Ngā mara hiko - ngā raruraru me ngā otinga

Ngā mara hiko - ngā raruraru me ngā otinga

1. Kei waenganui i ngā utu e rua te Pūwāhi A. He rite te rahi o ngā utu e rua engari he rerekē te tohu, ā, he tawhiti a te a kei waenganui i a rāua. Ko te rahi o te āpure hiko i te pūwāhi A he 36 N/C. Mena ka neke te pūwāhi A i te 1/2a tata ki tētahi o ngā utu e rua , he aha te rahi o te āpure hiko i te pūwāhi A?

Mōhiotia:

Utu 1 (q ₁ ) = +Q

Utu 2 (q ₂ ) = -Q

Ko te tawhiti i waenganui i te utunga 1 me te pūwāhi A (r _1A ) = ½ a

Ko te tawhiti i waenganui i te utunga 2 me te pūwāhi A (r _2A ) = ½ a

Ko te rahi o te papa hiko i te pūwāhi A (E _A ) = 36 NC ^-1

E hiahiatia ana: Te rahi o te mara hiko

Rongoā:

Hipanga 1.

Ka puta te āpure hiko i te utu +Q i te pūwāhi A :

He pai te utu whakamātautau, ā, he pai te utu 1, kia anga ai te ahunga o te mara hiko ki te utu 2.

Ko te utu hiko i whakaputaina e te utu -Q i te pūwāhi A :

He pai te utu whakamātautau, ā, he kino te utu 2, nō reira ka tohu te ahunga o te mara hiko ki te utu 2.

Ko te hua o te mara hiko i te pūwāhi A:

Hipanga 2.

Mena ka nekehia te pūwāhi A ki te taha tata o te utunga 1, koia ēnei:

Te tawhiti i waenganui i te utunga 1 me te pūwāhi A (r _1A ) = ¼ a

Ko te tawhiti i waenganui i te utunga 2 me te pūwāhi A (r _2A ) = ¾ a

Ko te papa hiko i hangaia e te utu +Q i te pūwāhi A :

He pai te utu whakamātautau, ā, he pai te utu 1, kia anga ai te ahunga o te mara hiko ki te utu 2.

Ko te papa hiko i hangaia e te utu -Q i te pūwāhi A :

He pai te utu whakamātautau, ā, he kino te utu 2, nō reira ka tohu te ahunga o te mara hiko ki te utu 2.

Ko te hua o te mara hiko i te pūwāhi A:

2. E rua ngā utu q _A = 1 μC me q _B = 4 μC e wehea ana e te tawhiti o te 4 cm (k = 9 x 10 ⁹ N m ² C ⁻² ). He aha te rahi o te āpure hiko i te pokapū i waenganui i a q _A me q _B?

Mōhiotia:

Utu A (q _A ) = 1 μC = 1 x 10 ⁻⁶ C

Utu B (q _B ) = 4 μC = 4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ N m ² C ⁻²

Te tawhiti i waenganui i ngā utu A me B (r _AB ) = 4 cm = 0.04 mita

Te tawhiti i waenganui i te utu A me te pūwāhi pokapū (r _A ) = 0.02 mita s

Te tawhiti i waenganui i te utu B me te pūwāhi pokapū (r _B ) = 0.02 mita s

E mōhiotia ana: Te rahi o te mara hiko

Rongoā:

Ko te papa hiko i hangaia e te utu A i te pūwāhi pokapū:

He pai te utu whakamātautau, ā, he pai te utu A, kia anga ai te ahunga o te mara hiko ki te utu B.

Ko te papa hiko i hangaia e te utu B i te pūwāhi pokapū:

He pai te utu whakamātautau, ā, he pai te utu B, kia anga ai te ahunga o te mara hiko ki te utu A.

Ko te hua o te papa hiko i te pūwāhi pokapū:

He rerekē te ahunga o E _A me E _B.

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

3. E ai ki te pikitia i raro nei, kei hea te pūwāhi P kia rite ai te rahi o te āpure hiko i te pūwāhi P ki te 0? ( k = 9 x 10 ⁹ Nm ² C ⁻² , 1 μC = 10 ⁻⁶ C)

otinga

Mena kei te taha maui o Q1 _te pūwāhi P ; ka tohu te mara hiko i hangaia e Q1 i te pūwāhi P ki te taha maui ( atu i Q1 ₎ ā, ka tohu te mara hiko i hangaia e _Q2 i te pūwāhi P ki _te taha matau (tohu ki Q1 ). He ritenga kē te ahunga o te mara hiko , nō reira ko _te mara hiko i te pūwāhi P = 0.

Mōhiotia:

Q ₁ = +9 μC = +9 x 10 ⁻⁶ C

Q ₂ = -4 μC = -4 x 10 ⁻⁶ C

k = 9 x 10 ⁹ Nm ² C ⁻²

Te tawhiti i waenganui i te utu 1 me te utu 2 = 3 cm

Te tawhiti i waenganui i a Q ₁ me te pūwāhi P (r _1P ) = a

Te tawhiti i waenganui i a Q ₂ me te pūwāhi P (r _2P ) = 3 + a

E hiahiatia ana: Te tūnga o te pūwāhi P

Rongoā:

Kei te taha mauī o Q ₁ te Pūwāhi P.

Ko te mara hiko i hangaia e Q ₁ i te pūwāhi P:

He pai te utu whakamātautau, ā, he pai hoki a Q ₁ , nō reira kei te taha mauī te ahunga o te āpure hiko.

Ko te mara hiko i hangaia e Q ₂ i te pūwāhi P :

He pai te utu whakamātautau, ā, he kino te Q ₂ , nō reira kei te taha matau te ahunga o te āpure hiko.

Te hua o te papa hiko i te pūwāhi A:

Whakamahia te tātai tapawhā hei kimi i tētahi:

Te tawhiti i waenganui i a Q ₂ me te pūwāhi P (r _2P ) = 3 + a = 3 – 1.8 = 1.2 cm , 3 + a = 3 – 9 = -6 cm rānei.

Te tawhiti i waenganui i a Q ₁ me te pūwāhi P (r _1P ) = a = -9 cm, -1.8 cm rānei.

Kei te 1.2 cm te tawhiti ki te taha matau o Q _{2 te Pūwāhi P.}

4. Kei te 5 cm te tawhiti o te utu q _{3 ki te taha matau o q 2} , e whakaaturia ana i te pikitia i raro nei. He aha te rahi o te āpure hiko i te utu q ₃ (1 µC = 10 ^-6 C).

Rongoā:

He pai te utunga q _3, ā, ko te ahunga o te mara hiko i te utunga q ₃ e tohu ana ki te utunga tango q ₂ (E ₂ ) ā, e matara atu ana i te utunga tāpiri q ₁ (E ₁ ). Ko te hua o te mara hiko ko te tapeke o ngā mara hiko E ₁ me E ₂.

Mōhiotia:

Utu q ₁ = 5 µC = 5 x 10 ^-6 Coulomb

Utu q ₂ = 5 µC = -5 x 10 ^-6 Coulombs

Te tawhiti i waenganui i te utu q ₁ me te utu q ₃ (r ₁ ) = 15 cm = 0.15 m = 15 x 10 ^-2 mita

Te tawhiti i waenganui i te utu q ₂ me te utu q ₃ (r ₂ ) = 5 cm = 0.05 m = 5 x 10 ^-2 mita

k = 9 x 10 ⁹ N m ² C ^-2

E hiahiatia ana: Te āpure hiko i te utu q ₃

Rongoā:

Te mara hiko 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

Te mara hiko 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

Ngā hua o te mara hiko:

Ko te hua o te āpure hiko i te utu q ₃ :

E = E2 _– E1 ₌ (1.8 x ¹⁰⁷ ) – (0.2 x ¹⁰⁷ ) = 1.6 x ^107N /C

Ka anga te ahunga o te papa hiko ki te taha maui (he rite tonu ki te ahunga E ₂ ).

5. E rua ngā utu e wehea ana e whakaaturia ana i te pikitia i raro nei. He aha te āpure hiko i te pūwāhi P (k = 9 x 10 ⁹ N m ² C ^-2 )

otinga

Mōhiotia:

Utu q _A = +2.5 C

Utu q _B = -2 C

Te tawhiti i waenganui i te utu q _A me te pūwāhi P (r _A ) = 5 m

Te tawhiti i waenganui i te utu q _B me te pūwāhi P (r _B ) = 2 m

k = 9 x 10 ⁹ N m ² C ^-2

E hiahiatia ana: te rahi o te āpure hiko i te pūwāhi P.

Rongoā:

Te mara hiko A:

EA = _kqA / _rA ²_​

E _A = (9 x 10 ⁹ )(2.5) / (5) ²

EA = ₍ 22.5 x 10 ⁹ ) / 25

EA = 0.9 x ^{109 N} _/ C

Te mara hiko B:

E _B = kq _B / r _B ²

E _B = (9 x 10 ⁹ )(2) / (2) ²

E _B = (18 x 10 ⁹ ) / 4

EB = 4.5 x 109 ^N _/ C

Ngā hua o te mara hiko:

Te hua o te papa hiko i te pūwāhi P:

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

Ko te ahunga ki maui (ko te ahunga kotahi ki a E _B ).

6. E rua ngā utu Q ₁ = -40 µC me Q ₂ = +5 µC e whakaaturia ana i te pikitia i raro nei (k = 9 x 10 ⁹ Nm ² .C ^-2 me 1 µC = 10 ^-6 C),. He aha te rahi o te āpure hiko i te pūwāhi P.

Mōhiotia:

Utu q ₁ = -40 µC = -40 x 10 ^-6 C

Utu q ₂ = +5 µC = +5 x 10 ^-6 C

Te tawhiti i waenganui i a q ₁ me te pūwāhi P (r ₁ ) = 40 cm = 0.4 m = 4 x 10 ^-1 m

Te tawhiti i waenganui i a q ₂ me te pūwāhi P (r ₂ ) = 10 cm = 0.1 = 1 x 10 ^-1 m

k = 9 x 10 ⁹ N m ² C ^-2

E hiahiatia ana: te rahi o te āpure hiko i te pūwāhi P.

Rongoā:

Te mara hiko 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

Te mara hiko 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

Ngā hua o te mara hiko:

Ko te hua o te mara hiko i te pūwāhi P:

E = E ₂ – E1 = (45 – 22.5) x 10 ⁵ = 22.5 x 10 ⁵ N/C

E = 2.25 x ¹⁰⁶ N/C

Ko te ahunga o te mara hiko e anga ana ki te taha matau (he rite te ahunga ki te E ₂ ).

7. E rua ngā utu pūwāhi e whakaaturia ana i te pikitia i raro nei.

Kei hea te pūwāhi P e tū ai kia rite te rahi o te āpure hiko i te pūwāhi P ki te 0. k = 9.10 ⁹ Nm ² .C ^-2 , 1 µC = 10 ^-6 C.

Mōhiotia:

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

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

Te tawhiti i waenganui i a q1 _me q2 ₍ r12 ₎ = 1 cm

k = 9.10 ⁹ Nm ² .C ^-2

E hiahiatia ana: Te tūnga o te pūwāhi P

Rongoā:

E ₁ = te rahi o te papa hiko i hangaia e q ₁ i te pūwāhi P

Ko te ahunga o E ₁ ki q ₁ nā te mea he kino a q _{1 .}

E ₂ = te rahi o te āpure hiko i hangaia e q ₂ i te pūwāhi P

Kei tawhiti atu te ahunga o E ₂ i q ₂ nā te mea he pai a q _{2 .}

Ko te papa hiko i te pūwāhi = 0.

Whakamahia te tātai tapawhā:

Te tawhiti i waenganui i a P me q ₂ = x = 0.5 cm.

Kei te 0.5 cm te taha matau q₂ _, kei te 0.25 cm te taha maui q₂ rānei _te pūwāhi P.

8. E ai ki te ahua i raro nei, mēnā ko te rahi o te āpure hiko i te pūwāhi P = k Q/x ² , ko x = ….

Mōhiotia:

EP = k Q / _x ²

E hiahiatia ana: x

Rongoā:

E ₂ = Te rahi o te papa hiko i te pūwāhi P e te utu +32Q

r ₂ = Te tawhiti i waenganui i te utu +32Q me te pūwāhi P = a + x

Whakamahia te tātai tapawhā:

1. He aha te mara hiko?
   • WhakautuKo te papa hiko he rohe e karapoti ana i tētahi mea kua whakakīia, ka taea e ētahi atu mea kua whakakīia te pā ki ngā kaha hiko. He papa whārite tēnei, arā, he nui, he ahunga hoki tōna i ia pūwāhi.
2. Me pēhea te whakatau i te kaha o te papa hiko?
   • WhakautuTe kaha, te rahi rānei o te papa hiko $E$ i tētahi pūwāhi ka tautuhia ko te kaha $F$ i pāngia e te utu whakamātautau pai q₀​ i whakanohoia ki taua wāhi, ka wehea e te rahi o te utu whakamātautau tonu: E=​F/q₀​.
3. He pēhea te rerekētanga o te āpure hiko e hua mai ana i tētahi utu pūwāhi i runga i te tawhiti?
   • WhakautuTe mara hiko $E$ nā te utu tohu $Q$ he rite whakamuri ki te tapawhā o te tawhiti $r$ mai i te utu. Nā te E=kQ/r², i reira $k$ ko te pūmau a Coulomb.
4. He aha te ahunga o te papa hiko nā te utu pai?
   • WhakautuKo te mara hiko o te utu pai e anga atu ana ki waho mai i te utu. Mō te utu kino, ka anga atu te mara ki roto, ki te utu.
5. Me pēhea e taea ai e koe te whakaatu i ngā āpure hiko mā te kauwhata?
   • WhakautuKa taea te whakaatu i ngā mara hiko mā te whakamahi i ngā rārangi mara (ngā rārangi kaha rānei). Ko te ahunga o te mara i tētahi pūwāhi he pātata ki te rārangi mara i taua pūwāhi, ā, ko te kiato o ngā rārangi e tohu ana i te rahi o te mara.
6. He aha te mea ka pā ki te papa hiko i roto i te ara iahiko i roto i te taurite hiko?
   • WhakautuI roto i te ara iahiko i te taurite hiko, he kore te papa hiko. Nā te mea ka tukuna anōtia ngā irahiko kore utu i roto i te ara iahiko e tētahi ara iahiko o waho, ka whakakorea te papa o waho o roto.
7. He pēhea te whanonga o ngā rārangi papa hiko e tata ana ki te taha koi o tētahi ara iahiko?
   • WhakautuI te taha koi, i te pito koi rānei o te ara hiko, ka kukū ake ngā rārangi o te papa hiko, ā, ka kaha ake te papa hiko i taua rohe. Koinei te pūtake o te whakahaere o ngā taputapu pēnei i te tokotoko uira.
8. Me pēhea te pānga o ngā mātāpono taupatupatu ki ngā mara hiko?
   • WhakautuKo te papa hiko e puta mai ana i ngā utu maha i tētahi pūwāhi he tapeke noa iho o ngā papa hiko e puta mai ana i ia utu takitahi. E mōhiotia ana tēnei ko te mātāpono taupatupatu.
9. He aha te hononga o te mahi a te ākena o waho ki te papa hiko ina nekehia ana te utu i roto i te papa?
   • WhakautuTe mahi $W$ i mahia e tētahi āpiha o waho i te neke i tētahi utu $q$ mai i tētahi pūwāhi ki tētahi atu i roto i tētahi mara hiko he ōrite ki te kino o te huringa o te pūngao pūmanawa hiko, arā $W=q\times \Delta V$, i reira $\Delta V$ ko te huringa o te pūmanawa hiko.

10. Ka taea e ngā rārangi papa hiko te whiti tetahi ki tetahi?

    • WhakautuKāore, kāore e taea e ngā rārangi o te mara hiko te whiti tetahi ki tetahi. Mēnā ka whiti, ko te tikanga kei te pūwāhi e tūtaki ai, e rua ngā ahunga rerekē o te mara hiko, he mea kāore e taea.