※ [本文轉錄自 NTU-Exam 看板] 作者: tdk4 (大飛) 站內: NTU-Exam 標題: [試題] 94下石明豐普物第一次期中考題 時間: Tue Apr 11 19:27:11 2006 課程名稱︰普通物理學甲下 課程性質︰ 課程教師︰石明豐教授 開課系所︰電機系 考試時間︰2006/4/11 試題 : 1.Two identical thin rods of length 2a carry equal charges +Q uniformly distributed along their lengths. The rods lie along the axis with their centers separated by a distance b>2a. Find the force the left rod exerts on the right rod. 2.A sphere of radius R has a uniformly volume charge densityρ. Determine the magnetic field at the center of the sphere when it rotates as a rigid object with angular speed ω about an axis through its center. 3.As shown in Fig.3, two large parallel vertical conducting plates seperated by distance d are charged so that their potential are +V0 and -V0. A small conducting ball of mass m and radius R (where R<<d) is hung midway between the plates. The thread of length L supporting the ball is a conducting wire connected to ground so the ball is at V=0. The ball hangs straight down in stable equilibrium when V0 is suffiently small. Find the critical value of V0 such that the equlibrium of the ball is unstable. ground === | | | | |L | +V0| | |-V0 | ○ | | | | | |<----d--->| 4.The switch in Fig.4 closed when Vc is increasing and reaching 2V0/3 and opens when Vc is decreasing and reaching V0/3. The plot of Vc v.s. time is shown in Fig.4. Find the period T. R1 ----------^^^^^--- R1,R2 : 電阻為R1,R2的電阻器 | | | | >R2 | S : Switch | > | S | | B : 電動勢V0伏特的電池 | C B | | | C : 電容C的電容器 |------|---------| Vc : 電容器端電壓 ^Vc | | /\ /\ | / \ / \ ... (大概長這樣，不過沒有這麼尖。) |/ \/ \ (V最大為2V0/3，最小為V0/3) | (要求兩峰所相距時間T) |----------------->t 5.Consider two long, parallel and oppositely charged wires of radius d with their centers seperated by a distance D. Assume the charge is distributed uniformly on the surface of each wire. Find the capacitance per unit length. 6.A parallel plate capacitor consists of square plates of edge length L that are seprated by a distance d, where d<<L. A potencial difference V is maintained between the plates.A material of dielectric constant K fills half of the space between the plates. The dieletric slab is now withdrawn from the capacitor, as shown is Fig.6. (a)Find the capacitance when the left edge of the dielectric is at a distance x from the center of the capacitor (b)If the dielectric is removed at constant speed v, what is the current in the circuit as the dielectric is being withdrawn? <--------L---------> —————————— d |<--x-->██████ ==>v (兩板間電位差V) —————————— dieletric slab 7.A particle of charge q and mass m is subjected to gravity acting downward on the page, and a magnetic field of magnitude B acting in a direction perpendicular to tha page, poiting into the page. We assume the initial velocity of the particle is 0. At t=0, we release the particle form the origin to let it move freely. Please find the trajectory of the particle as a function of time. 8.Show that a test charge in the eletric field due to any given static charge distribution cannot be in stable equlibrium. [Hint:Use Gauss's Law] --

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