課程名稱︰普通物理學甲下
課程性質︰化工系定必修
課程教師︰趙治宇
開課系所︰物理系
考試時間︰2006/06/27 10:20~13:10
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試題 :
Do all problems in detail, full points 100. Good luck!
1. In unit-vector notation, what is the magnetic field at point P in Fig.1 if
i=10 A and a= 8.0 cm?
(Note that the wires are not long.) (8 pts)
2. Fig.2 shows a cross section of a hollow cylindrical conductor of radii a and
b, carrying a uniformly distributed current i. (a) Show that the magnetic field
magnitude B(r) for the radial distance r in the range b < r < a is given by
B=((μ0i)/2π(a^2-b^2))*((r^2-b^2)/r) (3 pts) (b) Show that when r= a, this
equation gives the magnetic field magnitude B at the surface of a long straight
wire carrying current i; when r= b, it gives zero magnetic field; and when b=0,
it gives the magnetic field inside a solid conductor of radius a carrying
current i (3 pts) (c) Assume that a= 2.0 cm, b= 1.8 cm, and i= 100 A, and then
plot B(r) for the range 0 < r <6 cm.
3. Fig.3 shows a coil of N2 turns wound as shown around part a toroid of N1
turns. The toroid's inner radius is a, its outer radius is b, and its height is
h. Show that the mutual inductance M for the toroid-coil combination is given
by M=(μ0*N1*N2*h/2π)*ln(b/a) (10 pts)
4. In an oscillating series RLC circuit, show that ΔU/U, the fraction of the
energy lost per cycle of oscillation, is given to a close approximation by
2πR/ωL, The quantity ωL/R is often called the Q of the circuit(for quality).
A high-Q circuit has low resistance and a low fractional energy loss(=2π/Q)
per cycle. (8 pts)
5. A parallel-plate capacitor with circular plates of radius R is being
discharged. The displacement current through a central circular area, parallel
to the plates and with radius R/2, is 2.0 A. What is the discharging current?
(8 pts)
6. A beam of partially polarized light can be considered to be a mixture of
polarized and unpolarized light. Suppose we send such a beam through a
polarizing filter and then rotate the filter through 360° while keeping it
perpendicular to the beam. If the transmitted intensity varies by a factor of
5.0 during the rotation, what fraction of the original beam is associated with
the beam's polarized light? (8 pts)
7. Fig. 7a shows a lens with radius of curvature R lying on a flat glass plate
and illuminated from above by light with wavelength λ. Fig 7b (a photograph
taken from above the lens) shows that circular interference fringes (called
Newton's rings) appear, associated with the variable thickness d of the air
film between the lens and the plate. Find the radii r of the interference
maxima assuming r/R << 1. (8 pts)
8. Derive this expression for the intensity pattern for a three-slit "grating"
I= 1/9 Im(1+4cosφ+4cos^2φ), where φ= (2πd sinθ)/λ and a << λ. (8 pts)
9. Describe the working principle of near-field optical microscope. (8 pts)
10. Describe thr working principle of recording and playback head for tape.
(8 pts)
11. Describe why Gecko's toes have strong adhesion force on any rough surface?
(6 pts)
12. Using classical model to explain the discovery of diamagnetic material.
(10 pts)
Figure 1,2,3,7a,7b來自於Fundamentals of Physics, Halliday 7th.
1.p.790, Fig.29-83
2.p.790, Fig.29-87
3.p.824, Fig.30-78
7a.p.985, Fig.35-46(a)
7b.p.985, Fig.35-46(b)
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