課程名稱︰普通物理學甲下
課程性質︰化學系必修 地質系選修兼通識
課程教師︰王名儒
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰2020/4/23
考試時限（分鐘）：120min
試題 :
1.Two isolated concentric conducting spherical shells have radii R1 and R2,
uniform charges Q1 and Q2, and negligible thickness. Find the magnitude of
electric field E(r) and the electric potential V(r), where V=0 at infinity.
2.Find the electric energy stored in a parallel-plate capacitor of area A and
seperation distance d with a total charge ±Q. Show that the energy density is
0.5ε0E^2.
3.There are two metal spheres with radii R1 and R2, and they are connected
electronically to maintain the same potential. Assuming a total charge Q is
distributed in these two spheresand the mutual interaction between the two
spheres can be negelcted, find out the surface charge density of each sphere.
4.A solar cell generates a potential difference of 0.10V when a 500Ω resistor
is connected across it, and a potential difference of 0.15V when a 1000Ω is
substituted. What are the internal resistance and the emf of the solar cell?
5.An initially uncharged capacitor C is fully charged by a device of constant
emf ε connected in series with a resistor R. Show that the final energy
stored in the capacitor is half of the energy supplied by the emf device. Show
that the energy dissipated by the resistor is also half the energy supplied
by the enf device.
6.The current density J inside a long, solid, cylindrical wire of radius a, is
in the direction of the central axis, and its magnitude varies linearly with
radial distancer from the axis according to J=J0r/a. Find the magnitude of the
magnetic field at (a) r=0 and (b) r=a/2.
7.Discuss the similarity and difference between an electric dipole and a
magnetic dipole.
8.Find the magnetic energy stored in a N-turn solenoid of length L and radius
R with current i. Show that the energy density is 0.5B^2/μ0.
9.One connects to the two ends of a resistor (resistance R), an inductor
(inductance L), and a capacitor (capacitance C) with an alternating voltage
source in parallel. Assuming thevoltage source has the functional form
V(t)=V0cos(ωt), find out the total current I as the function of t and related
parameters (e.g. R,L,C). What's the power dissipation in this circuit?
10.What capacitance would you connect across a 1.30 mH inductor to make a
resulting oscillator resonate at 3.50kHz?