課程名稱︰普通物理學(丙)
課程性質︰森林系某些學群必修
課程教師︰李慶德
開課學院：
開課系所︰森林系
考試日期（年月日）︰June 17,2009
考試時限（分鐘）：120 mins
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
Do any 5 of the seven problems given below!
1.)
In 1913,Niels Bohr proposed a model of the hydrogen atom in which an
electron (of charge -e) orbits a stationary proton (of charge +e) in a
circular path. In its lowest energy state, the radius of the circular
path of the electron is given by the so-called Bohr radius
ａ0 = 0.53*10^-10(次方)m. Find the total mechanical energy of the
electron in this lowest energy state.
2.)
Two large parallel conducting plates carry equal and opposite charges and
are separated by a distance of 5cm. An 9-μC point charge placed between the
plates experiences a force of (2.7*10^-2 N)[i](向量). Find the potential
difference between the plates.
3.)
An electron with a velocity [v]=(3*10^6 m/s)[i] enter a region in which the
electric field is [E]=(-300 V/m)[j].
(a) What is the magnetic field required for the electron not to be deflected.
(b) If the electric field is switched off, whit is radius of the path of the
electron in the magnetic field?
4.)
According to the Biot-Savart law, the differential magnetic field produced
by a current element Idl at a distance r from the current element is given
by
d[B]= {(μ0)/4π}{(Id[l] x ñ)/r^2}
(a) Use the biot-Savart law to evaluate the magnetic field strength at a
distance R from an infinite straight wire that carries a current I.
(b) Use Ampere's law ∮[B]˙d[l] = (μ0)I to find the magnetic field
strength at a distance R from an infinite straight wire that caries a
current I.
(c) Compare the results you obtain for (a) and (b). Also, comment on whether
the Biot-Savart law and Ampere's law can still be applied if the
current-carrying straight wire has only a finite length instead od an
infinite length.
5.)
The energy stord un a capacitor is equal to the work done --- for example,
by a battery --- to charge it. Suppose that at a particular time the
magnitude of the charge on either plate is q and the potential difference
between the plates is V = q/C. The work needed to transfer an infinitesimal
charge dq from the negative plate to the positive plate is dW = Vdq = (q/C)dq.
(a) Find the total work done to transfer charge Q.
This work is stored as electrical potential energy Ue between the plates.
Assume the capacitor consist of parallel plates of area A separated by a
distance d.
(b) Evaluate the energy density, or the energy per unit volume, ue = Ue/(Ad)
in terms of the electric field [E] between the plates.
6.)
A metal rod slides at a constant 40 cm/s over frictionless rails separated
by 25cm. A 0.30 T uniform magnetic field is directed out of the page. Assume
the resistance of the rod is 3.0Ω and that the rails have negligible
resistance. Find:
(a) the current flowing in the rails and the direction of the current.
(b) the magnetic force acting on the rod;
(c) the mechanic power needed to keep the rod moving at constant velocity;
(d) the electrical power dissipated.
7.)
The current in an ideal solenoid of radius a varies as a funcyion of time.
(a) Find the induced electric field at points inside the solenoid,
i.e. r < a. Express the result in terms of dB/dt.
(b) Find the induced electric field at points outside the solenoid,
i.e. r > a. Express the result in terms of dB/dt.
(c) What is the main difference between this induced electroc field and
those produced by point charges?
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