chinoitika kumagetsi kana daro riri pakati pekuchaja mbiri rikapetwa kaviri? mhinduro: Kana daro riri pakati pekuchaja mbiri rikapetwa kaviri, simba remagetsi rinova chikamu chimwe muzvina chehuwandu hwaro hwepakutanga, nekuti simba racho rinosiyana zvakasiyana zvichienderana neskweya yedaro.
4. Simba remagetsi rinoenzaniswa sei nesimba rinokwevera zvinhu pasi? mhinduro: Masimba emagetsi anogona kukwezva uye kunyangadza, nepo masimba egiravhiti achingokwezva chete. Pamusoro pezvo, pazvinhu zvakajairika uye daro, masimba emagetsi anowanzova akasimba kupfuura masimba egiravhiti, tichifunga kuti masimba egiravhiti haana simba zvakanyanya kana tichienzanisa nesimba remagetsi.
5. Ndeipi nheyo ye superposition maererano nemasimba emagetsi? mhinduro: Nheyo ye superposition inoti simba remagetsi rine simba guru pachaji inokonzerwa nekuunganidzwa kwemamwe machaji ndiyo vhekitori yesimba rinoitwa nechaji yega yega inotorwa zvakasiyana.
6. Sei tisinganzwi masimba emagetsi ari muzvinhu zvezuva nezuva kunyangwe zvakagadzirwa nezvidimbu zvinochajwa? mhinduro: Zvinhu zvezuva nezuva zvinowanzova zvisina simba remagetsi, zvichireva kuti zvine huwandu hwakaenzana hwechaji dzakanaka nedzisina simba. Masimba ari pakati pechaji idzi anoenzana, saka simba remagetsi remagetsi harisi zero.
7. Kuisa pasi kunokanganisa sei simba remagetsi pachinhu chakachajwa? mhinduro: Kudzika pasi kwechinhu chakachajwa kunoita kuti chaji ifambe pakati pechinhu nePasi kusvika chinhu chacho chapera simba, zvichibvisa simba remagetsi pachinhu chacho nekuda kwekuchajwa kwacho kwekutanga.
8. Simba remagetsi rinogona kushanda mu vacuum here? mhinduro: Ehe, simba remagetsi rinogona kushanda mu vacuum. Haridi nzira yekufambisa zvinhu. Izvi zvinoonekwa kubva panzira iyo minda yemagetsi inogona kuvapo uye inokanganisa zvidimbu zvine chaji muchadenga.
9. Basa rei rinoitwa nemagetsi asingachinji (kana kuti mvumo yenzvimbo yakasununguka) pakusarudza simba remagetsi? mhinduro: Chinogadzika chemagetsi, chinozivikanwawo sechinogadzika chenzvimbo yakasununguka, chinokanganisa simba remagetsi pakati pemachaji. Chinogadzika chakakwirira chingareva simba remagetsi risina simba, uye zvinopesana. Chinogadzika chaCoulomb, $k$, ine chekuita nehukuru uhwu se k=1/4πε₀​​.

10. Kana mhosva mbiri dziri kufamba zvichienderana, simba riri pakati padzo rinochinja here? mhinduro: Kana machaji maviri achifamba zvichienderana, anogona kugadzira magineti pamwe chete neminda yemagetsi. Izvi zvinoreva kuti kudyidzana pakati pemachaji anofamba hakuzongokonzerwa chete nemasimba emagetsi asiwo masimba emagnetic. Kudyidzana kwakabatana kunotsanangurwa nesimba remagetsi. Saka, nepo simba remagetsi rinokonzerwa nemachaji risingachinji nekuti riri kufamba, simba rese rinogona kuchinja nekuda kwemhedzisiro yemagineti.