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# 89ä¸‹é›»ç£å­¸æœŸä¸­&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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89ä¸‹é›»ç£å­¸æœŸä¸­&egrav

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