課程名稱︰普通物理學甲
課程性質︰系定必修
課程教師︰蔡爾成
開課系所︰大氣科學系
考試時間︰95/04/17
試題 :
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1.The electric potencial is given by ψ(x,y,z)=x -y +xz, what is the eletric
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field E at the point (x,y,z)?
2.At what distance along the central perpendicular axis of a uniformly charged
plastic disk of radius R is the magnitude of the eletric field equal to
one-half the magnitude of the field at the center of the surface of the disk?
3.Charge is distributed uniformly with the density ρ throughout the volume of
an infinitely long solid cylinder of radius R. At the distance (a) r < R,
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(b) r > R, give the expression for the magnitude E of the eletric field E.
4.Show that, according to the free-electron model of electrical conduction in
metals and classical physics, the resistivity of metals should be
proportional to √T, where T is the temperature in kelvins.
5.Two capacitors C and C are connected in series and are separated by a large
1 2
distance so that the electric field of one cannot affect the other. What is
the equivalent capacitance of the combination?
6.A wire of arbitrary shape carrying a current i between points a and b in a
uniform magnetic field. Prove that the force on the wire is the same as that
on a straight wire carrying current i directly from a to b.
7.In a certain cyclotron a charged particle with charge q, mass m, moves in a
circle of radius R. The magnitude of the magnetic field is B. (a) What is the
oscillator frequency? (b) What is the kinetic energy of the charged particle?
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8.Show that the charge density is zero in a region where the eletric field E
is uniform.
9.An initially uncharged capacitor C is fully charged by a device of constant
emf ξ, in series with a resistor R. Show that the final energy stored in the
capacitor is half the energy supplied by the emf device.
10.A single isolated spherical conductor of radius a may be considered as a
capacitor with the other conductor being a sphere at infinity. (a) What is
the capacitance? (b) Suppose charge Q is uniformly distributed on the
sphere. What is the electrostatic energy?
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