{dúwv Mwpå~H$s {gõm V VWm ñnoñq >moñh$monr

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1 MSCPH-07 June - Examination 2017 MSC (Final) Physics Examination Electromagnetic theory and Spectroscopy {dúwv Mwpå~H$s {gõm V VWm ñnoñq >moñh$monr Paper - MSCPH-07 Time : 3 Hours ] [ Max. Marks :- 80 Note: The question paper is divided into three sections A, B and C. Write answers as per the given instructions. Calculation are not allowed. In case of any discrepancy, English version will be final for all purpose check your paper code and paper title before starting the paper. {ZX}e : h àíz nì "A', "~' Am a "g' VrZ IÊS>m {d^m{ov h & àë oh$ IÊS> Ho$ {ZX}emZwgma àízm Ho$ CÎma Xr{OE& H $b³ wboq>a H$s AZw {V Zht h & {H$gr ^r àh$ma H$s {dg JVVm H$s pñw{v o A J«oOr ê$n hr ApÝV mzm Om ojm& àíznì ewê$ H$aZo go nyd àíznì H$moS> Ed àíznì erf H$ Om±M bo& Note: Section - A 8 2 = 16 (Very Short Answer Questions) Answer all questions. As per the nature of the question delimit your answer in one word, one sentence or maximum up to 30 words. Each question carries 2 marks. MSCPH-07 / 300 / 6 (1) (P.T.O.)

2 IÊS> - "A' (A{V bkw CÎmar àíz) {ZX}e : g^r àízm Ho$ CÎma Xr{OE& Amn AnZo CÎma H$mo àízmzwgma EH$ eãx, EH$ dm³ m A{YH$V 30 eãxm n[agr{ V H$s{OE& àë oh$ àíz 2 A H$m H$m h & 1) (i) Write a relationship between the electric field E and potential V. {dúwv joì H$s Vrd«Vm E VWm {dúwv {d^d V> g ~ Y {bio & (ii) What is gauge invariance of electromagnetic fields? {dúwv Mwå~H$s joì H$s "JoO BZdo[aE e' go Amn ³ m g PVo h? (iii) State Ampere s law. Write magnetic field due to an infinitely long, straight filament of current I. Epån a H$m {Z ³ m h, n[a^m{fv H$a & EH$ AZ V bå~mb Ho$ { $bm Q> àdm{hv Ymam I Ho$ H$maU CËnÝZ Mwå~H$s joì {bio & (iv) Write the continuity equation for charge density and current density. Amdoe KZËd VWm Ymam KZËd Ho$ {b o gvvvm g rh$au {bio & (v) State Poynting s theorem. nm± pýq> J à o H$mo n[a^m{fv H$amo& (vi) With the help of a diagram show the normal modes of vibration of a linear triatomic molecule e.g. CO 2 molecule. EH$ aoir {Ìna mpêdh$ AUw (CXmhaUmW CO 2 ) Ho$ {b o H$ånZ Ho$ Zm b mos> {M{ÌV H$a & (vii) What is Zeeman splitting of spectral lines. ñno³q >b aoimam H$s µor mz {dnmq>z ³ m h? MSCPH-07 / 300 / 6 (2) (Contd.)

3 Note: 546 (viii) Write relation between magnetic and mechanical angular momentum of a system of charge. {H$gr Amdoe {ZH$m Ho$ {b o Mwå~H$s AmKyU VWm H$m Ur g doj Ho$ Ü g ~ Y {bio & Section - B 4 8 = 32 (Short Answer Questions) Answer any four questions. Each answer should not exceed 200 words. Each question carries 8 marks. (IÊS> - ~) (bkw CÎmar àíz) {ZX}e : {H$Ýht Mma àízm Ho$ CÎma Xr{OE& Amn AnZo CÎma H$mo A{YH$V 200 eãxm n[agr{ V H$s{OE& àë oh$ àíz 8 A H$m H$m h & 2) Write complete set of Maxwell equations of macroscopic electromagnetism. Derive the wave equations for the scalar potential f and vector potential A in the Lorentz gauge. Write the solution for f and A. {H$gr ~ hx {ZH$m Ho$ {be o³gdob g rh$aum H$mo {bi & BZH$s ghm Vm go do³q>a {d^d A VWm ñho$ba {d^d f Ho$ {b o bmoa O JoµO Va J g rh$au àmßv H$a & f VWm A Ho$ {b o hb ^r àmßv H$a & 3) Using Maxwell s equations deduce the law of conservation of energy for the closed system consisting of electromagnetic field and particles present in it. o³gdob g rh$aum H$m Cn moj H$aVo hþ o "Amdo{eV H$Um Ho$ "~ÝX' {ZH$m Ho$ {b o D$Om g aju {Z àmßv H$a & MSCPH-07 / 300 / 6 (3) (P.T.O.)

4 4) Explain the displacement current. {dñwmnz Ymam H$mo g PmAmo& 5) Derive Larmor s formula for the power radiated by an accelerated charge. What is radiation resistance? Ëd[aV Amdoe go CËg{O V nmda Ho$ {b o bma^a gyì ñwm{nv H$a & "ao{s>eez à{vamoy' go Amn ³ m g PVo h? 6) Explain with the help of energy level diagram the Zeeman effect for two electron system. Derive an expression for the magnetic splitting of spectral lines. Xmo Bbo³Q >m Z {ZH$m Ho$ {b o Or mz à^md H$mo D$Om AmamoI Ûmam ì m» m H$a & ñno³q >b aoimam H$m Mwå~H$s joì Ûmam {dnmq>z Ho$ {b o ì OH$ àmßv H$a & 7) Explain rotational spectra of diatomic molecules. Treat diatomic molecule as a rigid rotator. Draw energy level diagram and show transitions. Ñ T> {Ûna mpêdh$ AUwAm Ho$ KyUu ñno³q > H$s ì m» m H$a & D$Om AmaoI Ho$ Ûmam g H«$ U Xem E±& 8) Explain Frank-Condon principle. Define dissociation energy of a molecule. «o$h$ - H$m±ÝS>Z {gõmýv ³ m h, ì m» m H$a & AUw H$s {dkq>z D$Om H$mo n[a^m{fv H$a & 9) Explain theory of vibrational-rotational spectra of diatomic molecules. {Ûnê$ mpêdh$ AUwAm Ho$ {b o H$ånÞ KyU Z ñno³q >m H$s ì m» m H$a & MSCPH-07 / 300 / 6 (4) (Contd.)

5 Section - C 2 16 = 32 (Long Answer Questions) Note: Answer any two questions. You have to delimit your each answer maximum up to 500 words. Each question carries 16 marks. (IÊS> - g) (XrK CÎmar àíz) {ZX}e : {H$Ýht Xmo àízm Ho$ CÎma Xr{OE& Amn AnZo CÎma H$mo A{YH$V 500 eãxm n[agr{ V H$s{OE& àë oh$ àíz 16 A H$m H$m h & 10) What is Raman effect? Give classical or quantum theory of Raman effect. The occurrence of a Raman spectrum depends on the polarizability of the molecules, but is entirely independent of the presence of permanent dipole moment. Discuss. a Z à^md ³ m h? a Z à^md H$s ³bmgrH$b ({Magå V) AWdm ³dmÝQ> Ï m ar H$mo g PmE±& ""a Z ñno³q > AUwAm H$s nmobo[aoo{~{bq>r (Yw«dU) na {Z^ a H$aVm h Z {H$ AUwAm Ho$ {ÛY«wd AmKyU na, ""Bg H$WZ H$s {ddomzm H$a & 11) (i) What is Born-Oppenheimer approximation? Discuss its significance in the molecular spectra. ~moz -Am noz hmb a Eàmo³gr oez (g{þh$q>vm) ³ m h? AmpÊdH$ ñno³q > BgH$s gmw H$Vm H$mo g PmB o& (ii) Discuss the isotope effect on the vibrational spectra. H$ånZ ñno³q > AmBgmoQ>mon g ñwm{zh$ à^md H$s ì m» m H$a & MSCPH-07 / 300 / 6 (5) (P.T.O.)

6 12) Derive Fresnel s laws for the reflection and refraction of a plane monochromatic electromagnetic wave at a plane boundary between two homogeneous media. Discuss the case when the electric field the incident wave is (i) Perpendicular to the plane of incidence (ii) Lies in the plane of incidence. Xmo g m Jr mü Ho$ g Vb n[agr m na AmnmVr g Vb EH$dUu {dúwv Mwå~H$s Va J Ho$ {be namdv Z Ed AndV Z Ho$ {be «o$zb Ho$ {Z {ZJ Z H$amo& CZ pñw{v m H$s {ddomzm H$amo O~ AmnmVr Va J H$m {dúwv joì (i) AmnVZ Vb Ho$ bå~dv hmo& (ii) AmnVZ Vb hmo& 13) Write Maxwell s equations for a monochromatic field. Deduce the wave equation propagating in an infinite homogeneous medium. If the medium is non-absorbing (transparent) and homogeneous, then find the refractive index of the medium. o³gdob Ho$ g rh$au {bi Ed o³gdob g rh$aum H$s ghm Vm go AZÝV g m Jr mü Va J g rh$au àmßv H$a & {X mü Ademofr Zht hmo AWm V nmaxeu hmo Vmo Cg g m Jr mü H$m AndV Zm H$ kmv H$a & MSCPH-07 / 300 / 6 (6)