89下電磁學期中&egrav

89下電磁學期中&egrav

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Unformatted text preview: i. Electro-magneticsi First Examination (2001.113); Let P and P’ be the pointsw-itli spherical Igoordinates (1,9,5) and *(1,9’.,p’), reSpectively. Let 0 be the origin of the coordinate Find the angle 3! between the two vectors 51-5 and or: ( wnwe'mrcpqiyr meme'fi12%) In Cartesian coordinate system, let S be the plane through The points (1,0,0), (0,2,0) , (0,0,3) . Find the unit normal vector to theplane S . (12%) Show that Exotixfi) = (REE—(Hi)? (13%) Two point charges +Q and —Q are located at (Mid/2) and (0.0,—d;’2), respectively. Such an arrangement is known as the electric dipole. Find the electric field intensity Ear) at the point 1"", due to the electric dipole, such that the I spacing d is much smaller than the distance r =|Fl from the origin. (13%). Determine the electric field intensity of an infinitely long straight line charge of a uniform density p, (C I m) in air. (12%) Find the magnetic flux density at a point (0,51) on the axis of a circular loop of radius 59 that carries a direct current I . (12%) The electrostatic deflection system of a cathode-ray tube is depicted in Fig.1. The electrons, with initial velocity in = Eve , enter at z z 0 into a region of deflection plates where a uniform electric field E7 = —37Ed is maintained over a width w. By ignoring gravitational effects, find the vertical deflection a? of the electrons on the fluorescent screen at z = L . (13%) Infinite plane sheets of uniform surface charge densities pdid) = ¥pm(Cl m2) occupy the planes z = id . The region - b < z < b is a dielectric of permittivity 450 . Find the values of 13,5, and 5 in the regions [2:] < b and b < < d. y (13%) Deflection plates {q Fig.1 l. 2. Use the Maxwell’s equations to show the electric field E and magnetic field H Electromagnetic t1 ) 0600110 Exammauofl VCI) V-A Vztb in cylindrical coordinates. (Note: V l A = lim J—-——) Av—a 0 l A-ds Av 2001/ 12/5 Given a scalar field (I) and a vector field 1—4 , derive the expressions of in the free space without any sources satisfy the following equations: (15%) (15%) 3. An infinitely extended positive jch‘arge p, is distributed over the axis of an 4. infinitely extended cylindrical”. of an inner radius RI. and outer radius R0, as shown in Fig. 1. The dielectric constant of the shell is 5,. l _ g» , . TQOL UQ _ —- _ _ electnc field , :‘electnc flux denSIty D, polanzation vector A Current I flows along a straight wire from a point charge Q10) located at (0,0,0) to a point charge Q20) at ( 1 1 shown in Fig. 2. absolute value of the line integral of H around the closed loop in terms of I. some (15%) 1.12 Fig. 1 Determine the P y and potential function V as functions of the radial distance r for O < r < co. Assume HR!) : O. (15%) Fig. 2 Electromagnetic (1) Second Examination 2001! 12/5 5. Two dielectric media with permittivities £1 and .52 are separated by a boundary with no free charge as shown in Fig. 3. The electric field intensity in medium 1 at the point P1 has a magnitude E] and makes an angle aI with the normal. Determine the magnitude and direction of the electric field intensity E2 at point P2 in media 2. in terms of 0:1 and El. (15%) 6. A volume charge is distributed throughout a sphere of radius a(m), and centered at the origin, with uniform density pD(C I m3). Find the energy stored in the electric field of this charge distribution. (15 9B) 7. What is the displacement current? Compare and contrast the displacement current with the current due to flow of charges. (10 % ) ...
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This note was uploaded on 02/21/2012 for the course EE 101 taught by Professor 張捷力 during the Spring '07 term at National Taiwan University.

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89下電磁學期中&egrav

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