浙江大学大学物理甲下 chapter 30

1、Chapter 30 Capacitance130-1 Capacitors A device that stores charge (and then energy in electrostatic field) is called a capacitor.21. Capacitance of a isolated conductorqVcapacitanceThe capacitance of an isolated spherical conductor reads:aThe SI unit of capacitance is farad (法拉): 1 farad = 1 F = 1

2、coulomb/volt32. CapacitorqADB-qq These two conductors are called plates (no matter what their shapes).4Symbolically, a capacitor is represented as: CC stands for the capacitance of a capacitor. Remarks :1. A capacitor is said to be charged if its plates carry equal and opposite charges +q and -q. q

3、is not the net charge on the capacitor, which is zero. 52. The capacitors can be used to produce electric field. +q-q For the time being, we assume that the plates of a capacitor exist in a vacuum. 3. In circuits, capacitors are often used to smooth out the sudden variations in line voltage that may

4、 destroy computer memories. 630-2 Capacitance The capacitance is a geometrical factor that depends on the size, shape and separation of the capacitor plates, as well as the material that occupies the space between the plates. 730-3 Calculating the CapacitanceProcedure: Suppose that the capacitor is

5、charged, with q on the two plates respectively. 2. Find the electric field E in the region between the plates.3. Evaluate the potential difference between the positive and negative plates, by using the formula: 84. The expected capacitance is then: A Parallel-plate Capacitor 9A Spherical Capacitor10

6、Example: What is the capacitance of the Earth, viewed as an isolated conducting sphere of radius R=6370km? 1 mF = 10-6 F 1 pF = 10-12 F 11A Cylindrical CapacitorThe capacitor has length L, and Lb. 12Quick quiz-1 A capacitor stores charge Q at a potential difference V. If the voltage applied by a bat

7、tery to the capacitor is doubled to 2V, the capacitance falls to half its initial value and the charge remains the same. (2) the capacitance and the charge both fall to half their initial values. (3) the capacitance and the charge both double. (4) the capacitance remains the same and the charge doub

8、les.13Quick quiz-2 Many computer keyboard buttons are constructed of capacitors, as shown in Figure. When a key is pushed down, the soft insulator between the movable plate and the fixed plate is compressed. When the key is pressed, the capacitance (1) increases, (2) decreases, or (3) changes in a w

9、ay that we cannot determine because the complicated electric circuit connected to the keyboard button may cause a change in V. 1430-4 Capacitors in Series and Parallel1. Capacitors connected in Parallel (并联):abC1C2Question: If we identify the above capacitors connected in parallel as a single capaci

10、tor, abCeqwhat is its capacitance? 15 We assume that a battery of potential difference V is connected between points a and b, so that the capacitors are charged: DVabC1C2 In according with the charge conservation, we have:abCeqDV16In general, for capacitors in parallel combination, 2. Capacitors con

11、nected in Series (串联):abC1C2DVDV2DV1-qqqq-q-qCeqab17In general, for capacitors in series combination, 1830-5 Energy Storage in an Electric Field When a capacitor is charged, it will store energy in the electrostatic field between its plates. Consider the process that a capacitor is charged. Suppose

12、that at the instant t, the capacitor has been charged with charge q, the voltage between its plates is V. qV19 During the next time interval t, t+dt, if an additional charge dq is added on the plates, If the process is continued until a total charge q has been transferred, the total potential energy

13、 is:dqqVthe increase of the electrostatic energy is, 20Question: Why do we say that the energy is stored in the electric field between the capacitor plates? Take the parallel-plate capacitor as an example. If the capacitor is charged with q, then: 21 Without changing q, we pull the plates apart unti

14、l their separation is twice as large as it was initially. Thus we conclude the energy is stored in the electric field that is present in this region. What we have done is to double the volume of the space between the plates.22 The electrostatic potential energy is expressed as: is just the volume of

15、 the space occupied by the electric field between the plates. Energy densityEnergy density u23Example: An isolated conducting sphere of radius R carries a charge q. 1 How much energy is stored in the electric field of this charged conductor? 2 What is the energy density at the surface of the sphere?

16、 3 What is the radius b of an imaginary spherical surface such as a thirds of the stored energy lie within it? Solution: 242 Because the electric field distribution is,Checking:Expected !253 The required parameter b satisfies the equation:26Quick Quiz-3 You have three capacitors and battery. In whic

17、h of the following combinations of the three capacitors will the maximum possible energy be stored when the combination is attached to the battery? (1) series (2) parallel (3) both combinations will store the same amount of energy. 27Quick Quiz-4 You charge a parallel-plate capacitor, remove it from

18、 the battery, and prevent the wires connected to the plates from touching each other. When you pull the plates apart to a larger separation, do the following quantities increase, decrease, or stay the same? (1) C; (2) Q; (3) E between the plates; (4)V; (5) energy stored in the capacitor. Quick Quiz-

19、5 Repeat Quick quiz above, but this time answer the questions for the situation in which the battery remains connected to the capacitor while you pull the plate apart. 28 Application: RC Circuits Combine Resistor and Capacitor in SeriesStart: Switch at position (a),Use Loop ruleTime dependent quanti

20、ties:i(t), VC(t), q(t);Solve to get:CaRb29Time constant for RC circuit:At t=0, q(0)=0 At t=, q() = C Charged capacitor like an opposing batteryThe voltage is slowing increased.30Then switch turn to b, C discharges:The voltage is slowing decreased.31Example: rectification3230-6 Capacitor with Dielect

21、ric We now consider the effect of filling the interior of a capacitor with a dielectric material: The effect of the dielectric material is to reduce the strength of the electric field in its interior from the initial E0 in vacuum to E =E0/e. 33 If the potential difference between the capacitor plate

22、s are the same, the electric fields inside the capacitor must be the same also. DVDV This implies that, in two situations, the capacitor is charged differently. -qqq-qRecalling, we get:34As a result, The presence of dielectric increases the capacitance by a factor e. If we fill the capacitor with dielectric when we disconnect the battery, (the charge is not changer) 35Quick Quiz-6 A filly charged parallel-plate capacitor remains connected to a