課程名稱︰普通物理學甲下
課程性質︰化工系系定必修
課程教師︰趙治宇
開課系所︰物理系
考試時間︰2006/4/27 10:20~13:10
是否需發放獎勵金：是的，謝謝
（如未明確表示，則不予發放）
試題 :
Total 12 problems, each 10 points, full point 120.
1. Figure 1 shows an electric quadrupole. It consists of two dipoles with
dipole moments that are equal in magnitude but opposite in direction. Show that
the value of E on the axis of the quadrupole for a point P a distance z from
its center (assume z>>d) is given by E = 3Q/4πεz^4, in which Q (=2qd^2) is
known as the quadrupole moment of the charge ° distribution.
2. Figure 2 shows two concentric rings, of radii R and R'= 3.00R, that lie on
the same plane. Point P lies on the central z axis, at distance D = 2.00R from
the center of the rings. The smaller ring has uniformly distributed charge +Q,
what is the uniformly distributed charge on the larger ring if the net electric
field at P is zero?
3. Figure 3 shows, in cross section, two solid spheres with uniformly
distributed charge throughout their volumes. Each has radius R. Point P lies on
a line connecting the centers of the spheres, at radial distance R/2.00 from
the center of sphere 1. If the net electric field at point P is zero, what is
the ratio q2/q1 of the total charge q2 in sphere 2 to the total charge q1 in
sphere 1?
4. In Figure 4a, a particle of charge +e is initially at coordinate z= 20 nm on
the dipole axis through an electric dipole, on the positive side of the dipole.
(The origin of z is at the dipole center.) The particle is then moved along a
circular path around the dipole center until it is at coordinate z=-20 nm.
Figure 4b gives the work Wa done by the force moving the particle versus the
angle θ that locates the particle. What is the magnitude of the dipole moment?
5. In Figure 5, a charged particle (either an electron or a proton) is moving
rightward between two parallel charged plates separated by distance d= 2.00 mm.
The plate potentials are V1=-70.0V and V2=-50.0V. The particle is slowing from
an initial speed of 90.0 km/s at the left plate. (a)Is the particle an electron
or a proton? (b)What is its speed just as it reaches plate 2?
6. A slab of copper of thickness b= 2.00 mm is thrust into a parallel-plate
capacitor of plate area A= 2.40 cm^2 and plate separation d= 5.00 mm, as shown
in Figure 6; the slab is exactly halfway between the plates. (a) What is the
capacitance after the slab is introduced? (b) If a charge q= 3.40μC is
maintained on the plates, what is the ratio of the stored energy before to that
after the slab is inserted? (c) How much work is done on the slab as it is
inserted? (d) Is the slab sucked in or must it be pushed in?
7. In Figure 7, current is set up through a truncated right circular cone of
resistivity 731Ω‧m, left radius b= 2.30 mm, and length L= 1.94 cm. Assume
that the current density is uniform across any cross section taken
perpendicular to the length. What is the resistance of the cone?
8. In Figure 8, the resistances are R1= 1.0Ω and R2= 2.0Ω, and the ideal
batteries have emfsε1= 2.0V andε2=ε3= 4.0V. What are the (a) size and
direction (up or down) of the current in battery 1, the (b) size and direction
of the current in battery 2, and the (c) size and direction of the current in
battery 3? (d) What is the potential difference Va-Vb?
9. In Figure 9, R1= 5.00Ω, R2= 10.0Ω, R3= 15.0Ω, C1= 5.00μF, C2= 10.0μF,
and the ideal battery has emf ε= 20.0V. Assuming that the circuit is in the
steady state, what is the total energy stored in the two capacitors?
10. Figure 10 shows a wood cylinder of mass m= 0.250 kg and length L= 0.100m,
with N= 10.0 turns of wire wrapped around it longitudinally, so that the plane
of the wire coil contains the long central axis of the cylinder. The cylinder
is released on a plane inclined at an angleθ to the horizontal, with the plane
of the coil parallel to the incline plane. If there is a vertical uniform
magnetic field of magnitude 0.500T, what is the least current i through the
coil that keeps the cylinder form rolling down the plane?
11. In Figure 11, a metal wire of mass m= 24.1 mg can slide with negligible
friction on two horizontal parallel rails separated by distance d=2.56 cm. The
track lies in a vertical uniform magnetic field of magnitude 56.3 mT, At time
t= 0, device G is connected to the rails, producing a constant current i=9.13
mA in the wire and rails (even as the wire moves). At t= 61.1 ms, what are the
wire's (a) speed and (b) direction of motion (left to right)?
12. Figure 12 shows, in cross section, four thin wires that are parallel,
straight, and very long. They carry identical currents in the directions
indicated. Initially all four wires are at distance d= 15.0 cm from the origin
of the coordinate system, where they create a net magnetic field ->
B.
(a) To what value of x must you move wire 1 along the x axis in order to rotate
->
B counterclockwise by 30°? (b) With wire 1 in that new position, to what value
of x must you move wire 3 along the x axis to rotate -> by 30° back to its
initial orientation? B
Figure 1~12來自於Fundamentals of Physics, Halliday 7th.
Figure 1~12分別為
1.p.599, Fig.22-39
2.p.602, Fig.22-57
3.p.625, Fig.23-52
4.p.648, Fig.24-35
5.p.650, Fig.24-50
6.p.681, Fig.25-65
7.p.702, Fig.26-29
8.p.727, Fig.27-40
9.p.734, Fig.27-84
10.p.760, Fig.28-44
11.p.762, Fig.28-53
12.p.783, Fig.29-44
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