课程名称︰普通物理学甲下 课程性质︰系必修 课程教师︰张宝棣 开课学院：电资学院 开课系所︰资工系 考试日期（年月日）︰2008/03/26 考试时限（分钟）：120 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.An electric dipole in a uniform electric field is displaced slightly from its equilibrium position, as shown in Fig.1, where θ is small. The separation of the charges is 2a, and the moment of inertial of the dipole is I. Assuming the dipole is released from this position, prove that its angular orientation exhibits simple harmonic motion and find its frequency (10%) 2.Four identical particles, each having charge +q, are fixed at the corners of a square of side L. A fifth point charge -Q lies a distance z along the line perpendicular to the plane of the square and passing through the center of the square. (a) What is the force exerted by the other four charges on -Q? (b) If z is small compared with L, the above expression reduces to vector(F) = -(constant)(vector(z)). What is the period of this motion if the mass of -Q is m? 3.An infinately long insulating cylinder of radius R has a volume charge density that varies with the radius as ρ = ρ0 * ( a - r / b ) where ρ0, a and b are positive constant. Use Gauss' law to determine the magnitude of the electric field at radial distance (a) r < R and (b) r > R (10%) 4.A hadrogen atom can be regarded as a proton with charge +e in the center of a sphere and an electric cloud circulating spherically around the center. Assume that the charge density of the cloud at radius r is ρ(r) = -C * e^(-2 * r / a0 ), where a0 is called the Bohr radius whose value is 0.53 * 10E-8 cm and C is a constant, please find (a) the total charge, Q(r), inside a sphere with radius r (8%), (b) the constant C such that the total charge of a hadrogen atom is 0 (4%), and (c) the electric field and the electric potential at the Bohr radius a0 (8%). (Hint: Since the total charge of a hadrogen atom is 0, Q(∞) = 0.) 5.The electric field inside a nonconducting aphere of radius R, with charge spread uniformly throughout its volume, is radially directed and has magnitude E(r) = ( q * r ) / ( 4 * π * ε0 * R ) Here q (positive or negative) is the total charge within the aphere and r is the distance from the sphere's center. (a) Taking V = 0 at the center of the sphere, find the electric potential V(r) inside the sphere. (b). What is the difference in electric potential between a point on the surface and the sphere's center? (c) If q is positive, which of those two point is at higher potential? (15%) 6.What is the capacitance of the capacitor, of plate area A shown in Fig. 3? (5%) 7.For the circuit shown in Fig. 4, switch S has been open for a long time. At time t = 0 the switch is then closed. (a) What is the battery current just after switch S is closed? (b) What is the battery current a long time after switch S is closed. (c) The switch has been closed for a long time. At time t = 0 the switch is then opened. Find the current through the 600-kΩ resistor as a function of time. (15%) 8.Consider two parallel-plate capacitors, C1 and C2, that are connected in parallel. The capacitors are identical except that C2 has a dielectric inserted between its plates. A voltage source of 200V is connected across the capacitors to charge them and is then disconnected. (a) What is the charge on each capacitor? (b) What is the total stored energy of the capacitors? (c) The dielectric is removed from C2. What is the final total stored energy of the capacitors? (d) What is the final voltage across the two capacitors? (15%) --

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