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課程名稱︰普通物理學甲下
課程性質︰系必修
課程教師︰張寶棣
開課學院：電資學院
開課系所︰資工系
考試日期（年月日）︰2008/03/26
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.An electric dipole in a uniform electric field is displaced slightly from
its equilibrium position, as shown in Fig.1, where θ is small. The
separation of the charges is 2a, and the moment of inertial of the dipole
is I. Assuming the dipole is released from this position, prove that its
angular orientation exhibits simple harmonic motion and find its frequency
(10%)
2.Four identical particles, each having charge +q, are fixed at the corners
of a square of side L. A fifth point charge -Q lies a distance z along the
line perpendicular to the plane of the square and passing through the
center of the square. (a) What is the force exerted by the other four
charges on -Q? (b) If z is small compared with L, the above expression
reduces to vector(F) = -(constant)(vector(z)). What is the period of this
motion if the mass of -Q is m?
3.An infinately long insulating cylinder of radius R has a volume charge
density that varies with the radius as
ρ = ρ0 * ( a - r / b )
where ρ0, a and b are positive constant. Use Gauss' law to determine the
magnitude of the electric field at radial distance (a) r < R and (b) r > R
(10%)
4.A hadrogen atom can be regarded as a proton with charge +e in the center
of a sphere and an electric cloud circulating spherically around the
center. Assume that the charge density of the cloud at radius r is
ρ(r) = -C * e^(-2 * r / a0 ), where a0 is called the Bohr radius whose
value is 0.53 * 10E-8 cm and C is a constant, please find (a) the total
charge, Q(r), inside a sphere with radius r (8%), (b) the constant C such
that the total charge of a hadrogen atom is 0 (4%), and (c) the electric
field and the electric potential at the Bohr radius a0 (8%). (Hint: Since
the total charge of a hadrogen atom is 0, Q(∞) = 0.)
5.The electric field inside a nonconducting aphere of radius R, with charge
spread uniformly throughout its volume, is radially directed and has
magnitude
E(r) = ( q * r ) / ( 4 * π * ε0 * R )
Here q (positive or negative) is the total charge within the aphere and r
is the distance from the sphere's center. (a) Taking V = 0 at the center
of the sphere, find the electric potential V(r) inside the sphere. (b).
What is the difference in electric potential between a point on the surface
and the sphere's center? (c) If q is positive, which of those two point is
at higher potential? (15%)
6.What is the capacitance of the capacitor, of plate area A shown in Fig. 3?
(5%)
7.For the circuit shown in Fig. 4, switch S has been open for a long time.
At time t = 0 the switch is then closed. (a) What is the battery current
just after switch S is closed? (b) What is the battery current a long time
after switch S is closed. (c) The switch has been closed for a long time.
At time t = 0 the switch is then opened. Find the current through the
600-kΩ resistor as a function of time. (15%)
8.Consider two parallel-plate capacitors, C1 and C2, that are connected in
parallel. The capacitors are identical except that C2 has a dielectric
inserted between its plates. A voltage source of 200V is connected across
the capacitors to charge them and is then disconnected. (a) What is the
charge on each capacitor? (b) What is the total stored energy of the
capacitors? (c) The dielectric is removed from C2. What is the final total
stored energy of the capacitors? (d) What is the final voltage across the
two capacitors? (15%)
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