作者choral (An die Freude)
看板NTU-Exam
标题[试题] 96下 李尚凡 普通物理学甲 期中考
时间Mon Apr 21 12:49:18 2008
课程名称︰普通物理学甲
课程性质︰必修
课程教师︰李尚凡
开课学院:工学院
开课系所︰机械工程系
考试日期(年月日)︰2008/4/18
考试时限(分钟):240
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
1.A point charge Q is located on the axis of a desk of radius R at a distance
b from the plane of the disk .If one fourth of the electric flux from the
charge passes through the disk , find the ratio R/b.
2. A sphere of radius 3a is made of a nonconducting material that has an
uniform volume charge density ρ.(Assume that the material does not affect the
electric field.) A spherical cavity of radius a ,with its center at (x,y,z)=
(0,0,a) is now removed from the sphere, as shown in the figure .Find the ele-
ctric field component Ex,Ey and Ez within the cavity.
3.Determine the equivalent capacitance of the combination shown in the figure.
3C 2C
┌∥——┬──∥──┐
│ │ │
┤ ﹦C ├─
│ │ │
└∥──┴──∥──┘
2C 3C
4.A capacitor is constructed from two square plates of sides l and separation
d.A material of dielectric constant k is inserted a distance x into capacitor.
Assume that d is much smaller than x (a)find the equivalant capacitance of the
device .(b)calculate the energy stored in the capacitopr ,letting ΔV represe-
nt the potential difference.(c)find the direction and magnitude of the force
exerted on the dielectric, assuming a constant potential differenceΔV.Ignore
friction.
l
██████████
← x → ↑
k d
↓
██████████
5.When an uncharged conducting sphere of radius a is placed ar the origin of
an xyz coordinate system that lies in an initially uniform electric field E=
→
Eok the resulting electric potential is V(x,y,z)=Vo for the point the sphere
and
V(x,y,z)=Vo-Eoz+Eoa︿3.z/(xx+yy+zz)︿3/2
for points ouside thesphere, where Vo is the (constant)electric potential on
the conductor .Use the equation to determine the x,y and z components of the
resultingelectric field.
6.Assume that the magnitude of the magnetic field outside the sphere of radius
R is B=Bo(R/r)(R/r), where Bo isa constant,r is distance from the center.Dete-
rmine the total energy stored in the magnetic field outside the sphere and ev-
aculate your result for Bo=0.00005T and R=0.000006m,values appropriate for the
Earth's magnetic field.
7. A cylinder of radius R and height 2R has uniform charge density ρ. Determ-
ine the magnetic dipole moment when it rotates as a rigid body with angular
volocity ω about an axis through its center.
8. The bar of mass m in the figure is pulled horizontally cross paraelle rails
by a massless string that passes over an ideal pulley and is attached to a su-
spended object of mass M. The uniform magntic field has a magnitude B, and the
distance between the rails is l.The rails are connected at one end by a load
resistor R. Derive an expression that gives the horizontal speed of the bar as
a function of time, assuming that the suspended object is released with the
bar at rest at t=0.Assume no fricton between rails and bar.
9. The switch in the figure(a)closes when ΔVc<ΔV/4. The volumeter reads a
voltage as plotted in the figure(b).What is the period T of the waveform in t-
erms of R1, R2 and C ?
10. Electrons in a beam are accelerated from rest through a potential differ-
ence ΔV.The beam enters an experimental chamber through a small hole. As sho-
wn in the figure,the electron velocity vectors lie within a narrow cone of ha-
lf angle ψ oriented along the beam axis .We wish to use a uniform magnetic
field directed parallel to the axis to focus the beam, so that all of the
electrons can pass through a small exit port on the opposite side of the cham-
ber after they travel the length d of the chamber.What is the required magnit-
ude of the magnetic field? (Hint:Because everyelectron passes through the same
potential difference and the angle ψis small, they all requirethe same time
interval to travel the axial distance d.)
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1F:→ choral:其他题的图正在制作中 04/21 17:54
2F:→ choral:算了 有人要图再说 04/30 18:48