課程名稱︰普通物理學甲 課程性質︰必修 課程教師︰李尚凡 開課學院：工學院 開課系所︰機械工程系 考試日期（年月日）︰2008/4/18 考試時限（分鐘）：240 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.A point charge Q is located on the axis of a desk of radius R at a distance b from the plane of the disk .If one fourth of the electric flux from the charge passes through the disk , find the ratio R/b. 2. A sphere of radius 3a is made of a nonconducting material that has an uniform volume charge density ρ.(Assume that the material does not affect the electric field.) A spherical cavity of radius a ,with its center at (x,y,z)= (0,0,a) is now removed from the sphere, as shown in the figure .Find the ele- ctric field component Ex,Ey and Ez within the cavity. 3.Determine the equivalent capacitance of the combination shown in the figure. 3C 2C ┌∥——┬──∥──┐ │ │ │ ┤ ﹦C ├─ │ │ │ └∥──┴──∥──┘ 2C 3C 4.A capacitor is constructed from two square plates of sides l and separation d.A material of dielectric constant k is inserted a distance x into capacitor. Assume that d is much smaller than x (a)find the equivalant capacitance of the device .(b)calculate the energy stored in the capacitopr ,letting ΔV represe- nt the potential difference.(c)find the direction and magnitude of the force exerted on the dielectric, assuming a constant potential differenceΔV.Ignore friction. l ██████████ ← x → ↑ k d ↓ ██████████ 5.When an uncharged conducting sphere of radius a is placed ar the origin of an xyz coordinate system that lies in an initially uniform electric field E= → Eok the resulting electric potential is V(x,y,z)=Vo for the point the sphere and V(x,y,z)=Vo-Eoz+Eoa︿3.z/(xx+yy+zz)︿3/2 for points ouside thesphere, where Vo is the (constant)electric potential on the conductor .Use the equation to determine the x,y and z components of the resultingelectric field. 6.Assume that the magnitude of the magnetic field outside the sphere of radius R is B=Bo(R/r)(R/r), where Bo isa constant,r is distance from the center.Dete- rmine the total energy stored in the magnetic field outside the sphere and ev- aculate your result for Bo=0.00005T and R=0.000006m,values appropriate for the Earth's magnetic field. 7. A cylinder of radius R and height 2R has uniform charge density ρ. Determ- ine the magnetic dipole moment when it rotates as a rigid body with angular volocity ω about an axis through its center. 8. The bar of mass m in the figure is pulled horizontally cross paraelle rails by a massless string that passes over an ideal pulley and is attached to a su- spended object of mass M. The uniform magntic field has a magnitude B, and the distance between the rails is l.The rails are connected at one end by a load resistor R. Derive an expression that gives the horizontal speed of the bar as a function of time, assuming that the suspended object is released with the bar at rest at t=0.Assume no fricton between rails and bar. 9. The switch in the figure(a)closes when ΔVc＜ΔV/4. The volumeter reads a voltage as plotted in the figure(b).What is the period T of the waveform in t- erms of R1, R2 and C ? 10. Electrons in a beam are accelerated from rest through a potential differ- ence ΔV.The beam enters an experimental chamber through a small hole. As sho- wn in the figure,the electron velocity vectors lie within a narrow cone of ha- lf angle ψ oriented along the beam axis .We wish to use a uniform magnetic field directed parallel to the axis to focus the beam, so that all of the electrons can pass through a small exit port on the opposite side of the cham- ber after they travel the length d of the chamber.What is the required magnit- ude of the magnetic field? (Hint:Because everyelectron passes through the same potential difference and the angle ψis small, they all requirethe same time interval to travel the axial distance d.) --

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