課程名稱︰普物甲下
課程性質︰
課程教師︰張顏暉
開課系所︰電機系
考試時間︰2006/04/20
試題 :
1. A spherically symmetrical but non-uniform distribution of charge produces
an eletric field of magnitude E=Kr^5, directed radially outward from the
center of the sphere. Here r is the radial distancefrom that center.
What is the volume density ρ(r) of the charge density? (10)
2. A large flat non-conducting surface has a uniform charge density σ.
A small circular hole of radius R has been cut in the middle of the surface
as shown in Fig.-1. What is the eletric field at point P, a distance z from
the center of the hole along its axis? (10)
‧ p
｜＿＿＿
／｜ ／
／ ○ ／
／ ／
￣￣￣￣
3. A capacitor is made of two concenteric spheres of radii a1 and a2
respectively, see Fig.-2. The space between the two spheres is filled with
dielectric constant k=k0/r. What is the capacitance of this capacitor? (10)
4. Describe the operation of a cyclotron as shown in Fig.-3. Express the
kinetic energy of a particle with mass m, charge q existing from a cyclotron
with radius R and magnetic field B. (10)
5. Fig.-4 shows a cross section of a long cylindrical conductor of radius a
containing a long cylindrical hole of radius b. The axes of the cylinder and
hole are parallel and are a distance d apart. A current i is uniformly
distributed over the tinted area. Find the magnetic field B at any point
inside the hole. (10)
6. What is the magnetic moment of an electron orbiting around a uniform circle
of radius a with speed v. Find the ratio between the angular momentum and
magnetic moment of this orbiting electron. The electron is orbiting in the x-y
plane, and the z-axis passes through the center of the orbit. Find the magnetic
field produced by this electron at point p at the z-axis, and is at a distance
z above the center of the x-y plane. (10)
7. Show that the energy density in a solenoid is B^2/2μ0 and the energy
density in a parallel capacitor is ε0E^2/2 (10)
8. In Fig.-6, a rectangular loop of wire with length a, width b and resistance
R isplaced near a infinitely long wire carrying current i. The loop then is
moved away from the wire with constant speed v. When the center of the loop is
at a distance r=2b, what are (a) The magnitude of the magnetic flux through the
loop? and (b) the current induced in the loop? (15)
a
┌────┐
v↑┬│ │b
r│└────┘
┴───────
i
9. Find the total current of the parallel RCL circuit, as shown in Fig.-7. (15)
ε=εsinωt
┌─┬─┬─┐
│ │ │ │
ε⊙ R︴ Lξ C╪
│ │ │ │
└─┴─┴─┘
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