| 所組別： | 應用物理學系 | 科目： | 古典物理 | 考試時間： | 6月14日第1節 |
| 1. | (10%)A total charge Q is distributed uniformly throughout the volume of a
sphere of radius R. The electric field(radial) is By calculating the line integral from infinity to r,determine the potential for (a) r>R;(b) r=R; (c)r<R;and (d)r=0. |
| 2. | (15%) Two flat metal plates of area A are separated by a distance d,A
third metal plate of thickness t is placed midway between the plates. Determine (a) the capacitance before inserting, (b) the capacitance after inserting, (c) the capacitance differnce for parts(a) and (b) |
| 3. | (15%) A long coaxial transmission line carries current. I that, flows down
the surface of inner cylinder, radius R1 and back along the outer cylinder,
radius R2, the space between the conductors is filled with a substance having a
permeability μ Find (a) the auxiliary field  between the coaxial conductors,(b) the magnetic energy stored in this system, (c) the self-inductance per unit length for this transmission line. |
| 4. | (10%) The equation of state of a van der Waals gas consisting of N
molecules is given as Determine the potential energy U for this system. |
| 5. | (10%) Monochromatic light,strikes a thin film in air at normal incidence.If λ denotes the wavelength in the film, determine the least thickness of the film for which the reflected light will be a maximum. |
| 6. | (10%) A disk of radius R is oriented in a vertical plane and spinning about its axis with angular velocity ω . If the spinning disk is set down on a horizontal surface. with what translational CM velocity will it roll away? |
| 7. | (15%) Two masses m1 and m2 are constrained by the
spring-and-pulley system shown in the accompanying sketch.Assume a massless pulley and a
frictionless surface.Let x be the extension of the spring from its relaxed length.Derive
the equations of motion by Lagrangian methods.Solve for X as a function of time with the
initial conditionsx=0, =0 at t=0. |
| 8. | (15%) A flat rectangular plate of mass M and sides a and 2a rotates with
angular velocity ω about an axle through two diagonal corners, as shown, The bearings
supporting the plate are mounted just at the corners.Find the force on each bearing
(magnitude as well as direction).  |