課程名稱︰普通物理學甲下 課程性質︰必修 課程教師︰傅昭銘 開課學院：工學院 開課系所︰機械工程學系 考試日期（年月日）︰? 考試時限（分鐘）：120分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 一、選擇題 1.If the net flux through a gaussian surface is zero,the following four statements could be true.Which of the statements must be true? (a) There are no charges inside the surface. (b) The net charge inside the surface is zero. (c) The electric field is zero everywhere on the surface. (d) The number of electric field lines entering the surface equals the number leaving the surface. (e) (b)and(d) 2.Equipotentials are lines along which (a) the electric field is constant in magnitude and direction. (b) the electric charge is constant in magnitude and direction. (c) maximum work against electrical forces is required to move a charge at constant speed. (d) a charge may be moved at constant speed without work against electrical forces. 3.Four equa1-magnitude point charges, two negative and two positive, are arranged at the corners of a square as shown below. Let V and E be the potential and the electric field magnitude, respectively, at the center of the square, and let Vo and Eo be the same quantities at the same point if the upper right negative charge only were present. Which of the following expresses the values of V and E?(圖略) 4.The electric potential inside a charged solid spherical conductor in equi1ibrium (a) is constant and equal to its value at the surface. (b) decreases from its value at the surface to a value of zero at the center. (c) increases from its value at the surface to a value at the center that is a multiple of the potential at the surface. (e) is equal to the charge passing through the surface per unit time divided by the resistance. 5.One of Maxwell's equations is ▽‧ B = 0 . Which of the following sketches shows the magnetic field lines that clearly violate this equation within the region bounded by the dashed lines? (圖略) 6. The segment of wire (total length = 6R) is formed into the shape shown and carries a current I .What is the magnitude of the resulting magnetic field at the point P?(圖略，圖為一四分之一圓弧，P在圓心) (a) μI/8R (b) μI/2R (c) μI/4R (d) μI/2πR (e) μπI/8R 7. A current may be induced in a coil by (a) moving one end of a bar magnet through the coil. (b) moving the coil toward one end ofthe bar magnet. (c) holding the coil near a second coil while the electric current in the second coil is increasing. (d) all of the above. (e) none of the above. 8. The emf that appears in Faraday's law is (a) around a conducting circuit. (b) around the boundary of the surface used to compute the magnetic flux. (c) throughout the surface used to compute the magnetic flux. (d) perpendicular to the surface used to compute the magnetic flux. (e) none of the above. 9. For an inductor, battery and capacitor connected in series, the equation describing the motion of charge is L(d^2 Q / d t^2)+ (1/C)Q=ε where L is the inductance, C is the capacitance,ε is the voltage and Q is the charge.An analogous equation can be written for a simple harmonic oscillator with force f ,acceleration a,position x,mass m,and the spring constant k. Which of the following correctly lists the mechanical analogs of L,C,Q,andε? L C Q ε (a) m k x a (b) m 1/k x f (c) k x m f (d) 1/k 1/m x a (e) x 1/k 1/m f 10. In an electromagnetic wave, i) how are the electric and magnetic field directions related and ii) what is the speed of 1ight (expressed as c)? (a) E∥B, c=(εμ)^(1/2) (b) E⊥B, c=(εμ)^(1/2) (c) E∥B, c=1/(εμ)^(1/2) (d) E⊥B, c=1/(εμ)^(1/2) (e) E⊥B, c=(ε/μ)^(1/2) 二、簡答題 1. A metal sphere of radius R, carring charge Q, is surrounded by a thick concentric metal shell (inner radius a, outer redius b ). The shell carries no net charge. The surface charge density σ at R is σ(R) =_____,at a is σ (a)=____,and at b is σ(b) =_____.The potential at the center (using infinity as the reference point) is V(0)=_____.(圖略) 2.The energy density of electric field E in vacuum is u(E) = _____ The energy density of magnetic field B in vacuum is u(B) = _____ 3. A parallel-plate capacitor has charge Q, area A and separation d . The force between the plates of the capacitor is_____. Is the force attrictive or repulsive? _____. 4. Two infinite parallel wires at a distance d carry constant current I(1) and I(2) respectively in the opposite direction, the force per unit length on the second wire is _____. Is the force per unit length attrictive or repulsive? __ 三、計算或問答題 1. (a) Calculate the electric field inside and outside a uniformly charged nonconducting solid sphere of radius R that has a total charge Q . Plot the electric field variation inside and outside the sphere. (b) Find the electric potential inside and outside the sphere. Plot the electric potential variation inside and outside the sphere. (c) Calculate the magnetic field inside and outside a long straight wire of radius R that carries a uniformly distributed current I . Plot the magnetic field variation inside and outside the wire. 2. (a) A solid cylindrical conductor of radius a and charge Q is coaxial with a cylindrical shell of negligible thickness, radius b>a, and charge –Q. Find the capacitance of this cylindrical capacitor if its length is l. (b) Calculate the inductance for the coaxial cable of radius a and radius b (b>a). 3. Consider the circuit as shown below. What are the currents through the resistors at (a) t=0, and (b) t=∞. (c)Show that the current charging the capacitor is given by I(t)=(V/R1)e^(1/τ) where τ=R1R2C/(R1+R2). (圖略，一個電壓源先串連一電阻R1，一起並連一電容C,在一起並連一電阻R2) 4. (a) What is the origin of magnetism? (b) Describe properties of paramagnetism(順磁性),diamagnetism(抗磁性) and ferromagnetism(鐵磁性). 5. (a)寫出電磁學 Maxwell's Equations, 並詳述各式之物理意義。 (b)何謂位移電流(displace current),解釋其於空間傳遞電磁之物理意義。 6.對本課程教學與上課內容的意見。(5分) 考卷照片(共四面) http://tinyurl.com/6afwkfg http://tinyurl.com/5v84g5d http://tinyurl.com/6b38th8 http://tinyurl.com/5rbulkx --

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