課程名稱︰普通物理學下
課程性質︰必修
課程教師︰陳智泓
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰103/06/19
考試時限（分鐘）：2小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(10%)Two wires, parallel to a z-axis and a distanc 4r apart, carry equal
currents i in opposite directions, as shown in the fig.1. A circular cylinder
of radius r and length L has its axis on the z-axis onthe z-axis, midway
between the wires. Use Gauss'Law for magnetism to derive an expression for
the net outward magnetic flux through the half of the cylinder surface above
the x-axis. write your answer in terms of the variables given and μ0.
2.In the fig. 2, a capacitor with circular plates of radius R is connected to
a source of emf E=Vsin(wt). The maxium value of the displacement current is Id.
Neglect fringing of the electric field at the edges of plates.(a)(5% What is
the maxium value of the current i in the circuit? (b)(5%) What is the
separation d between of dΦE/dt, where dΦE is the flux in the region between
the palces? (c) (5%) what is the separation d between the plates. Find the
maxium value (in time) of the magnetic field as a function of radial distance r
from the center of the plates, for (d)(5%)r≧R and (e)(5%)r≦R. Given your
answer in terms of R,V w,Id,μ0,E0.
3.(是非題) __ Consider a star which is 6 light year away. Aphoton from the star
takes 6 years to reach the earth in our frame. However, it takes zero second
from that photon's point of view.
4.(是非題) __ Einstein is the first person who derives that the length along
the moving direction of an object becomes shorter than it is at rest.
5.(是非題) __ An object weights more when it is moving than a rest.
6.A rocket ship leaves eath at a speed 3/5c. When a clock pn the rocket says
1 hour has elaosed, the rocket sends a light signal back to earth. (a)(5%)
According to earth clocks, when was the sighnal sent? (b)(5%) According to
earth clocks, how long after the rocket left did the signs arrive back on the
earth? (c)(5%) According to the rocket observer, how long after the rocket
left the signal arrive back on earth?
7.Sophie and her twin brother are separated 500 km away. When her brother was
hit by a hammer, she cries at the same time. A scientist observed both events
(brother's accident and Sophie's cry) from an airplane traveling at 12/13c to
right(Sophie was on right), where c is the speed of light. (4%) Which event
occurred first, according to the scientist? (6%) How much earier was it, in
seconds?
8.(25%) The Compton scattering is a scattering process between a photon and an
electron is deflected by an angle θ and the electron is deflected by an angle
ψ. The energy of photon is quantized by E0=hυ, where h is the Planck constant
and theυis the frequency. Show that the wavelength of the photon λafter
scatted satisfies the relation
λ=λ0+(h/mc)(1-cosθ)
where c is the speed of light.