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88年 - 88 淡江大學 轉學考 理論力學#56176
> 申論題
1. A particle of mass m has velocity v = a/x ， where x is its displacement. Fin4 the force F(x) responsible, 25%
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2, For a system of particles, prove that its total angular momentum about an origin is the sum of the angular momentum of the center of mass about that origin and the angular momentum of the system about the position of the center of mass . 25%
#213594
3, Calculate the inertia tensor of a homogeneous cube of density p ，mass M，and side of length b. Let one comer be at the origin，and let three adjacent edges lie along the coordinate axes, 25%
#213595
(a) Find the electric field inside and outside the spherical shell (10 %)
#213604
(b) Find the potential inside and outside the spherical shell. (10 %)
#213605
(a) Find the magnetic field of the toroid both inside and outside the coil. (10 %)
#213606
(b) Find the self-inductance of the coil, (5 %)
#213607
(c) Calculate the energy stored in the coil (5 %)
#213608
(a) Write down the differential form of the four Maxwell’s equations in terms of free charges p f and currents Jf for E，B，D，and H respectively* (10 %)
#213610
(b) Derive the boundary conditions for these fields at the interface between two different media (medium 1 and medium 2)，where the interface carries free charge density p f or current density Kf‘ (15 %)
#213611
(c) In the case of linear media (medium 1 and medium 2)，show the boundary conditions in terms of E and B alone. (5 %)
#213612
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