課程名稱︰普通物理學甲下 課程性質︰數學系大一必修 課程教師︰張寶棣 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2015/5/14 考試時限（分鐘）：10:20~12:40 試題 : 1. Please answer the following questions. ‧Explain why capacitance and inductance are independent on the amounts of charge in a capacitor and current in an inductor, respectively. (5%) ‧What is Eddy current? What is Hall effect? (5%) ‧Is Ampere's law valid for the straight wire with finite length? How do you know? List the causes of the resistance. (5%) 2. Two spherical conductors of radii 20 mm and 100 mm are connected by a thin wire and carry charges q and q , respectively. If the wire is cut and the 1 2 centers of the spheres are 250 mm apart, there is a repulsive force of 3.5 N between them. Use this information to calculate (a) q and q and (b) the 1 2 electric fields at the surfaces of the conductors when they are connected by the wire. (Neglect the charge on the wire). (10%) 3. Two identical capacitors of capacitance C are connected in series across a total potential V, as shown in Fig.1. A dielectric slab of dielectric constant κ can fill one of the two capacitors and is slowly inserted into that capacitor. Compute the canges in the total electric energy of the two capacitors, in the charge on each capacitor, and in the potential drop across each capacitor. Account for any energy change by a corresponding change in energy in some other part of the system. (15%) 4. Two resistors and two capacitors are connected in series to a battery as shown in Fig.2. Calculate the potential at B relative to that at A: (a) shortly after the closing of the switch and (b) a long time after the closing of the switch. (c) How fast does the circuit reach a steady state? (Given a time scale τ. Hint: in any time current should be the same everywhere in the circuit). (15%) -19 -15 5. An electron, of charged q = -1.6 ×10 C, has a size of about 3 ×10 m, called its classical radius. The magnetic dipole moment of the electron is -23 2 roughly 10 A‧m . (a) Suppose that this magnetic moment were due to the entire charge q orbiting at the classical radius. What would the speed of the charge be to generate this magnetic moment? (b) Suppose that the electron's magnetic moment were perpendicular to a magnetic field of magnitude 1 T. What is the torque on the electron? (8%) 6. A long cylindriacl conductor of radius a has two cylindrical cavities of diameter a through its entire length, as shown in Fig.3. A current I is directed out of the paper and is uniform through a cross section of the conductor. Find the magnitude and direction of magnetic field in terms of μ, I, r and a at (a) point P and (b) point P . (10%) 0 1 2 7. Consider a 9-V battery attached two conducting, frictionless rails 0.1 m → apart. There is a magnetic field B of magnitude 0.5 T perpendicular to the rails, and a conducting bars can slide over the rails perpendicular to them as well as to the field(Fig.4). The bar is placed on the rails, starts from rest, and accelerates. (a) What is the direction of its motion? (b) the direction of the emf induced? (c) Given that the total resistance of the closed circuit is 3Ω, calculate the current in the bar when its speed 3 m/s. (15%) 8. The switch in the current shown in Fig.5 has been closed for a long time. (a) What is the current in each leg of the circuit? (b) When the switch is opened, the current in the inductor drops by a factor of 2 in 8 μs. What is the value of the inductor? (c) What is the current passing in each leg at 12 μs? (12%) 12V ▕ ————▕▕ ———— ▕ ▕ ▕ ▕ ▕ ╲ ▕ ╱ ○ ╱ ▕ S ╲ ▕ 5000Ω ╲ ○ ╱ ▕ ╱ ▕ ╲ ▕ ▕ 24Ω ▕ ▕ /\ /\ ▕ —— \ / \ ——— ▕ \/ \/ ▕ ▕ ▕ ▕ ▕ ▕ ▕ ————﹏﹏﹏———— L --

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