課程名稱︰普通物理學甲下 課程性質︰化學系必帶,地質系選修 課程教師︰蔡政達 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2010.04.20 考試時限（分鐘）：120 mins 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. Fig A shows, in cross section, two solid spheres with uniformly distributed charge throughout their volumes. Each has radius R. (1)Point P1 lies on a line connecting the centers of the spheres, at radial distance 2R/3 from the center of sphere 1. If the net electric field at point P1 os zero, what is the ratio q2/q1 of the total charge q2 in sphere 2 to the total charge q1 in sphere 1? (10 points) (2) In another case, point P2 lies on the same line at radial distance 5R/4 from the center of sphere 2. If the net electric field at point P2 is zero, what is the ratio q2/q1 ?(10 points) ___ ___ ╱ ╲ ╱ ╲ 好難畫囧 ∕ ﹨∕ ﹨ 兩球有接觸 半徑都是R ∣ ●○│∣ ● ∣○ 實心圈是球心 右邊空心是P2 左邊是P1 ﹨ ∕﹨ ∕ (相對位置 沒有照比例) ╲___╱ ╲___╱ 2. Fig B shows a wood cylinder of mass m=0.4kg and length L=0.2m, with N=20 turns of wire wrapped around it longitudinally, so that the plane of the wire coil contants the long central axis of the cylinder. the cylinder is released on a plane inclined at an angle θ to the horizontal, with the plane of the coil parallel to the incline plane. If there is a vertical uniform magnetic field of magnitude 0.5T. what is the least current i through the coil that keep the cylinder from rolling down the plane?(20 points) ↑↑ ↑ ↑↑ ↑ ╱╲↑↑ ↑B ↑↑╱ ↗╲↑ ↑ ╱ L ╱○ ╱↑↙ ╱ ╱╲↑ │╲ ↑╱ ╱↗i ↑ │↑╲ Θ╱ ↑ ╱ │ ↑ ╲ ↑ ╱ │ ↑↑ ╲ ╱ │ θ╲╱ └───── 3. In Fig C, R1=5.00Ω, R2=10.0Ω, R3=15.0Ω,C1=5.00uF,C2=10.0uF,and the ideal battery has emfε=20.0V. Assuming that the circuit is in the steady state, what is the total energy stored in the two capacitors? (20 points) C1 R2 ┌││──┬─﹏─┐ │ │ │ │ │ │ │ │ C2 │ ├─﹏──┴─││┤ │+ │ ==-ε │ │ R3 │ └───﹏────┘ 4. A pIatic disk of radius R=60.0cm is charged on one side with a uniform surface charge densuty σ=8.00fC/m^2, and then three quadrants of the disk are removed. The remaining quadrant is shown in Fig D. With electric potential V=0 at infinity, then (I) What is the potential due to the remaining quadrant at point P, which is on the central axis of the original disk at distancc D=0.26cm from the origin center? (14 points) (2) What is the electric field at point P? (6 points) ●P │↑ │ D （圓形側視圖）囧 ＿＿＿ ／ │ ＼ ／ │↓ ＼ ( ● ) ╲ ↙R ╱ ╲_____ ╱ 5. Fig E shows a cross section of a long cylindrical conductor of radius a=4.00 cm containing a long cylindrical hole of radius b=1.50 cm. The central axes of the cylinder and hole are parallel and are distance d=2.00cm apart; current i=5.25 A is uniformly distributed over the tinted area. (a) What is the magnitude of th magnetic field the at the center of the hole? (10 points) (b) Discussthe two special cases b=0 and d=0(10 points) __ ╱ ╲ ∕ ﹨ 大圓圓心到小圓圓心距離＝d 大圓半徑a ∣ ○∣ ﹨ ∕ ╲__╱ --

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