Lub zog fais fab - cov teeb meem thiab cov kev daws teeb meem

Lub zog fais fab - cov teeb meem thiab cov kev daws teeb meem

1. peb nqi raws li pom hauv daim duab hauv qab no. Dab tsi yog qhov lub zog hluav taws xob tau ntsib los ntawm tus neeg them nqi B. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

Paub:

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

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

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

r_AB = 0.1 m = 10^-1 m

r_BC = 0.1 m = 10^-1 m

k = 9 x 10⁹ Nm²C^-2

Xav tau: Lub zog fais fab uas raug los ntawm tus nqi B

Tshuaj:

Muaj ob lub zog hluav taws xob ua rau lub zog B, uas yog lub zog hluav taws xob ntawm lub zog A thiab lub zog B (F_AB) thiab lub zog hluav taws xob ntawm cov nqi B thiab C (F_BC). Lub zog hluav taws xob uas raug los ntawm tus nqi B yog qhov tshwm sim ntawm lub zog F_AB thiab lub zog F_BC.

Lub zog hluav taws xob ntawm cov nqi A thiab B:

them A yog qhov zoo thiab tus nqi B yog qhov zoo yog li ntawd yog qhov kev taw qhia ntawm F_AB cov ntsiab lus kom them C.

Lub zog hluav taws xob ntawm cov nqi B thiab C:

Tus nqi B yog qhov zoo thiab tus nqi C yog qhov zoo yog li ntawd F_BC cov ntsiab lus kom them A.

Lub zog fais fab uas raug them los ntawm tus nqi B:

F_B =F_BC - F_AB = 180 – 90 = 90 N.

Qhov loj ntawm lub zog hluav taws xob uas tus nqi B raug (F_B) is 90 Newton. Qhov kev taw qhia ntawm F_B yog tib yam li qhov kev taw qhia ntawm F_BC , cov ntsiab lus kom them A.

2. Lub zog hluav taws xob ntawm lub zog B muaj qhov loj thiab qhov kev taw qhia li cas. (k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

Paub:

Them A (q_A) = +Q

Tus nqi B (q_B) = -2Q

Them C (q_C) = -Q

Qhov nrug ntawm cov nqi A thiab B (r)_AB) = r

Qhov nrug ntawm cov nqi B thiab C (r)_BC) = 2r

k = 9 x 10⁹ Nm²C^-2

Xav tau: Qhov loj thiab qhov kev taw qhia ntawm lub zog hluav taws xob ntawm tus nqi B.

Tshuaj:

Lub zog hluav taws xob ntawm cov nqi A thiab B:

Tus nqi A yog qhov zoo thiab tus nqi B yog qhov zoo yog li ntawd yog qhov kev taw qhia ntawm F_AB cov ntsiab lus kom them A.

Lub zog hluav taws xob ntawm tus nqi B thiab tus nqi C:

Tus Nqi B is tsis zoo thiab tus nqi C yog tsis zoo yog li ntawd yog qhov kev taw qhia ntawm F_BC cov ntsiab lus kom them A.

Lub zog net ua rau ntawm tus nqi 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

Lub zog hluav taws xob taw qhia rau lub zog A (sab laug).

3. Ob lub zog fais fab, raws li qhia hauv daim duab hauv qab no. Lub zog fais fab ntawm qhov chaw A yog 8 µC thiab lub zog fais fab ua rau ob lub zog yog 45 N. Yog tias lub zog A txav mus rau sab xis 1 cm, lub zog nyiam ua rau ob lub zog yog dab tsi. k = 9.10⁹ Nm².C^-2.

Paub:

Lub zog hluav taws xob ntawm qhov chaw A (q)_A) = 8 µC = 8 x 10^-6 Coulomb

Lub zog hluav taws xob ua rau ob qho nqi (F) = 45 Newtons

Qhov nrug ntawm ob qho nqi (r)_AB) = 4 cm = 0.04 meters = 4 x 10^-2 meters

Qhov tsis hloov pauv (k) = 9 x 10⁹ Nm².C^-2

Xav tau: Lub zog hluav taws xob ntawm ob qho tib si yog tias lub zog A txav mus rau sab xis 1 cm.

Tshuaj:

Lub zog hluav taws xob ntawm qhov chaw B :

Kev sib piv ntawm lub zog fais fab:

F = k (q)_A)(q_B) / r²

F r² = k (q)_A)(q_B)

q_B = F r² / k (q_A)

Lub zog hluav taws xob ntawm qhov chaw 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 Luas = 10 x 10^-7 Coulomb

Lub zog hluav taws xob ntawm cov nqi hluav taws xob A thiab B:

Yog tias tus nqi ntawm A txav mus rau sab xis 1 cm ces qhov nrug ntawm ob tus nqi yog 3 cm = 0.03 meters = 3 x 10^-2 meters.

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 Newtons

4. Ob lub zog hluav taws xob ntawm cov ntsiab lus P thiab Q sib cais los ntawm qhov deb ntawm 10 cm, paub txog lub zog nyiam ntawm 8 Newton. Yog tias lub zog Q txav mus 5 cm los them P, ces lub zog hluav taws xob yog dab tsi. (1 µC = 10^-6 C thiab k = 9 x 10⁹ Nm².C^-2).

Paub:

Qhov nrug ntawm cov nqi P thiab Q (r)_PQ) = 10 cm = 0.1 m = 1 x 10^-1 m

Lub zog hluav taws xob ntawm cov nqi P thiab Q (F) = 8 N

Lub zog hluav taws xob Q (q_Q) = 40 µC = 40 x 10^-6 C

Qhov tsis hloov pauv (k) = 9 x 10⁹ Nm².C^-2

Xav tau: Lub zog hluav taws xob ntawm cov nqi P thiab Q yog tias cov nqi Q raug txav 5 cm mus rau cov nqi P.

Tshuaj:

Ua ntej, xam lub zog hluav taws xob P, thiab tom qab ntawd xam lub zog hluav taws xob ntawm ob lub zog, yog tias lub zog hluav taws xob Q raug txav 5 cm los them P.

Lub zog fais fab P :

q_P = F r² / 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

Lub zog hluav taws xob ntawm cov nqi hluav taws xob P thiab Q:

Yog tias tus nqi ntawm qhov chaw Q raug txav mus rau sab laug 5 cm ces qhov deb ntawm ob tus nqi yog 5 cm = 0.05 meters = 5 x 10^-2 meters

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 Newtons

5. Lub zog hluav taws xob uas raug los ntawm tus nqi q_B yog 8 N (1 µC = 10^-6 C thiab k = 9.10⁹ Nm².C^-2). Yog tias them q_B txav mus 4 cm ntawm A, ces lub zog hluav taws xob uas q raug yog dab tsi?_B.

Paub:

Qhov nrug ntawm cov nqi A thiab B (r)_AB) = 2 cm = 0.02 m = 2 x 10^-2 m

Lub zog hluav taws xob ntawm cov nqi A thiab B (F) = 8 N

Lub zog hluav taws xob A (q)_A) = 2 µC = 2 x 10^-6 C

Qhov tsis hloov pauv (k) = 9 x 10⁹ Nm².C^-2

Xav tau: Lub zog hluav taws xob ntawm cov nqi A thiab B yog tias qhov deb ntawm ob qho nqi yog 4 cm.

Tshuaj:

Ua ntej, xam lub zog fais fab B, thiab tom qab ntawd xam lub zog fais fab ntawm ob lub zog, yog tias qhov deb ntawm ob lub zog yog 4 cm = 0.04 meters = 4 x 10^-2 meters.

Lub nqi hluav taws xob ntawm B :

q_B = F r² / 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

Lub zog hluav taws xob ntawm cov nqi A thiab B:

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 Newtons

6. Peb lub nqi A, B thiab C raws li qhia hauv daim duab hauv qab no. AB = BC = 20 cm thiab cov nqi yog tib yam (q = 2µC). k = 9.10⁹ Nm².C^-2, 1 µ = 10^-6Lub zog hluav taws xob ua rau ntawm qhov B loj npaum li cas.

Paub:

Them ntawm qhov chaw A (q)_A) = 2 µC = 2 x 10^-6 Coulomb

Them ntawm qhov chaw B (q)_B) = 2 µC = 2 x 10^-6 Coulomb

Them ntawm qhov chaw C (q)_C) = 2 µC = 2 x 10^-6 Coulomb

Qhov nrug ntawm B mus rau C (r)_BC) = 20 cm = 0.2 meters = 2 x 10^-1 meters

Qhov nrug ntawm B mus rau A (r)_BA) = 20 cm = 0.2 meters = 2 x 10^-1 meters

k = 9.10 hli⁹ Nm².C^-2

Xav tau: Qhov loj ntawm lub zog hluav taws xob ua rau ntawm qhov chaw B

Tshuaj:

Lub zog hluav taws xob ntawm cov nqi ntawm cov ntsiab lus B thiab C:

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 Luas = 9 x 10^-1

F_BC = 0.9 Newtons

Cov nqi hluav taws xob ntawm cov ntsiab lus B thiab C yog qhov zoo yog li qhov kev taw qhia ntawm lub zog hluav taws xob F_BC mus rau sab laug ntawm qhov chaw C.

Lub zog hluav taws xob ntawm cov nqi ntawm cov ntsiab lus B thiab A:

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 Luas = 9 x 10^-1

F_BA = 0.9 Newtons

Cov nqi hluav taws xob ntawm cov ntsiab lus B thiab A yog qhov zoo yog li qhov kev taw qhia ntawm lub zog hluav taws xob F_BA downward, deb ntawm qhov A.

Cov txiaj ntsig ntawm lub zog fais fab:

7. Peb qhov nqi Q₁, Q₂, thiab Q₃ raws li pom hauv daim duab hauv qab no. Qhov ntev ntawm AB = qhov ntev ntawm BC = 30 cm. Paub: k = 9.10 hli⁹ Nm².C^-2 thiab 1 µ = 10^-6 ces qhov tshwm sim ntawm lub zog hluav taws xob ntawm tus nqi Q₁.

Paub:

Them ntawm qhov chaw A (q)_A) = 3 µC = 3 x 10^-6 Coulomb 

Them ntawm qhov chaw B (q)_B) = -10 µC = -10 x 10^-6 Coulomb

Them ntawm qhov chaw C (q)_C) = 4 µC = 4 x 10^-6 Coulomb

Qhov nrug ntawm B mus rau C (r)_BC) = 30 cm = 0.3 meters = 3 x 10^-1 meters

Qhov nrug ntawm B mus rau C (r)_BA) = 30 cm = 0.3 meters = 3 x 10^-1 meter s

k = 9.10 hli⁹ Nm².C^-2

Xav tau: Qhov tshwm sim ntawm lub zog hluav taws xob ntawm qhov chaw B

Tshuaj:

Lub zog hluav taws xob ntawm cov nqi ntawm cov ntsiab lus B thiab C:

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 Luas = 40 x 10^-1

F_BC = 4 Newtons

Lub zog hluav taws xob ntawm qhov chaw B yog qhov tsis zoo thiab lub zog hluav taws xob ntawm qhov chaw C yog qhov zoo, yog li ntawd yog qhov kev taw qhia ntawm lub zog hluav taws xob F._BC mus rau sab xis, mus rau taw tes C.

Lub zog hluav taws xob ntawm cov nqi ntawm cov ntsiab lus B thiab A:

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 Luas = 30 x 10^-1

F_BA = 3 Newtons

Lub zog hluav taws xob ntawm qhov chaw B yog qhov tsis zoo thiab lub zog hluav taws xob ntawm qhov chaw A yog qhov zoo, yog li ntawd yog qhov kev taw qhia ntawm lub zog hluav taws xob F._BA mus rau sab saud ntawm qhov chaw A.

Qhov tshwm sim ntawm lub zog hluav taws xob:

1. Lub zog fais fab yog dab tsi? tebLub zog hluav taws xob yog lub zog tseem ceeb uas tshwm sim ntawm cov khoom vim lawv cov nqi hluav taws xob. Nws tuaj yeem yog qhov nyiam (ntawm cov nqi sib txawv) lossis qhov tsis nyiam (ntawm cov nqi zoo sib xws).
2. Yuav txiav txim siab qhov loj ntawm lub zog hluav taws xob ntawm ob lub ntsiab lus them nqi li cas? tebQhov loj ntawm lub zog hluav taws xob ntawm ob lub ntsiab lus them nqi yog muab los ntawm Coulomb txoj cai. Nws yog proportional ncaj qha rau cov khoom ntawm qhov loj ntawm cov nqi thiab inversely proportional rau lub square ntawm qhov deb ntawm lawv. F=kx q₁​x q₂​/ ​ r², qhov twg $k$ yog Coulomb tus nqi tas mus li.
3. Yog tias qhov deb ntawm ob lub nqi hluav taws xob raug ob npaug, yuav ua li cas rau lub zog hluav taws xob? tebYog tias qhov deb ntawm ob lub nqi hluav taws xob raug ob npaug, lub zog hluav taws xob yuav dhau los ua ib feem plaub ntawm nws tus nqi qub, vim tias lub zog hloov pauv rov qab nrog lub xwmfab ntawm qhov deb.
4. Lub zog hluav taws xob piv rau lub zog gravity li cas? tebCov zog hluav taws xob muaj peev xwm nyiam thiab tsis nyiam, thaum cov zog gravitational tsuas yog nyiam xwb. Tsis tas li ntawd, rau cov khoom thiab qhov deb, cov zog hluav taws xob feem ntau muaj zog dua li cov zog gravitational, vim tias cov zog gravitational tsis muaj zog ntau dua li cov zog hluav taws xob.
5. Lub hauv paus ntsiab lus ntawm kev sib tshooj hauv kev sib raug zoo rau cov zog hluav taws xob yog dab tsi? tebLub hauv paus ntsiab lus ntawm kev sib tshooj hais tias lub zog hluav taws xob ntawm ib qho nqi vim yog kev sib sau ua ke ntawm lwm cov nqi yog qhov sib npaug ntawm cov zog uas siv los ntawm txhua tus nqi uas tau muab cais.
6. Vim li cas peb thiaj tsis hnov ​​​​​​cov zog hluav taws xob hauv cov khoom siv txhua hnub txawm tias lawv yog ua los ntawm cov khoom me me uas raug them? tebFeem ntau cov khoom siv niaj hnub tsis muaj hluav taws xob, uas txhais tau tias lawv muaj cov nqi zoo thiab cov nqi tsis zoo sib npaug. Cov zog ntawm cov nqi no sib npaug, yog li lub zog hluav taws xob tag nrho yog xoom.
7. Kev grounding cuam tshuam li cas rau lub zog hluav taws xob ntawm ib yam khoom uas raug them? teb: Kev muab ib yam khoom uas raug them rau hauv av ua rau lub zog ntws ntawm yam khoom thiab lub ntiaj teb kom txog thaum yam khoom ntawd raug tshem tawm, ua rau lub zog hluav taws xob ntawm yam khoom ntawd ploj mus vim nws qhov kev them thawj zaug.
8. Lub zog hluav taws xob puas tuaj yeem ua haujlwm hauv qhov chaw nqus tsev? tebYog, lub zog hluav taws xob tuaj yeem ua haujlwm hauv qhov chaw nqus tsev. Nws tsis xav tau ib qho nruab nrab los nthuav dav. Qhov no pom tseeb los ntawm txoj kev uas cov teb hluav taws xob tuaj yeem muaj thiab cuam tshuam rau cov khoom me me hauv qhov chaw.
9. Lub zog hluav taws xob tas li (lossis qhov chaw tso cai) ua lub luag haujlwm dab tsi hauv kev txiav txim siab lub zog ntawm lub zog hluav taws xob? tebTus nqi hluav taws xob tas li, tseem hu ua qhov permittivity ntawm qhov chaw dawb, cuam tshuam rau lub zog ntawm lub zog hluav taws xob ntawm cov nqi. Qhov permittivity siab dua yuav txhais tau tias lub zog hluav taws xob tsis muaj zog, thiab vice versa. Coulomb tus nqi tas li, $k$, muaj feem cuam tshuam nrog tus nqi no li k=1/4πε₀​​.

10. Yog tias ob lub zog txav mus los sib piv rau ib leeg, lub zog ntawm lawv puas hloov pauv? tebYog tias ob lub zog hluav taws xob txav mus los sib piv rau ib leeg, lawv tuaj yeem tsim cov teb sib nqus ntxiv rau cov teb hluav taws xob. Qhov no txhais tau tias kev sib cuam tshuam ntawm cov zog hluav taws xob txav mus los yuav tsis yog vim muaj zog hluav taws xob xwb tab sis kuj yog lub zog sib nqus. Kev sib cuam tshuam ua ke yog piav qhia los ntawm lub zog hluav taws xob. Yog li, thaum lub zog hluav taws xob vim yog cov zog hluav taws xob tsis hloov pauv vim lawv txav mus los, lub zog tag nrho yuav hloov pauv vim yog cov teebmeem sib nqus.