課程名稱︰普通物理學甲下
課程性質︰必修
課程教師︰王建萬老師
開課系所︰生工系
考試時間︰6/24 10:20~12:10
試題 :
1.In Fig.1, R=14.0Ω, C=6.20F, and L=54.0mH, and the ideal battery has emf
ε=34.0V. The switch is kept in position a for a long time and then thrown to
position b. What are (a) frequency and (b) current amplitude of the resulting
oscillations? (10%)
2.A parallel-plate capacitor with circular plates of radius R is being charged
as in Fig.2.
(a) Derive an expression for the magnetic field at radius r for the case r≦R
(b) Evaluate the field magnitude B for r=R/5=11.0mm and dE/dt=1.50×10^12
V/ms.
(c) Derive an expression for the induced magnetic field for the case r≧R.
(15%)
3.Fig.3 shows the cross section of a long conducting cylinderwith inner radius
a=4.0cm and outer radius b=6.0cm. The cylinder carries a current out of the
page, and the magnitude of the current density in the cross section is given
by J=cr^2, with c=3.0×10^6 A/m^4 and r in meters. What is the magnetic field
B at a point that is 5.0cm from the central axis of the cylinder? (10%)
4.A retangular coil of N turns and of length a and width b is rotated at frequ-
ency f in a uniform magnetic field B, as shown in Fig.4. The coil is connect-
ed to co-rotating cylinders, against which metal brushes slide to make conta-
ct.
(a) Show that the emf induced in the coil is given (as a function of time t)
by ε=2πfNabBsin(2πft)=εosin(2πft)
(b) What value of Nab gives an emf with εo=150V when tje loop is rotated at
60.0rev/s in a uniform magnetic field of 0.500T? (15%)
5.Fig.5, a real inverted image I of an object O is formed by a certain lens (
not shown) ; the object-image seperation is d=40.0cm, measured along the cen-
tral axis of the lens. The image is just half the size of the object. (a) Wh-
at kind of lens must be used to produce this image? (b) How far from the obj-
ect must the lens be placed? (c) What is the focal length of the lens? (15%)
6.What is the distance on screen C in Fig.6 between adjacent maxima near the
center of the interference pattern? The wave length λ of the light is 550nm
, the slite seperation d is 0.10mm, and the slit-screen seperation D is 60cm
. Assume that θ in Fig.6 is small enough to permit use of the approximatio-
ns sinθ≒tanθ≒θ, in which θ is expressed in radian measur. (10%)
7.Sunlight just outside Earth's atomsphere has an intensity of 1.40kW/m^2. Cal-
culate Em and Bm for sunlight there, assuming it to be a plane wave. (10%)
8.A long, rigid conductor, lying along x axis, carries a current of 5.0A in the
negative x direction. A magnetic field B is present, given by B=3.0i+8.0x^2j,
with x in meter and B in militesla. find the force on the 2.0m segment of the
conductor that lies between x=1.0m and 3.0m. (15%)
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