Elektrostatik maydon energiyasi
-------------------------------

Elektrostatik energiya - bu elektrostatik tizimdagi zaryadlar o'rtasidagi o'zaro ta'sir natijasida yuzaga keladigan potentsial energiya. Elektrostatik energiya Coulomb qonuniga asoslanadi va ikki zaryad o'rtasidagi o'zaro ta'sir bu zaryadlarning bir-biriga ta'sir qiladigan kuchi bilan belgilanadi.

Ikki nuqta zaryadlari (q1 va q2) orasidagi elektrostatik energiya quyidagi formula bilan ifodalanadi:



U
=

k
⋅

q

1

⋅

q

2

r

{\displaystyle U={\frac {k\cdot q\_{1}\cdot q\_{2}}{r}}}

{\displaystyle U={\frac {k\cdot q_{1}\cdot q_{2}}{r}}}
* {\displaystyle U}, elektrostatik energiya (julda),
* {\displaystyle k}, Kulumbo sabiti ({\displaystyle (8.99\times 10^{9}Nm^{2}/C^{2})}),
* {\displaystyle q\_{1}}​ va {\displaystyle q\_{2}} joylarning kattaliklari (kulumbda),
* {\displaystyle r}, joylar orasidagi masofa (metrda).

  

Bu formul, elektrostatik energiyasining joylar orasidagi masofaga va joylar kattalikiga qarab qanday o'zgarganligini namoyish qiladi. Elektrostatik energiya, joylar bir-biriga yaqinlashganda o'sadi va uzoqroq bo'lganda kamayadi. Elektrostatik energiya, joylar orasidagi ta'sir energiyasining saqlanish shakli bo'lib, umumiy ravishda tizimdagi joylar tartibiga qarab o'zgarganlik ko'rsatadi.

**Elektrostatik maydon energiyasi** - potensial maydondir, shuning uchun unga kiritilgan zaryadlar potensial energiyaga ega bo'ladilar

{\displaystyle q1} va q2 nuqtaviy zaryadlarning potensial energiyalarini baxolaymiz. Xar bir zaryad, boshqa zaryad maydonida potensial energiyaga ega bo'ladi 



W

1

=

q

1

∗

φ

12

=

q

2

,

W

2

=

q

2

∗

φ

12

{\displaystyle W\_{1}=q\_{1}\*\varphi \_{12}=q\_{2},W\_{2}=q\_{2}\*\varphi \_{12}}

{\displaystyle W_{1}=q_{1}*\varphi _{12}=q_{2},W_{2}=q_{2}*\varphi _{12}}{\displaystyle \varphi \_{12}-q\_{2}} - zaryadlarning {\displaystyle q1} zaryad turgan joyda xosil kilgan potensialidir. 



φ

12

=

1

4
π

ε

0

ε



q

2

r

,

φ

21

=

1

4
π

ε

0

ε
r


{\displaystyle \varphi \_{12}={\frac {1}{{4\pi }\varepsilon \_{0}\varepsilon }}{\frac {q\_{2}}{r}},\varphi \_{21}={\frac {1}{{4\pi }\varepsilon \_{0}\varepsilon r}}}

{\displaystyle \varphi _{12}={\frac {1}{{4\pi }\varepsilon _{0}\varepsilon }}{\frac {q_{2}}{r}},\varphi _{21}={\frac {1}{{4\pi }\varepsilon _{0}\varepsilon r}}}shuning uchun 



W

1

=

W

2

=
W

{\displaystyle W\_{1}=W\_{2}=W}

{\displaystyle W_{1}=W_{2}=W}

W
=

q

1

∗

φ

12

=

q

2

∗

φ

21

=

q
1
∗

φ

12

+

q

2

∗

φ

21

2

{\displaystyle W=q\_{1}\*\varphi \_{12}=q\_{2}\*\varphi \_{21}={\frac {q1\*\varphi \_{12}+q\_{2}\*\varphi \_{21}}{2}}}

{\displaystyle W=q_{1}*\varphi _{12}=q_{2}*\varphi _{21}={\frac {q1*\varphi _{12}+q_{2}*\varphi _{21}}{2}}}

Yakkalangan zaryadli o'tkazgich energiyasi
------------------------------------------

Yakkalangan zaryadli o'tkazgichin energiyasi, elektrostatik potensial enerji formulasi yordamida ifodalangan. Bir qutbli o'tkazgich (q) yakkalangan joy (V) bo'ylab o'tqazilgandagi potensial energiya (U) quyidagi formulaga ega:


U
=
q
⋅
V

{\displaystyle U=q\cdot V}

{\displaystyle U=q\cdot V}
Bu formulda:

* *U*, potensial energiya (julda),
* *q*, o'tkazgichning zaryadi (kulum cinsida),
* *V*, o'tkazgichga o'tqazilgan joy (voltda).

Bu formul, o'tkazgichning zaryadi va unga o'tqazilgan joy orasidagi aloqani ifodalaydi. O'tkazgichdan o'tqazilgan joy o'sib, zaryadning potensial energetik energiyasini hosil qiladi.

Bu formul elektrostatik sistemlarda ishlatiladi, masalan, kondensatorlarda, elektr o'lchovlarda va boshqa elektr energiyasini saqlash va o'tkazish vositalarida.

  

O'tkazgich {\displaystyle q} - zaryadga , {\displaystyle C} - sig'imga va {\displaystyle \varphi } potensialiga ega bo'lsin. O'tkazgich zaryadini {\displaystyle dq} ga oshiramiz. Uning uchun cheksizlikdan (yani {\displaystyle \varphi =0} bo'lgan joydan) {\displaystyle dq} zaryadni o'tkazgichga ko'chiramiz Bu xolda bajarilgan ish :


d
A
=
φ
∗
d
q
=
φ
∗
C
∗
d
φ

{\displaystyle dA=\varphi \*dq=\varphi \*C\*d\varphi }

{\displaystyle dA=\varphi *dq=\varphi *C*d\varphi }ga teng bo'ladi chunki 


q
=
C
φ
,
d
q
=
C
∗
d
φ

{\displaystyle q=C\varphi ,dq=C\*d\varphi }

{\displaystyle q=C\varphi ,dq=C*d\varphi }To'la bajarilgan ish 


A
=

∫

0

φ

C
∗
φ
d
φ
=

∫

0

φ

φ
d
φ
=
C

φ

2

2

{\displaystyle A=\int \_{0}^{\varphi }C\*\varphi d\varphi =\int \_{0}^{\varphi }\varphi d\varphi =C{\frac {\varphi ^{2}}{2}}}

{\displaystyle A=\int _{0}^{\varphi }C*\varphi d\varphi =\int _{0}^{\varphi }\varphi d\varphi =C{\frac {\varphi ^{2}}{2}}}

W
=
A
=

C
∗

φ

2

2

=

q
∗
φ

2

=

q

2

2
C


{\displaystyle W=A={\frac {C\*\varphi ^{2}}{2}}={\frac {q\*\varphi }{2}}={\frac {q^{2}}{2C}}}

{\displaystyle W=A={\frac {C*\varphi ^{2}}{2}}={\frac {q*\varphi }{2}}={\frac {q^{2}}{2C}}}Zaryadlangan kondensator energiyasi quyidagiga teng bo'ladi: 


W
=

C
(

φ

1

−

φ

2

)

2

2

=

C
(
△
φ

)

2

2

=

q
∗
△
φ

2

{\displaystyle W={\frac {C(\varphi \_{1}-\varphi \_{2})^{2}}{2}}={\frac {C(\bigtriangleup \varphi )^{2}}{2}}={\frac {q\*\bigtriangleup \varphi }{2}}}

{\displaystyle W={\frac {C(\varphi _{1}-\varphi _{2})^{2}}{2}}={\frac {C(\bigtriangleup \varphi )^{2}}{2}}={\frac {q*\bigtriangleup \varphi }{2}}}

Manbalar
--------

O'zbekiston aloqa va qxborotlashtirish agentligi Toshkent axborot texnologiyalari universiteti Fikzika kursi kitobi Darslik 1-qism 98 - 99 betlar