Chapter 22 Capacitance, Dielectrics, Electric Energy Storage 5. Calculating the Capacitance Assume qE=△VB2()=C= Determining capacitance(求电容步骤): 1)Assuming a charge g to have been placed on the plates(让导体带等量异号电荷); 2) Finding e due to this charge(求两极板间电场); 3) Evaluating y(求两极板间电压); 4) Calculating c from definition(用定义C=qV求O)
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage 5.Calculating the Capacitance Determining capacitance (求电容步骤)： 1) Assuming a charge q to have been placed on the plates(让导体带等量异号电荷）； 2) Finding E due to this charge (求两极板间电场)； 3) Evaluating V (求两极板间电压)； 4) Calculating C from definition (用定义C=q/V求C)。 Assume q E V (V) AB V q C =
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage DAParallel-Plate Capacitor (p527) Assume o (charge per unit area), s(area) and d The field between E O the plates is 0 A E di=Edl= ed AB C与Q无关
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage 1) A Parallel-Plate Capacitor (p527) Assume (charge per unit area), S (area) and d. 0 E = = A B AB V E dl = dEdl 0 = Ed 0 d = VAB Q C = 0 / d S = d 0S = C 与 Q 无关。 d S + + + + + + Q -Q - - - - - - The field between the plates is
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage 2) A Spherical capacitor(球形电容器):P529 a spherical capacitor consist of two thin concentric spherical conducting shells. Determine the capacitance of the two shells. Solution: The inner shell carries a uniformly distributed charge o on its surface, and the outer shell an equal but opposite charge-O (R1<r<R2) R E Q RW 兀CF
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage 2) A Spherical Capacitor (球形电容器): P529 R1 R2 ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ - - - - - - - - r 2 r 4π 0 e r Q E = ( ) 1 R2 R r P * A spherical capacitor consist of two thin concentric spherical conducting shells. Determine the capacitance of the two shells. Solution: The inner shell carries a uniformly distributed charge Q on its surface, and the outer shell an equal but opposite charge –Q
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage ,R, dr V=E di 4兀0 R Q11 4T Eo r R2 Q R ab RI 4兀ER1R R 2 R 可看出C只与几何尺寸有关,而与q无关
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage = = 2 1 2 0 d 4 π d R l R r Q r V E l ) 1 1 ( 4π 0 R1 R2 Q = - 2 4 0 r q E = R1 R2 ＋ ＋ ＋ ＋ ＋ ＋ ＋ ＋ - - - - - - - - r P * Vab Q C = 2 1 4 0 1 2 R R R R - = 可看出C只与几何尺寸有关，而与 q 无关
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage 3) A Cylindrical Capacitor(圆柱形电容器):P528 In the region of r, <r<R 1>>RB E 2兀E0r R B R edr= 2兀Er 2 R R RI AL 2丌EL R 28 R R
Chapter 22 Capacitance, Dielectrics, Electric Energy Storage 3) A Cylindrical Capacitor (圆柱形电容器): P528 1 2 0 0 ln 2 d 2 d 2 1 R R r r V E r R R B A = = = r E 2 0 = In the region of , 1 R2 R r RA RB l RB l + + + + - - - - 1 2 0 1 2 0 ln 2 ln 2 R R L R R L V q C = = =