【站僕】摩檸Morning>試卷(2016/09/10)

92 年 - 92 淡江大學 轉學考 電磁學#56058

【非選題】
1.
1. Consider an electrostatic situation in which a charge Q is uniformly distributed over a sphere of radius R. Let the electric potential at infinity be zero.

【題組】 (a) Find the electric field and potential (V) as a function of the radial distance (r) from the center of the sphere.

【非選題】
2.【題組】(b) Calculate the electrostatic energy of the system. (20%)

【非選題】
3.2. Assume that a static charge distribution (ρ) produces an electric potential V ， where A and a are positive constants, is the position vector, r = | |. Now, it is given that ▽2(1 /r) = -4πδ( ). Find the electric field charge density and the total charge Q. (20%)

【非選題】
4.3. Jusitify that the vector potential of a uniform magnetic field may be expressed as (10 %)

【非選題】
5.
4. Assume that a long solenoid of radius R with n turns of thin wires per unit length is carrying a steady current /，and its axis of symmetry is along the z-direction.

【題組】 (a) Justify that the magnetic field (whenever nonzero) is in the z-direction.

【非選題】
6.【題組】(b)Show that (the magnetic flux through a surface enclosed by a closed path C), c where is the vector potential.

【非選題】
7.【題組】(c) Find the magnetic field intensity (H) and vector potential throughout the space. (20%)

【非選題】
8.
5. It is well known that the basic laws of classical electromagnetic phenomena are governed by the Maxwell's equations: and are the electric field, electric displacement, magnetic field, magnetic field intensity, free charge density, and free current density, respectively.

【題組】 (a) Write down the corresponding integral form for each of the four Maxwell’s equations, and specify the physical meaning for each of them.

【非選題】
9.【題組】(b) Show that the free charge density and free current density satisfy the continuity quation: (Hint: Two of the Maxwell equations may be useful).

【非選題】
10.【題組】(c) Show that the tangential component of the electric field must be continuous across any boundary surface. (30 %)

懸賞詳解

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