BACHELOR OF SCIENCE (B.Sc.) Term-End Examination 00 June, 2012.czt. PHE-07 : ELECTRIC AND MAGNETIC PHENOMENA

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1 No. of Printed Pages : 8 BACHELOR OF SCIENCE (B.Sc.) PHE-07 Term-End Examination 00 June, 2012.czt. PHE-07 : ELECTRIC AND MAGNETIC CD PHENOMENA Time : 2 hours Maximum Marks : 50 Note : All questions are compulsory. Marks allotted for each question are indicated against it. You may use log tables or calculators. Symbols have their usual meaning. Values of physical constants are given at the end. 1. Attempt any five parts : 3x5=15 (a) The electric potential at any point is given by : = y (x2-6xy) (b) (c) (d) Calculate the electric field E at that point. Why is the electric field zero inside a conductor? Invoking this concept in conjunction with Gauss' law, show that the charge resides only on the surface of a charged conductor. State Biot - Savart law. Plot the magnetic field due to a straight current carrying conductor at a point outside the conductor. Write the expressions for the incident, reflected and transmitted electromagnetic waves at the interface of two dielectrics. PHE-07 1 P.T.O.

2 (e) (f) Show that the tangential component of is continuous across a dielectric boundary. The electric field associated with an electromagnetic wave propagating in free space is given (in Vm -1) by (g) (h) = 20 f exp [ (106 t + (3z) ] Determine its direction of propagation, wave number and frequency. A beam of electrons passes undeflected through two mutually perpendicular electric and magnetic fields of strengths 8 kvm -1 and 2 x 10-3 T, respectively. While maintaining the same magnetic field, the electric field is cut off. The electrons then move in the magnetic field in a circular path of radius 1.15 cm. Determine the ratio of change to mass of the electron. Explain in brief the working of an electrolytic capacitor. What are the important specifications for these capacitors? 2. Attempt any five parts : 5x5=25 (a) State Ampere's Circuital law. Use this law (b) to calculate the magnetic field inside a toroid. An electron circulates around the nucleus in a path of radius 5.1 x m at a frequency of 6.8 x 1015 revolutions per second. Calculate the magnetic field (g) at the centre of the nucleus and the resulting magnetic dipole moment. PHE-07 2

3 (c) (d) (e) (f) (g) Derive the expression for the electric field at a point along the axis of an electric dipole. What is meant by atomic/molecular polarizability? What are its units? Derive the relation between polarizability and relative permittivity. What do you understand by self inductance of a coil? A solenoid 1.5 m long and 20 cm in diameter contains 1500 turns of insulated copper wire. A current of 3.0 A flowing through it is reduced to zero in 1.5 ms calculate the magnitude of the back e.m.f induced in the solenoid while the current is being switched off. What considerations led Maxwell to introduce the concept of displacement current? Discuss the physical significance of displacement current. The capacitance of a parallel-plate capacitor, whose plates are separated by a distance of 3 m, is 300 pf (picofarad). What will be the energy of the capacitor when it is charged to a potential of 1000 V. For the same charge on the capacitor plates, calculate the potential difference, if the plate separation is doubled. PHE-07 3 P.T.O.

4 3. Determine the self-inductance of a toroidal coil of rectangular cross-section, having N1 turns, inner radius a, outer radius b and height h. Suppose a coil of N2 turns is wound over the toroidal coil. Show that the mutual inductance of this arrangement is : M = 1T N N2 h In I b a 5+5=10 OR Write Guass' law in both integral and differential forms. Using Gauss' law obtain an expression for the electric field due to a spherical charge distribution at a point lying : =10 (a) (b) (c) outside, inside ; and on the surface of the charge distribution. Physical Constants : e = 1.67x10-19 C me = 9.1 X kg inp = 1.67 x kg eo = 8.85 X F m-1 = x 10-7 Tm A -1 c = 3 x108 m s-1 h = x Js 1 47r eo = 9.0 x 109 N m2 C-2 PHE-07 4

5 den ( *.7r 4". ) t : at1t Va-*--1Er s, ttldllq. cl/hei : 2 W2 : 50 ViE" : 79# M.Y-t 3lfT4T-4 vf;w UFA Iq" t 17l g- 37-fri 3.T2RT grue f gifuw I:N( R. rc' 77e/ 1. rriw 5tiPT q, 3x5=15 (a) f-*7t f fa-7 fall-4, Trri t:.13.= y (x2-6xy) faqq -14-ri oloct ct) I (b) f*7:11. Liqr21 TEN 74 Taff t? 3T-44R-urr aar 4116,q Fli44 err ft et-; rct> f-*-4r 3Tr-d-r-vm rim* It 31-r-4 t-4 - -z-trk tr-t t-1 7 t I (c) PV aTI ttru -9-a-rkff T4A-zr t Ore f-*-tft f4-1 -ER ch-i PHE-07 5 P.T.O.

6 (d) 1=RTA7 Liqr2fft atd F-0, ytiel 21-1 Lilt+111-1c1 fd7,--trzf fo-d I (e) ft 1,1.) t17147 ti t 'WE Erz* 4dd t- (0 -q*f 311*wr 4-ciirkd *I (vm 1 T*11 4) f9-pr : = 20 7 exp [ (106 t + (3z)] din 1-) 'obroci ei-) (g) 1, f*to-rci- fq7-rr, t-14r 4'&4I -ff.41 3Trqf LIR sill-ri: 8 kvm 1 72TT 2X10-3Tfalf-TqfffUtlAkklItIV ft-afd-u -grrff 7L- f chk f ẕrr \TIldIt I '41.15 cm flwrf 14 rifm.) 1th71c T9 WcdT t I 31r-d-vr 4 ce f 3-T1:17 tcb Oct ch I (h) fd7r-3d-t TftUrR7 Tf-)icr TfqrW 31-fiTFuur *ir 2. W) 77k 9.1TIT ch 5x5=25 (a)crfrorzr yr(9-)h -N4-1 t I ide.444.*t 3-1TIOT eh PHE-07 6

7 (b). -- q0" ft141 TfTrT -q71 3-T x mfl'eft 'Efff Tt arfrqt AlikstoiLif tat t gird 31*-ff 6.8 x 1015 if-wm Tifd tics t I 91531W t" ti7 I W2TE 4Ruto *-14?gag 374 (c) f4zik rap atat 31-1k-vr trt 1.04 (d) 4R1-1141/ 3-Tql-Zr VIA-4M 371:f all TriTga IrT- 7-*7-4Z:rr -t)tftt-? igaufitra-rw3p4rtt,aq(-114.) 4 Tt4q (e) f*1:ft dillf T11:124f t? 1.5 m WEIT 20 cm WTI trial Via, 1TR-id-cm 'ar t t I 7: ( A.z1T ms.4e.leht kit t I 31-dfiT 411-Cochi Fa tly faq-d ari Lirk.brqicr.{.> (f) rch1 Th171: tirt Li (q)c-till 3-1-curact c ? ffit-9-trcri q-ru (g) {, cati 3 m t, NTr ITM 300 pf t I efrq 7:1 7441r7q 1000 V fq91-4 3Trevru f*-71 Tff-4- d1\711 WE 1117 err? Fri 1:NTF77 t 41,4 ftirdit{ 79' LiRchkui qrq tor AR' PRE-07 7 P.T.O.

8 3. 3TPT-d-WR 3TI5R-21.-1TFT c pct) tco f91tiftffc ifs 4(y-ii N1 t awt altett "N TT at, flwit b t -ff2tt h t I cbc-4-11 chi F 'TT N2 latroi ) Aid1 t i fi:r4mz 14) M= µo N N h in ( 11 27r 2 ceisrich t : 5+5=10-11 to-i114,11&(-1 fir 4 I 4113i 3T Irr -) 3Tr-d-vr fa--d7t ehrui f-911f--43-ff fq--trt 1-(1 ceisgcb : (a) ich f 31T 71f-ddTur t; (b) i) 3-TT fl-d7171 att t; 2.TT (c) ic=11 f fqfftlif 'T #21-ff t I =10 %fri9"w ritidich : e = 1.67x10-19 C me = 9.1 x10-31 kg mp = 1.67 x kg 0 = 8.85 x F m-1 tio = zkr x 10 7 Tm A 1 c = 3x108 m s-1 h = x Js 4 1-e = 9.0 x 109 N m2 C-2 PHE-07 8

ELECTRO MAGNETIC FIELDS

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