{dÚwVMwå~H$s

PH-03

June - Examination 2017 B.Sc. Pt. I Examination

Electromagnetism

{dÚwVMwå~H$s

Paper - PH-03

Time : 3 Hours ] [ Max. Marks :- 50

Note: The question paper is divided into three sections. A, B and C.

Write answer as per the given instructions.

{ZX}e : ¶h àíZ nÌ "A', "~' Am¡a "g' VrZ IÊS>m| ‘| {d^m{OV h¢& à˶oH$

IÊS> Ho$ {ZX}emZwgma àíZm| Ho$ CÎma Xr{OE&

Section - A 10

×

1 = 10 (Very Short Answer Questions) (Compulsory)

Note: Answer all questions. As per the nature of the question delimit your answer in one word, one sentence or maximum upto 30 words. Each question carries 1 mark.

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$s{O¶o& à˶oH$ àíZ

1

A§H$ H$m h¡&

643

PH-03 / 900 / 5 (2) (Contd.)

1) (i) Define gradient of a scalar function.

A{Xe joÌ H$s àdUVm H$mo n[a^m{fV H$s{OE&

(ii) Write down the differential and integral forms of Gauss's Law.

Jm°g Ho$ {Z¶‘ Ho$ AdH$b VWm g‘mH$b én {b{IE&

(iii) What do you mean by positive value of divergence of electric field?

{dÚwV joÌ Ho$ S>mBdO}Ýg Ho$ YZmË‘H$ hmoZo H$m ³¶m ‘Vb~

^or

AW© h¡&

(iv) What is curl of a conservative field?

g§ajr joÌ H$m H$b© ³¶m hmoVm h¡?

(v) Define one volt.

EH$ dmoëQ> H$mo n[a^m{fV H$s{OE&

(vi) What is formula of the torque on a dipole in an electric field?

{dÚwV joÌ ‘| pñWV {dÚwV {ÛY«wd na ~bmKyU© H$m gyÌ ³¶m hmoVm h¡?

(vii) Write down the relation among Electric field ^ hE , Polarization density ^ hP and electric Displacement ^ hD .

{dÚwV joÌ

^{^ hE}

, Y«wdU KZËd

^{^ hP}

VWm {dÚwV {dñWmnZ

^{^ hD}

‘|

nañna gå~ÝY {b{IE&

(viii) Write down the larmer frequency.

bma‘a Amd¥{Îm {b{IE&

(ix) Write down the magnetic field B near a long current carrying conductor.

bå~o Ymamdmhr MmbH$ Ho$ {ZH$Q> Mwå~H$s¶ joÌ

^B

H$m ‘mZ {b{I¶o&

(x) Define self inductance.

ñdàoaH$Ëd H$mo n[a^m{fV H$s{OE&

Section - B 4

×

5 = 20 (Short Answer Questions)

Note: Answer any four questions. Each answer should not exceed 200 words. Each question carries 5 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$s{O¶o& à˶oH$ àíZ

⁵

A§H$m| H$m h¡&

2) Prove lnr r r

4^ h= 2 for position vector r= xit+ yjt+ zkt.

pñW{V g{Xe

^{r= xit+ yjt+zkt}

Ho$ {bE

^{4^lnrh=} _r^r2

H$mo {gÕ H$s{OE&

3) State and prove Gauss's divergence theorem.

Jm°g H$m S>mBdO}Ýg à‘o¶ H$m H$WZ {bIH$a {gÕ H$s{OE&

4) Calculate the classical radius of an electron.

Bbo³Q´>m°Z H$s {Magå‘V {ÌÁ¶m Ho$ ‘mZ H$m AmH$bZ H$a|&

5) Prove that (i) curl = B= n0J (ii) divergence B = 0

{gÕ H$s{OE -

⁽ⁱ⁾

H$b©

^{= B= n0J (ii)}

S>mBdO}Ýg

^{B = 0}

6) Define electrical susceptibility and relative permittivity. Establish a relation between them.

{dÚwV àd¥{Îm VWm Amno{jH$ {dÚwVerbVm H$mo n[a^m{fV H$s{OE& BZ‘o gå~ÝY ñWm{nV H$s{OE&

7) A uniform electric field of 6 × 10⁵ Volt/meter is applied on O₂ gas.

Calculate induced polarizability. (Given a = 16.4 ×10^–41 Farad-m² and N = 2.7 × 10²⁵ molecule/m³).

PH-03 / 900 / 5 (4) (Contd.)

Am°³grOZ J¡g na EH$ g‘mZ {dÚwV joÌ

^{6 × 105}

dmoëQ>/‘rQ>a bJmZo na ào[aV Y«wdUVm H$s JUZm H$s{OE& {X¶m J¶m h¡ Am°³grOZ J¡g H$s AmpÊdH$

Y«wdUVm

^{16.4 ×10–41}

’¡$amS> - ‘rQ>a

²

VWm

^O2

H$m AUw KZËd

^{2.7 × 1025}

AUw/‘rQ>a

³

&

8) Explain the inconsistancy of Ampere's Law and write down it's modified form.

Epån¶a Ho$ {Z¶‘ H$s Ag§J{V H$mo g‘PmB¶o VWm BgHo$ g§emo{YV én H$mo {b{I¶o&

9) Derive an expression for charging of a condenser in a R-C circuit.

EH$

^R-C

n[anW ‘| g§Ym[aÌ Ho$ AmdoeZ H$m 춧OH$ ì¶wËnÞ H$s{OE&

Section - C 2

×

10 = 20 (Long Answer Questions)

Note: Answer any two questions. You have to delimit your each answer maximum upto 500 words. Each question carries 10 marks.

(IÊS> - g) (XrK© CÎmar¶ àíZ)

{ZX}e : {H$Ýht Xmo àíZm| Ho$ CÎma Xr{O¶o& AnZo CÎma H$mo A{YH$V‘

500

eãXm| ‘| n[agr{‘V H$aZm h¡& à˶oH$ àíZ

¹⁰

A§H$m| H$m h¡&

10) Define divergence of a vector and derive an expression for divergence of a vector in Cartesian coordinate system. Explain its physical significance.

{H$gr g{Xe Ho$ S>mBdO}Ýg H$mo n[a^m{fV H$s{OE VWm H$mVu¶ {ZX}em§H$

nÕ{V ‘| g{Xe Ho$ S>mBdO}Ýg H$m 춧OH$ kmV H$s{OE& BgH$s ^m¡{VH$

gmW©H$Vm H$mo g‘PmB¶o&

11) Derive an expression of Clausius-Mossotti relation for dielectric medium.

{H$gr namd¡ÚwV ‘mܶ‘ Ho$ {bE ³bm°{g¶g ‘mogmoQ>r gå~ÝY kmV H$s{OE&

12) What do you mean by magnetic vector potential? Derive the poisson equation for magnetic vector potential and write down expression of its solution.

Mwå~H$s¶ g{Xe {d^d go Amn ³¶m g‘PVo h¡? BgH$m nm°¶gZ g‘rH$aU kmV H$s{OE VWm BgHo$ hb H$m 춧OH$ {b{IE&

13) Obtain all the four Maxwell's equation related to electromagnetic field.

{dÚwV Mwå~H$s¶ joÌ go gå~pÝYV ‘¡³gdob Ho$ g‘rH$aUm| H$mo kmV H$s{OE&