JEE TEORI ELEKTROMAGNET
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1 UNIVERSITI SAINS MALAYSIA Peperiksaan Kursus Semasa Cuti Panjang Sidang Akademik 2002/2003 April 2003 JEE TEORI ELEKTROMAGNET Masa : 3 Jam ARAHAN KEPADA CALON: Sila pastikan kertas peperiksaan ini mengandungi LAPAN (8) muka surat beserta Lampiran (2 muka surat) yang bercetak dan ENAM (6) soalan sebelum anda memulakan peperiksaan ini. Jawab LIMA (5) soalan. Agihan markah diberikan di sut sebelah kanan soalan berkenaan. Semua soalan hendaklah dijawab di dalam Bahasa Malaysia.
2 -2- [JEE234] 1. [a] jika A = -ax + 3 ay -2 az dan B = 2ax + 3 ay -2 az, Carl : (i) JAI; (ii) JBI ; (iri) A-B ; (iv) A xb ; (v) Sudut 9AB antara A dan B. IfA = -&z + 3 dy2&z and B = 2dx + 3 dy28z, find. (i) JAI ; (ii) (BI ; (iii) AB; (iv) A xb ; (v) Angle BAB between -A and B. [b] Bagi F = y ax - x lay hitung kamiran garis di sepanjang lintasan yang ditunjukkan dalam Rajah 1 bermula dari (0,0,0) dan berakhir pada (1,2,4). ForF = y &x - x dy calculate the line integral along the path indicated in the Figure 1 starting from (0,0,0) and ending at (1,2,4).
3 -3- [JEE234] z C X ( ), 11~ y Rajah 1 Figure 1 2. [a] Dapatkan medan elektrik yang terhasil dari cas garis tak terhingga yang mempunyai ketumpatan cas garis seragam pe. Obtain the electric field arising from an infinite line of charge with a uniform line-charge density pr. [b] Bagi cas gelung bulat seragam yang ditunjukkan dalam Rajah 2, dapatkan medan-e yang dihasilkan pada sebarang titik P (0,0,z) di sepanjang paksi-z, dimulakan dengan mencari nilai keupayaan V. Anggap jejari gelung ialah "a' dan ketumpatan cas garis ialah p t. For the uniform circular loop of charge shown in Figure 2, find the E-field it generates at an arbilrary point P (0,0,z) along the z-axis by first finding the potential V. Assume that the radius of the loop is 'a' and the line charge density, is p,.
4 Rajah 2 Figure 2 3. [a] Rajah 3 menunjukkan hubungan antara muka dua dielektrik yang sempurna. Dapatkan magnitud EZ dan sudut yang terhasil dari permukaan paksi normal, jika magnitud Ei dan sudutnya diketahui. Figure 3 shows the interface between two perfect dielectries. Find the magnitude. ofez and angle it makes with the surface normal, if the magnitude of EZ and the angle it makes with respect to the surface normal are both known. Rajah 3 Figure 3
5 4. [a] Menggunakan hukum Biot-Savart, dapatkan ketumpatan fluks magnet _ [b] Hitung medan E dan D yang dihasilkan oleh dua sfera cas seragam yang sepusat seperti ditunjukkan oleh di Rajah 4. Sfera dalam mempunyai jejari a dan cas Q, sementara sfera luar berjejari b dan cas- Q. Anggap dielektrik antara sfera ialah homogen dan berketelusan E. Calculate the E and D fields generated by two concentric, uniformly charged spheres shown in Figure 4. The inner sphere has radius a and charge Q, and the outer sphere has radius b and charge -Q. Assume that the dielectric between the spheres is homogeneous and has permittivity E. Rajah 4 Figure 4 B, yang dihasilkan oleh arus garis I tak terhingga dan seragam yang mengalir dalam arah.+ az di keseluruhan panjang paksi-z. Apply Biot-Savart law and obtain the magnetic flux density, B, arising from a uniform, infinite line of current I flowing in +a. z-axis. direction along the entire
6 -6- [JEE234] [b] Menggunakan hukum Ampere dapatkan ketumpatan fluks magnet B, yang dihasilkan oleh silinder tegar tak terhingga, berjejari a dan membawa arus seragam J = Jo az [A/mz] untuk kes p<a seperti ditunjukkan oleh Rajah 5. Apply Ampere's law and obtain the magnetic flux density, B, arising from an infinite solid cylinder ofradius a carrying a uniform current J = Ja &_ (A/m 1Jfor p<a as shown in Figure 5. Rajah 5 Figure 5 5. [a] Rajah 6 menunjukkan teras berketelapan tinggi, membawa medan seragam B dan berubah terhadap masa diberikan sebagai B = Ba cos wt AZ. Hitung medan-e yang dihasilkan dalam teras tersebut. Figure 6 shows a high permeability core that carries a uniform, time-varying B field given by B = Bo cos wt fiz. core. Calculate the E-field generated inside the
7 -7- [JEE234] A z ' Rajah 6 Figure 6 [b] Katakan medan-e dalam kawasan bebas sumber ruang bebas diberikan oleh E=E. sin (cot-(3z) a, Nilai cu can 0 ialah pemalar. Dapatkan medan H yang wujud. Suppose that the Efield.in a sourcefree region offree space is given by E =E. sin ((atpz) kx where w and,8 are constants. Find the Hfield that is also present. 6. [a] Hitung galangan masukan bagi talian penghantaran yang panjangnya 1 m dan ditamatkan oleh beban bergalangan Z,.=2052. Anggapkan galangan ciri talian penghantaran ialah 5052, pemalar dielektrik berkesan E.,.,=1.5 dan frekuensi operasi ialah 50MHz. Calculate the input impedance of a 1 m length of transmission line that is terminated in a load impedance of Zc=20S2. Assume that the characteristic impedance of the transmission line is 5052, its effective dielectric constant is E,N=1.5 and the frequency ofoperation is 50A4Hz....8/-
8 -8- [JEE234] [b] Rajah 7 menunjukkan talian penghantaran tanpa rugi, 5052, yang ditamatkan oleh galangan yang tidak diketahui. Mengguna corak VSWR yang diplotkan dalam rajah tersebut, hitung galangan beban. Figure 7 shows a lossless, 50D, transmission line that is terminated with an unknown impedance. Using the VSWR pattern plotted in the figure, calculate the load impedance. v a.2v 3.2V T L 0 Rajah 7 Figure
9 LAMPIRAN IJEE2341 NAME SMITH C]IART FQftM 8b95PRf9.6G1 TITLE DWO. NO. RAY ELECTRIC COMPANY, PINElROOK,NJ PRINTEOIHUSA. DATE IMPEDANCE OR ADMITTANCE COORDINATES "AOW.LY WALEO PARAYETER3 ~t ~a ~ a a 101wR0 Wa a ~ t. n "' 05 f vi ~ f 0 a 0 ~ _, o. U.. o.t.. UMtE11 i.llya+il-i. TWAM 4CwCIAb - -C"-C-7 Figure 4.8 Smith chart, reprinted by permission of P. H. Smith, renewal copyright, 1976.
10 :_ [JEE234] Gradient, Divergence, Curl, and Laplacian Operations Cartesian Coordinates (x, y, z) of = ax i" + af f a ay a,. + az a: V.A= "A, + ax VXA r A-. l ay VZf 2 ax2+az+a?i ay az az $x + I-aẔ-A aaz] az y Cylindrical Coordinates (p, 0, z) Vf apa +pa45 a.+aa, _8A VxA=[l. ~a + [!A I _ i[a p ao az az ap $m + p ap(pa +) z ( f\ o2f pptp ap) + PZ + dz2 Spherical Coordinates (r, 9, 0) Vf 1 arafa. _afaea af +r_t s + rsin 0 do V,A = i[a r2 1 ] _a 1!A r2 dr( (A,)+ rsinb [a? (A B sine)j + r sin 8 do V X A = -i _a A sin B _ 'Ael a d rsin B [do ( ) _1[ 1 da, _ d ]. a _aa,l + r [sin 8 d a (ra o) am + r dr (ra e ) - a9 J a m V2f= 1_a(2a 1 _a( I _a2 r2 ar r dr + r2 sin 0 a8 Sin 09 a9 "Tel + r2sin29 a.02
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