Ka mana uila - nā pilikia a me nā hoʻonā

Ka mana uila - nā pilikia a me nā hoʻonā

1. ʻekolu ka uku e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo neiHe aha ka ka ikaika uila i ʻike ʻia e ka hoʻopiʻi B. k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C.

ʻIke ʻia:

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

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

q_C = 20 µC = 20 x 10^-6 = 2x10^-5 ʻO Coulomb

r_AB = 0.1 m = 10^-1 m

r_BC = 0.1 m = 10^-1 m

k = 9 x 10⁹ Nm²C^-2

Makemake ʻia: Ka ikaika uila i ʻike ʻia e ka uku B

Lōlā:

ʻElua mau mana uila e hana ana ma ka hoʻouku B, ʻo ia ka mana uila ma waena o ka hoʻouku A a me ka hoʻouku B. (F_AB) a me ka ikaika uila ma waena o nā uku B a me C (F_BC). ʻO ka ikaika uila i ʻike ʻia e ka uku B ka hopena o ka ikaika F_AB a me ka ikaika F_BC.

ʻO ka ikaika uila ma waena o nā uku A a me B:

kauoha A he maikaʻi a he maikaʻi ke kumukūʻai B no laila ʻo ia ke kuhikuhi o F_AB nā helu e hoʻopiʻi ai C.

ʻO ka ikaika uila ma waena o nā uku B a me C:

He maikaʻi ke kumukūʻai B a he maikaʻi ke kumukūʻai C no laila F_BC nā helu e hoʻopiʻi ai A.

ʻO ka ikaika uila i ʻike ʻia e ka uku B:

F_B =F_BC - F_AB = 180 – 90 = 90 N.

ʻO ka nui o ka ikaika uila i ʻike ʻia e ka uku B (F_B) is 90 Newtons. Ke kuhikuhi o F_B ua like ia me ke kuhikuhi o F_BC , nā kiko e hoʻopiʻi ai A.

2. He aha ka nui a me ke kuhikuhi o ka ikaika uila ma ka hoʻopiʻi B. (k = 9 x 10⁹ Nm²C^-2, 1 μC = 10^-6 C)

ʻIke ʻia:

Hoʻopiʻi A (q_A) = +Q

Hoʻopiʻi B (q_B) = -2Q

Hoʻopiʻi C (q_C) = -Q

ʻO ka mamao ma waena o nā uku A a me B (r_AB) = r

ʻO ka mamao ma waena o nā uku B a me C (r_BC) = 2r

k = 9 x 10⁹ Nm²C^-2

Makemake ʻia: ʻO ka nui a me ke kuhikuhi o ka ikaika uila ma ka hoʻopiʻi B.

Lōlā:

ʻO ka ikaika uila ma waena o nā uku A a me B:

He maikaʻi ke kumukūʻai A a he maikaʻi ke kumukūʻai B no laila ʻo ia ke kuhikuhi o F_AB nā helu e hoʻopiʻi ai A.

ʻO ka ikaika uila ma waena o ka uku B a me ka uku C:

Hoʻopiʻi B iʻaʻole maikaʻi ʻo s a ʻaʻole maikaʻi ka hoʻopiʻi C no laila ʻo ia ke kuhikuhi o F_BC nā helu e hoʻopiʻi ai A.

Hana ka ikaika upena ma ka hoʻopiʻi 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

Ke kuhikuhi nei ke kuhikuhi o ka ikaika uila i ka hoʻouka kaua A (hema).

3. ʻElua mau uku uila, i hōʻike ʻia ma ke kiʻi ma lalo nei. ʻO ka uku ma ke kiko A he 8 µC a ʻo ka ikaika uila e hana ana ma nā uku ʻelua he 45 N. Inā neʻe ka uku A i ka ʻākau he 1 cm, he aha ka ikaika huki e hana ana ma nā uku ʻelua. k = 9.10⁹ Nm².C^-2.

ʻIke ʻia:

Uila uila ma ke kiko A (q)_A) = 8 µC = 8 x 10^-6 ʻO Coulomb

Hana ka ikaika uila ma nā uku ʻelua (F) = 45 Newtons

ʻO ka mamao ma waena o nā uku ʻelua (r_AB) = 4 kenimika = 0.04 mika = 4 x 10^-2 mau mika

Paʻa (k) = 9 x 10⁹ Nm².C^-2

Makemake ʻia: ʻO ka ikaika uila ma waena o nā uku ʻelua inā neʻe ka uku A i ka ʻākau 1 kenimika.

Lōlā:

Uila uila ma ke kiko B :

ʻO ke kaulike o ka ikaika uila:

F = k (q_A)(q_B) / r²

F r² = k (q_A)(q_B)

q_B = F r² / k (q_A)

Uila uila ma ke kiko 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 = 10x10^-7 ʻO Coulomb

ʻO ka ikaika uila ma waena o nā uku uila A a me B:

Inā neʻe ka uku ma A i ka ʻākau 1 kenimika a laila ʻo ka mamao ma waena o nā uku ʻelua he 3 kenimika = 0.03 mika = 3 x 10^-2 mika.

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. ʻElua mau uku uila ma nā kiko P a me Q i hoʻokaʻawale ʻia e kahi mamao o 10 cm, e ʻike i ka ikaika huki o 8 Newton. Inā neʻe ka uku Q i 5 cm i ka uku P, a laila he aha ka ikaika uila. (1 µC = 10^-6 ʻO C a me k = 9 x 10⁹ Nm².C^-2).

ʻIke ʻia:

ʻO ka mamao ma waena o nā uku P a me Q (r_PQ) = 10 kenimika = 0.1 m = 1 x 10^-1 m

ʻO ka ikaika uila ma waena o nā uku P a me Q (F) = 8 N

Uila uila Q (q_Q) = 40 µC = 40 x 10^-6 C

Paʻa (k) = 9 x 10⁹ Nm².C^-2

Makemake ʻia: ʻO ka ikaika uila ma waena o nā uku P a me Q inā e neʻe ʻia ka uku Q he 5 kenimika i ka uku P.

Lōlā:

ʻO ka mea mua, e helu i ka uku uila P, a laila e helu i ka ikaika uila ma waena o nā uku ʻelua, inā e hoʻoneʻe ʻia ka uku uila Q he 5 cm i ka uku P.

ʻO ka uku uila 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 ʻO Coulomb

ʻO ka ikaika uila ma waena o nā uku uila P a me Q:

Inā hoʻoneʻe ʻia ka uku ma ke kiko Q he 5 kenimika i ka hema a laila ʻo ka mamao ma waena o nā uku ʻelua he 5 kenimika = 0.05 mika = 5 x 10^-2 mau mika

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. ʻO ka ikaika uila i ʻike ʻia e ka uku q_B ʻo 8 N (1 µC = 10^-6 C a me k = 9.10⁹ Nm².C^-2). Inā hoʻouka ʻia ʻo q_B ua neʻe ʻia he 4 kenimika mai A mai, a laila he aha ka ikaika uila i ʻike ʻia e q_B.

ʻIke ʻia:

ʻO ka mamao ma waena o nā uku A a me B (r_AB) = 2 kenimika = 0.02 m = 2 x 10^-2 m

ʻO ka ikaika uila ma waena o nā uku A a me B (F) = 8 N

ʻO ka uku uila A (q_A) = 2 µC = 2 x 10^-6 C

Paʻa (k) = 9 x 10⁹ Nm².C^-2

Makemake ʻia: ʻO ka ikaika uila ma waena o nā uku A a me B inā he 4 kenimika ka mamao ma waena o nā uku ʻelua.

Lōlā:

ʻO ka mea mua, e helu i ka uku uila B, a laila e helu i ka ikaika uila ma waena o nā uku ʻelua, inā ʻo ka mamao o nā uku ʻelua he 4 cm = 0.04 mika = 4 x 10^-2 mika.

ʻO ka uku uila ma 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 ʻO Coulomb

ʻO ka ikaika uila ma waena o nā uku A a me 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 Newton

6. ʻEkolu mau uku A, B a me C e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. AB = BC = 20 cm a ua like nā uku (q = 2µC). k = 9.10⁹ Nm².C^-2, 1 µ = 10^-6He aha ka nui o ka ikaika uila e hana ana ma ke kiko B.

ʻIke ʻia:

Hoʻouka ma ke kiko A (q_A) = 2 µC = 2 x 10^-6 ʻO Coulomb

Hoʻouka ma ke kiko B (q_B) = 2 µC = 2 x 10^-6 ʻO Coulomb

Hoʻouka ma ke kiko C (q_C) = 2 µC = 2 x 10^-6 ʻO Coulomb

ʻO ka mamao mai B a i C (r_BC) = 20 kenimika = 0.2 mika = 2 x 10^-1 mau mika

ʻO ka mamao mai B a i A (r_BA) = 20 kenimika = 0.2 mika = 2 x 10^-1 mau mika

k = 9.10⁹ Nm².C^-2

Makemake ʻia: Hana ka nui o ka ikaika uila ma ke kiko B

Lōlā:

ʻO ka ikaika uila ma waena o nā uku ma nā kiko B a me 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 = 9x10^-1

F_BC = 0.9 Newton

He maikaʻi nā uku uila ma nā kiko B a me C i hiki ai i ke kuhikuhi o ka ikaika uila F_BC i ka hema mai ke kiko C.

ʻO ka ikaika uila ma waena o nā uku ma nā kiko B a me 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 = 9x10^-1

F_BA = 0.9 Newton

He maikaʻi nā uku uila ma nā kiko B a me A i hiki ai i ke kuhikuhi o ka ikaika uila F_BA i lalo, mai kahi A.

ʻO ka hopena o nā mana uila:

7. ʻEkolu mau uku Q₁,Q₂, a me Q₃ e like me ka mea i hōʻike ʻia ma ke kiʻi ma lalo nei. ʻO ka lōʻihi o AB = ka lōʻihi o BC = 30 kenimika. ʻIke ʻia: k = 9.10⁹ Nm².C^-2 a me 1 µ = 10^-6 a laila ka hopena o ka ikaika uila ma ka hoʻopiʻi Q₁.

ʻIke ʻia:

Hoʻouka ma ke kiko A (q_A) = 3 µC = 3 x 10^-6 ʻO Coulomb 

Hoʻouka ma ke kiko B (q_B) = -10 µC = -10 x 10^-6 ʻO Coulomb

Hoʻouka ma ke kiko C (q_C) = 4 µC = 4 x 10^-6 ʻO Coulomb

ʻO ka mamao mai B a i C (r_BC) = 30 kenimika = 0.3 mika = 3 x 10^-1 mau mika

ʻO ka mamao mai B a i C (r_BA) = 30 kenimika = 0.3 mika = 3 x 10^-1 mika

k = 9.10⁹ Nm².C^-2

Makemake ʻia: ʻO ka hopena o ka ikaika uila ma ke kiko B

Lōlā:

ʻO ka ikaika uila ma waena o nā uku ma nā kiko B a me 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 = 40x10^-1

F_BC = 4 Newton

He maikaʻi ʻole ka uku uila ma ke kiko B a he maikaʻi ka uku uila ma ke kiko C, no laila ʻo ia ke kuhikuhi o ka ikaika uila F._BC i ka ʻākau, i ke kiko C.

ʻO ka ikaika uila ma waena o nā uku ma nā kiko B a me 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 = 30x10^-1

F_BA = 3 Newton

He maikaʻi ʻole ka uku uila ma ke kiko B a he maikaʻi ka uku uila ma ke kiko A, no laila ʻo ia ke kuhikuhi o ka ikaika uila F._BA i luna a hiki i ka kiko A.

ʻO ka hopena o ka ikaika uila:

1. He aha ka ikaika uila? paneʻO ka ikaika uila kahi ikaika kumu e kū nei ma waena o nā mea ma muli o kā lākou mau uku uila. Hiki iā ia ke huki (ma waena o nā uku kū'ē) a i ʻole ke kipaku (ma waena o nā uku like).
2. Pehea e hoʻoholo ʻia ai ka nui o ka ikaika uila ma waena o nā uku kiko ʻelua? paneʻO ke kānāwai o Coulomb ka mea i hāʻawi ʻia ai ka nui o ka ikaika uila ma waena o nā uku kiko ʻelua. He kūlike pololei ia me ka huahana o nā nui o nā uku a kūlike ʻole i ka huinahā o ka mamao ma waena o lākou. F=kx q₁​x q₂​/ r², kahi $k$ ʻo ia ke kūpaʻa o Coulomb.
3. He aha ka mea e hana ʻia i ka ikaika uila inā e pāpālua ʻia ka mamao ma waena o nā uku ʻelua? paneInā pāpālua ʻia ka mamao ma waena o nā uku ʻelua, lilo ka ikaika uila i hapahā o kona waiwai mua, no ka mea, ʻokoʻa ke ʻano o ka ikaika me ka huinahā o ka mamao.
4. Pehea e hoʻohālikelike ai ka ikaika uila me ka ikaika umekaumaha? paneHiki i nā ikaika uila ke hoihoi a hoʻopailua hoʻi, ʻoiai he hoihoi wale nō nā ikaika umekaumaha. Eia kekahi, no nā mea maʻamau a me nā mamao, ʻoi aku ka ikaika o nā ikaika uila ma mua o nā ikaika umekaumaha, no ka mea, ʻoi aku ka nāwaliwali o nā ikaika umekaumaha ma nā kauoha he nui o ka nui i hoʻohālikelike ʻia me ka ikaika uila.
5. He aha ke kumumanaʻo o ka superposition e pili ana i nā mana uila? paneʻO ke kumumanaʻo o ka superposition e ʻōlelo nei ʻo ka ikaika uila net ma luna o kahi uku ma muli o ka hōʻiliʻili ʻana o nā uku ʻē aʻe ʻo ia ka huina vector o nā ikaika i hoʻokau ʻia e kēlā me kēia uku i lawe ʻia ma ke kaʻawale.
6. No ke aha kākou e ʻike ʻole ai i nā mana uila i nā mea o kēlā me kēia lā ʻoiai ua hana ʻia lākou me nā ʻāpana i hoʻopiʻi ʻia? paneʻO nā mea o kēlā me kēia lā, he kūlike ʻole ka uila, ʻo ia hoʻi, he like ka nui o nā uku maikaʻi a me nā uku maikaʻi ʻole. Kaulike nā mana ma waena o kēia mau uku, no laila ʻo ka ikaika uila net he ʻole.
7. Pehea ka hopena o ka hoʻokumu ʻana i ka honua i ka ikaika uila ma luna o kahi mea i hoʻopiʻi ʻia? paneʻO ka hoʻokumu ʻana i kahi mea i hoʻopiʻi ʻia e ʻae i ka hoʻopiʻi e kahe ma waena o ka mea a me ka Honua a hiki i ka wā e hoʻopau ʻia ai ka mea, e hoʻopau pono ana i ka ikaika uila ma luna o ka mea ma muli o kona hoʻopiʻi mua.
8. Hiki i ka ikaika uila ke hana i loko o kahi hakahaka? paneʻAe, hiki i ka ikaika uila ke hana i loko o kahi hakahaka. ʻAʻole pono ia i kahi waena e hoʻolaha. ʻIke ʻia kēia mai ke ʻano e hiki ai i nā kahua uila ke noho a hoʻohuli i nā ʻāpana i hoʻopiʻi ʻia ma ka lewa.
9. He aha ke kuleana o ke kūpaʻa uila (a i ʻole ka permittivity o kahi hakahaka) i ka hoʻoholo ʻana i ka ikaika o ka ikaika uila? paneʻO ke kūpaʻa uila, i ʻike ʻia hoʻi ʻo ka permittivity o ka hakahaka manuahi, e hoʻopilikia i ka ikaika o ka ikaika uila ma waena o nā uku. ʻO ka permittivity kiʻekiʻe e hōʻike ana i nā ikaika uila nāwaliwali, a ʻo ka hope. ʻO ke kūpaʻa o Coulomb, $k$, pili i kēia waiwai e like me k=1/4πε₀​​.

10. Inā e neʻe ana nā ʻāpana ʻelua kekahi i kekahi, e loli anei ka ikaika ma waena o lāua? paneInā e neʻe ana nā uku ʻelua kekahi i kekahi, hiki iā lākou ke hana i nā kahua magnetic ma waho aʻe o nā kahua uila. ʻO ke ʻano kēia, ʻo ka pilina ma waena o nā uku e neʻe ana ʻaʻole wale ma muli o nā ikaika uila akā ʻo nā ikaika magnetic pū kekahi. Ua wehewehe ʻia ka pilina i hui pū ʻia e ka ikaika electromagnetic. No laila, ʻoiai ʻaʻole e loli ka ikaika uila ma muli o nā uku no ka mea e neʻe ana lākou, hiki ke loli ka ikaika holoʻokoʻa ma muli o nā hopena magnetic.