課程名稱︰普通物理
課程性質︰必修
課程教師︰蔡爾成
開課系所︰電機系
考試時間︰2005/4/21
試題 :
1.The electric potential at poit (x,y,z) is given by
V = (2.0V/m^2)x^2 -(3.0V/m^2)y^2 + (4.0V/m^2)z^2
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What is the electric field E at the point (3.0m, 2.0m ,1.0m)?
2.Find the expression for the oscillation frequency of a magnetic dipole
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moment υ and rotational inertial I for small amplitudes of oscillation
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about its equilibrium position in a uniform magnetic field B.
3.The following figure shows a long cylindrical conductor of radius a
containing a long cylindrical hole of radius b. The central axes of the
cylinder and hole are parallel and are distance d apart. Current i is
uniformly distributed over the tinted area. Show that the magnetic field
in the hole is uniform.
4.An initially uncharged capacitor C is fully charged by a device of constant
emf E, in series with a resistor R. Show that the final energy stored in the
capacitor is half the energy supplied by the emf device.
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5.Evaluate the torque τ = i∮l × (dl × B ) exerted by a uniform magnetic
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field B on a circular loop of radius R lying on the x-y plane with current
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i and show that it is equal to iπR^2 k × B.
6.Prove that the static electric field is perpendicular to the equipotentential
surface and points to the direction of decreasing electric potential.
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7.Prove that the magnetic field B must be tangent to the surface of a conductor
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if B = 0 inside the conductor.
8.At a distance r away from a current loop of finite size carrying a steady
current i, show that the magnitude of magnetic field B due to the current
loop is proportional to 1/(r^3).
9.Charge Q is uniformly distributed in a spherical region of radius a with
uniform charge density ρ = Q/(4/3 πa^3) inside the sphere. What is the
electrostatic energy?
10.What is the magnitude of magnetic field produced at the center of a
equilateral triangular loop of wire carrying current i? Assume that the
length of each side of triangle is a. You may need to make use of the
indefinite integral ∫dx/(x^2 + 1 )^1.5 = x/(x^2 + 1 )^0.5.
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