同济大学：《大学物理》课程教学资源（电子教案，英文版）第十四章 直流电路

Capacitor and Dielectric -1000773510

Capacitor and Dielectric

Agenda today l.Capacitance(电容) 2.Combination of capacitor 2.Gauss's law in dielectrics(电介质） 3.Energy of electric field

Agenda today 1. Capacitance（电容） 2. Combination of capacitor 2. Gauss’s law in dielectrics （电介质） 3. Energy of electric field

Capacitor: A pair of conductors,whether separated by empty space or nonconducting material,forms a capacitor Capacitor is a useful device to store energy and charge Capacitance:(电容) The constant that is the charge on either plate of the capacitor divided by potential difference of two plates 1F=1C/V AU

Capacitor: A pair of conductors, whether separated by empty space or nonconducting material , forms a capacitor Capacitance:（电容） The constant that is the charge on either plate of the capacitor divided by potential difference of two plates Capacitor is a useful device to store energy and charge 1F=1C/V

The parallel plate Capacitor(平行板电容器 E= E 0 U,-Un=[E.di-Ed-9d S A Capacitance: U

The parallel plate Capacitor(平行板电容器) -Q d + + + + + - - - - - A B +Q E S d S U U q C o A B    Capacitance: 

The cylindrical Capacitor(柱形电容器) By Gauss's law: E 2m8,rl s-E-2 qdr △U= R 2πE R capacitance C=. 2π61 △U In Rg/Ra

The cylindrical Capacitor（柱形电容器） l RA By Gauss’s law： RB A B o R R l q U ln 2    h r B A o R R l U q C ln 2    capacitance 

The spherical capacitor(球电容器 E= 4π6。r1 △U= gdr ,4rr 4π6。 R Ra C=9 RARB △U =4rR。-R4 when Rg-→oo C=4π6R

The spherical capacitor（球电容器） RA RB B A A B o R R R R U q C     4 

Energy in capacitor dq a If we want move dq from the plate with negative charge to the positive one,the work needed is: duuldid

Energy in capacitor dq -q +q If we want move dq from the plate with negative charge to the positive one, the work needed is:

5小12g呈 Because Q=CU,the result can also be written as: 号r 2

Because Q=CU, the result can also be written as:

Capacitors in parallel g=CV,4=C,U,…UC宁c宁c= 9=q+9+…+qn=(C+C2+…Cn)U The equivalent capacitance =号=G+C++C

Capacitors in parallel , ,  U C1 C2 C3 q1 C1 U q2 C2 U q  q1  q2  qn  C1 C2 Cn U The equivalent capacitance

Capacitor in series 号培共 U-+,…U,-G++ The equivalent 1J11.1 一十 capacitance

Capacitor in series C1 C2 Cn U The equivalent capacitance