简单学习网 让学习变简单
当前位置:首页 >> 学科竞赛 >>

物理竞赛试题1 (20)

Theoretical Question 1

Page 1/2

Theoretical Question 1:

"Ping-Pong" Resistor
A capacitor consists of two circular parallel plates both with rad

ius R separated by distance d, where d << R , as shown in Fig. 1.1(a). The top plate is connected to a constant voltage source at a potential V while the bottom plate is grounded. Then a thin and small disk of mass m with radius r ( << R, d ) and thickness t ( << r ) is placed on the center of the bottom plate, as shown in Fig. 1.1(b). Let us assume that the space between the plates is in vacuum with the dielectric constant ε 0 ; the plates and the disk are made of perfect conductors; and all the electrostatic edge effects may be neglected. The inductance of the whole circuit and the relativistic effects can be safely disregarded. The image charge effect can also be neglected.
side view R d V


d t q





Figure 1.1 Schematic drawings of (a) a parallel plate capacitor connected to a constant voltage source and (b) a side view of the parallel plates with a small disk inserted inside the capacitor. (See text for details.) (a) [1.2 points] Calculate the electrostatic force Fp between the plates separated by d before inserting the disk in-between as shown in Fig. 1.1(a). (b) [0.8 points] When the disk is placed on the bottom plate, a charge q on the disk of Fig. 1.1(b) is related to the voltage V by q = χV . Find χ in terms of r , d , and ε 0 . (c) [0.5 points] The parallel plates lie perpendicular to a uniform gravitational field g . To lift up the disk at rest initially, we need to increase the applied voltage beyond a

Theoretical Question 1

Page 2/2

threshold voltage Vth . Obtain Vth in terms of m , g , d , and χ . (d) [2.3 points] When V > Vth , the disk makes an up-and-down motion between the plates. (Assume that the disk moves only vertically without any wobbling.) The collisions between the disk and the plates are inelastic with the restitution coefficient η ≡ ( v after / v before ) , where v before and v after are the speeds of the disk just before and after the collision respectively. The plates are stationarily fixed in position. The speed of the disk just after the collision at the bottom plate approaches a "steady-state speed" vs , which depends on V as follows:
v s = αV 2 + β .


Obtain the coefficients α and β in terms of m , g , χ , d , and η . Assume that the whole surface of the disk touches the plate evenly and simultaneously so that the complete charge exchange happens instantaneously at every collision. (e) [2.2 points] After reaching its steady state, the time-averaged current I through the capacitor plates can be approximated by I = γV 2 when qV >> mgd . Express the coefficient γ in terms of m , χ , d , and η . (f) [3 points] When the applied voltage V is decreased (extremely slowly), there exists a critical voltage Vc below which the charge will cease to flow. Find Vc and the corresponding current I c in terms of m , g , χ , d , and η . By comparing Vc with the lift-up threshold Vth discussed in (c), make a rough sketch of the I V characteristics when V is increased and decreased in the range from V = 0 to 3 Vth .



2014 年第二十四届全国初中应用物理竞赛(巨人杯)试题注意事项: 1.请在密封线内填写所在地区、学校、姓名和考号。 2.用蓝色或黑色钢笔、圆珠笔书写。 3.本试卷...


20 届全国中学生物理竞赛复赛试卷 2003 年 9 月 20 日 题号 得分 复核人 二 三 四 五 六 七 总计 全卷共七题,总分为 140 分。 、 分)图中 ...


第二十一届全国中学生物理竞赛决赛试题(附参考答案)_学科竞赛_初中教育_教育专区。第 二十一 届全国中学生物理竞赛决赛试题一(20 分)有一光光导纤维,光芯折...


第二十一届全国中学生物理竞赛复赛试题本卷共七题,满分 140 分. 一、(20 分)薄膜材料气密性能的优劣常用其透气系数来加以评判.对于均匀薄膜材料,在一定温度下,...


第二十届全国中学生物理竞赛预赛题 第 1 页 四、 (20 分)从 z 轴上的 O 点发射束电量为 q(>0) 、质量为 m 的带电粒子,它们速度统方向分布在 以 ...


第32届全国中学生物理竞赛预赛试卷及答案(标准word版)_学科竞赛_高中教育_教育...16 . (20 分 ) 如示意图所示,一垂直放置的高为 15.0cm 的圆柱形中空...


第21 届全国中学生物理竞赛复赛题试卷题号 得分 阅卷人 本卷共七题,满分 1 4 0 分. 一、(20 分)薄膜材料气密性能的优劣常用其透气系数来加以评判.对于均匀...

第二十六届全国物理竞赛复赛试题及答案 届全国物理竞赛复赛试卷 第 26 届全国物理竞赛复赛试卷 一、填空(问答)题(每题 5 分,共 25 分)http://...


2014年第31届全国中学生物理竞赛复赛试题及答案(全Word版)_学科竞赛_高中教育_教育专区。2014年 第31届全国中学生物理竞赛复赛试题及答案(全Word版) 原版无水印第...


初中物理竞赛试题及答案一、选择题:以下各题所列答案中只有一个是正确的。把...1.西 5 2.水平向前 水平向后 3.20 24 57 4.356 12 5.响度(或音量,...

网站首页 | 网站地图
All rights reserved Powered by 简单学习网
copyright ©right 2010-2021。