課程名稱︰普通物理學甲下 課程性質︰必修 課程教師︰楊忠喜 開課學院： 開課系所︰生機系 考試日期（年月日）︰2012/3/15 考試時限（分鐘）：120分 是否需發放獎勵金：是 （如未明確表示，則不予發放） 應該是從課本習題影印而來，所以題號順序不規則請見諒 部分圖形請參考課本@@ 試題： 25. Positive charge Q is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A positive point charge Q is placed at x = 2R on the x axis. Find the magnitude of the electric field at x =R/2 R R on the x axis and (2) V( — ) = ? (1) E(—) = ? 2% 2 2 1. Charge Q is on the y axis a distance a from the origin and charge q is on the x axis a distance d from the origin. Find the value of d in terms of a for which the x component of the force on q is the greatest. 1% _ 3. An electric dipole moment p = (3.00i + 4.00j)(1.24 ×10^-30 C‧m) is in an _ electric field E = (2000N/C)i. (a) What is the potential energy of the electric dipole? (b) What is the torque acting on it? (c) If an external agent turns the dipole until its electric dipole moment is _ p = (-4.00i + 3.00j)(1.24 ×10^-30 C‧m), how much work is done by the agent? 2% (a) Ｕ = ＿＿＿＿＿(J) _ (b) i = ＿＿＿＿＿(N-m) (c) Ｗext = ＿＿＿＿＿ (J) 15. A parallel-plate capacitor of plate area A and plate separation d. A potential difference Ｖ0 is applied between the plates. The battery is then disconnected, and a dielectric slab of thickness b and dieletric constant κe is placed between the plates as shown. Assume A = 115cm^2, d = 1.24cm, b = 0.78cm, κe = 2.61, Ｖ0 = 85.5V. (a) What is the capacitance Ｃ0 before the slab is inserted? (b) What free charge appears on the plates? (c) What is the electric field Ｅ0 in the gaps between the plates and the dielectric slab? (d) Calculate the electric field Ｅ in the dielectric slab. (e) What is the potential difference between the plates after the slab has been introduced? (f) What is the capacitance with the slab in place? 3% 5. Two rods of different materials but having the same lengths L and cross- sectionl areas A are arranged end-to-end between fixed, rigid supports, as shown in Fig.. The temperature is T and there is no initial stress. The rods are heated, so that their temperature increases by △T. That the rod interface is displaced upon heating by an amount. 2% □ ←—Ｌ—→ | ←—Ｌ—→□ □■■■■■■■■■■■■□ T □ α1,E1 | α2,E2 □ (a)| | □ | △Ｌ| □ □■■■■■■■■■■■■□ T + △T □ □ (b) 30. A thin glass rod is bent into a semicircle of radius r. A charge +q is uniformly distributed along the upper half and a charge -q is uniformly distributed along the lower half, as shown in Fig.. Find the electric field E at P, the center of the semicircle. 1% +＿ + ╱ +∕ | .P - \ ↙r - ＼＿ - 2. A spherically symmertrical but nonuniform distribution of charge produces an electric field of magnitude E = kr^5, directed radially outward from the center of the sphere. Here is the radial distance from that center. What is the volume density ρ of the charge distribution? 1% _ 72. A nonconducting solid sphere has a uniform volume charge density ρ. Let r be the vector from the center of the sphere to a general point P within the _ _ sphere. (a) Show that the electric field at P is given by E = ρr/3ε0. (Note that the result is independent of the radius of the sphere.) (b) A spherical cavity is hollowed out of the sphere, as shown in Fig.. Using superposition concepts, show that the electric field at all points within _ _ _ the cavity is uniform and equal to E = ρr/3ε0, where a is the position vector from the center of the sphere to the center of the cavity. 2% 3. A solid nonconducting sphere of radius R has a nonuniform charge distribution of volume charge density ρ = Ar where A is a constant and r is the center of the sphere. (The total charge on the sphere is Q) (a) Find E(R/3) = ? (用R, Q,ε0, π表示) 1% 　 (b) Find the total electrostatic potential energy Ｖtot = ? for this charge distribution. 2% (c) If V(∞) = 0 find V(R/2) = ? 2% _ _ 3. Find E at P due to the induced charge of the conducting sphere. E(P) = ? 1% ↑ 電中性金屬球 ∣ P ↙ ┼───⊙─── ∣+Q ← R → --

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