APEX CARE INSTITUTE FOR TRB, SLET AND NET IN PHYSICS ELECTROMAGNETIC THEORY- SLET / NET QUESTION BANK

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1 ELECTROMAGNETC THEORY- SLET / NET QUESTON BANK. The electosttic potentil V(, ) in fee spce in egion whee the chge densit ρ is eo is given b V, e f. Given tht the -component of the electic field E, nd V e eo t the oigin, f is () e 8 (b) e 6 e 8 ( d) e. E V E 8e f Solution: V e f. Since V 6e f 6 Since E t oigin, 8 f f 8 E. Since V, f f Solve eqution 6e f 6 f 6 6e f 6 8e c, since f8c 8c. Agin ntegte f 6 8e f e c since f c c. Thus f e. o constnt unifom electic nd mgnetic field E E nd B B, it is possible to choose guge such tht the scl potentil nd vecto potentil A e given b () nd A B (b) E nd A B E nd A (d) nd A Et Solution: Let E E nd B B Loent Guge condition is A t since the e constnt vecto. Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

2 since B B B B () nd A (b), nd A t t nd A (d) nd A t t. A plne electomgnetic wve is popgting in lossless dielectic. The electic field is given b E,,, t E A ep ik ct, whee c is the speed of light in vcuum, E, A nd k e constnt nd nd ẑ e unit vectos long the - nd -es. The eltive dielectic constnt of the medium nd the constnt A e () nd A (b) nd A nd nd A E,, t E A epik ct. Solution:, i Comping with tem k t e k k Since nd k c. kc c v Refctive inde n. k k k Since k n k A k A A A K. A sttic, spheicll smmetic chge distibution is given b e whee A nd K e positive constnts. The electosttic potentil coesponding to this chge distibution vies with s () K e (b) K e K e K (d) e Solution: since V / Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

3 V must be popotionl to A k e, whee V. 5. The mgnetic field of the TE mode of ectngul wveguide of dimensions b s V shown in the figue is given b H H cos. cos. cm. b whee nd e in A. The dimensions of the wveguide e (). cm, b.5 cm (b). cm, b. cm.8 cm, b.6 cm (d).66 cm, b.5 cm Solution: Since H H cos. cos. m n. whee m nd. whee n b.cm, b. 5cm B. The entie nge of fequencies f fo which the TE mode will popgte is () 6.GH f.gh 7.5GH < f <.GH (b) 7.5GH f 9.GH (d) f Solution: f m, n c m n b c f, 7. 5GH. b o popgtion, fequenc of incident wve must be gete thn cutoff fequenc. Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

4 6. Conside thee polie s P, P nd P plced long n is s shown in the figue. (unpolied) P P P The pss is of P nd P e t ight ngles to ech othe while the pss is of P mkes n ngle with tht of P. A bem of unpolied light of intensit is incident on P s shown. The intensit of light emeging fom P is () (b) 8 sin (d) sin Solution: cos (Mlus Lw), cos, cos cos 9 sin ou equl point chges e kept fied t the fou vetices of sque. How mn neutl points (i.e. points whee the electic field vnishes) will be found inside the sque? () (b) 5 (d) 7 Solution: nside the sque, thee is onl one point whee field vnishes. / R 8. A sttic chge distibution gives ise to n electic field of the fom E e Ans:, whee nd R e positive constnts. The chge contined within sphee of dius R, cented t the oigin is e e R () (b) (d) e R R None of the options given e coect / R Solution: Qenc E d e sin d d / R e R sindd e Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

5 t R, Q enc. So none of the options given e coect. e 9. n Young s double slit intefeence epeiment, the slits e t distnce L fom ech othe nd the sceen is t distnce D fom the slits. f glss slb of efctive inde nd thickness d is plced in the pth of one of the bems, the minimum vlue of d fo the centl finge to be dk is D () D L D (b) L (d) n Solution: o centl finge to be dk, d d. Conside solenoid of dius R with n tuns pe unit length, in which time dependent cuent sint (whee R/ c ) flows. The mgnitude of the electic field t pependicul distnce R fom the is of s met of the solenoid, is () (b) n R cost n sint (d) n cost B Solution: E dl d; B n t. t d E n d n cost dt E n cost. A constnt electic cuent in n infinitel long stight wie is suddenl switched on t t. The vecto potentil t pependicul distnce fom the wie is given k b A ln ct c t. The electic field t distnce ct is Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

6 6 () (b) j i t j i t c c (d) k t c c Solution:. t c t c c t c ct E t A t A E k t c c E. The mgnetic field coesponding to the vecto potentil A, whee is constnt vecto, is () (b) (d) Solution: A B. Since is constnt vecto, let,,. Thus B. An electomgnetic wve is incident on wte-i intefce. The phse of the pependicul component of the electic field, E, of the eflected wve into the wte is found to emin the sme fo ll ngles of incidence. The phse of the mgnetic field H () does not chnge (b) chnges b / chnges b / (d) chnges b Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

7 () R (b). The mgnetic field t distnce R fom long stight wie cing sted cuent is popotionl to / R / R (d) / R 5. Which of the following questions is Loent invint? () E B (b) E B E B (d) E B 6. Chges Q, Q nd Q e plced on the vetices of n equiltel tingle ABC of sides of length, s shown in the figue. The dipole moment of this configution of chges, iespective of the choice of oigin, is - Q ĵ C () Qi (b) Q j A B Q Q Q j (d) î Solution: Let coodintes of A is (l, m), then p q Q li p Q li i i mj Ql i mj Q l i m mj Ql i mj Q l i m j j p Qj m 7. The vecto potentil A due to mgnetic moment m t point is given b A. f m is diected long the positive -is, the - component of the mgnetic field, t the point, is m () 5 m m (b) 5 5 m (d) 5 Solution: m m m nd B A cos sin m m m B m m B 5 Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

8 8. Thee chges e locted on the cicumfeence of cicle of dius R s shown in the figue below. The two chges Q subtend n ngle 9 t the cente Q of the cicle. The chge q is smmeticll plced with espect to Q the chges Q. f the electic field t the cente of the cicle is eo, wht is the mgnitude of Q? () q / (b) q q (d) q q Q q Solution: E E nd E R R Resultnt of E nd E is E E E E, Thus E E Q 9. Conside hollow chged shell of inne dius nd oute dius b. The volume k chge densit is ( k is constnt) in the egion b. The mgnitude of the electic field poduced t distnce is () (b) (d) k b k b k k fo ll, kb fo b nd fo b fo b nd fo b nd k b k b fo b fo b q Solution: o : k Ed E Q dv ddd. ( ) enc sin k k E E( ) d ( ) k Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

9 o b: k b k E E d ( b ) k b. Conside the intefeence of two coheent electomgnetic wves whose electic field vectos e given b E ie cos t E je cos t whee is the phse nd diffeence. The intensit of the esulting wve is given b E time vege of () E. The totl intensit is, whee (b) E sin (d) E cos E E is the Solution: Since wves e polied in pependicul diection hence thee will be no intefeence.. ou chges (two q nd two q ) e kept fied t the fou vetices of sque of side s shown. At the point P which is t distnce R fom the cente R, the q q potentil is popotionl to () / R (b) / R R P / R (d) / R q q Solution: Given configution is qudupole.. A point chges q of mss m is kept t distnce d below gounded infinite conducting sheet which lies in the - plne. o wht vlue of d will the chge emins sttion? Ans: Solution: Thee is ttctive foce between point chge q nd gounded conducting sheet tht cn be clculte fom method of imges i.e. q mg d mg q d Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

10 . An infinite solenoid with its is of smmet long the -diection cies sted cuent. The vecto potentil A t distnce R fom the is () is constnt inside nd vies s R outside the solenoid (b) vies s R inside nd is constnt outside the solenoid vies s R inside nd s R outside the solenoid ẑ R (d) vies s R inside nd s R outside the solenoid. Conside n infinite conducting sheet in the -plne with time dependent cuent densit Kt i, whee K is constnt. The vecto potentil t,, is given K b A ct i. The mgnetic field B is c Kt () j (b) K K j ct i K (d) ct j c c c A K B A = ct j c 5. When chged pticle emits electomgnetic dition, the electic field E nd the Ponting vecto S E B t lge distnce fom emitte v s n nd m espectivel. Which of the following choices fo n nd m e coect? n m nd m n nd m (d) n nd m Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

11 6. A pticle of chge e nd mss m is locted t the midpoint of the line joining two fied colline dipoles with unit chges s shown in the figue. (The pticle is constined to move onl long the line joining the dipoles). Assuming tht the length of the dipoles is much shote thn thei seption, the ntul fequenc of oscilltion of the pticle is R R e, m d d () 6eR md 5 6eR (b) md 6ed mr 5 6ed (d) mr R R Solution: Let us displce the chge pticle b smll mount t A. Then the esultnt electic field t e, m A point A is given b d d E p 6d, R R R 6ed ee R. Then, k 6ed (whee p d d ) m mr 7. A cuent is ceted b now bem of potons moving in vcuum with constnt velocitu. The diection nd mgnitude, espectivel of the Ponting vecto S outside the bem t dil distnce (much lge thn the width of the bem) fom the is, e () S u nd S u (b) S u nd S u S u nd S u (d) S u nd S u Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

12 Solution: Let chge pe unit length be, hence u in -diection. The mgnetic field t distnce is B. The electic field t distnce is E. u Hence Ponting vecto S E B u 8. f the electic nd mgnetic fields e unchnged when the potentil A chnges (in suitble units) ccoding to A A, whee t, then the scl potentil must simultneousl chnge to () (b) / t (d) / t Solution: A A A / C V V / t V / t 9. Conside n ill smmetic sttic chge distibution of the fom, / e cos The dil component of the dipole moment due to this chge distibution is () (b) (d) / / Solution: p d e cos sind dd V / sin cos p e d d d. The components of vecto potentil A A, A, A A A k, t, t, t, e given b whee k is constnt. The thee components of the electic field e () k,, (b) k,,,, (d) k t, t, t Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

13 Ans: Solution: A, A, A, A k, A kt, A kt, A kt A t Since k nd k E A t k k E,,. An oscillting cuent t ep it thin metl sheet of e flows in the diection of the -is though.cm kept in the -plne. The te of totl eneg dited pe unit e fom the sufces of the metl sheet t distnce of m is () / c (b) / c / c (d) / c A hoiontl metl disc ottes bout the veticl is in unifom mgnetic field pointing up s hown in the figue. A cicuit is mde b connecting one end A of esisto to the cente of the disc nd the othe end B to its edge though sliding contct. The cuent tht flows though the esisto is B A B S () eo DC fom B to A (b) DC fom A to B (d) AC. The foce between two long nd pllel wies cing cuents nd nd septed b distnce D is popotionl to () / D (b) / D / D (d) / D Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

14 . The electic field of n electomgnetic wve is given b E E cos.. t k. The ssocited mgnetic field B is () E cos.. t (b) E cos.. t k i j.. t. i. j cos.. t i j E cos (d) E.., Solution: k k E B.. E cos.. t.. t i j B E cos 5. A point chge q is plced smmeticll t distnce d fom two pependicull plced gounded conducting infinite pltes s shown in the figue. The net foce on the chge (in units of/ ) is q () 8d q (b) 8d w fom the cone towds the cone k d q d q d towds the cone q (d) 8d w fom the cone q q Solution: k nd k d 8d q Resultnt of, is k. 8d q q d d d q d d q Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

15 q Net foce k 8d (towds the cone) 6. f the electosttic potentil V,, in chge fee egion hs the fom f V,, cos constnts) is: () b, then the functionl fom of b (b) f (in the following nd b e b (d) ln b Solution: V sin V V V sin sin f cos sin f sin sin cos f f f sin cos sin f f f f b stisf the bove eqution. 7. Let fou point chges q, q /, q nd q / be plced t the vetices of sque of side. Let nothe point chge q be plced t the cente of the sque (see the figue). q / q q Let V be the electosttic potentil t point P t distnce fom the cente of the sque. Then V / V () (b) q is q / (d) 8 Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

16 q q Solution: Accoding to multipole epnsion Q mono q q q q q q q q q q qq q pq q 8 V Thus, V. V 8. Let A V, nd V A, denote two sets of scl nd vecto potentils, nd is scl function. Which of the following tnsfomtions leve the electic nd mgnetic fields (nd hence Mwell s equtions) unchnged? () A A nd V V t A A nd V V t (b) (d) A A nd V V t A A nd V V t 9. A time-dependent cuent t Kt (whee K is constnt) is switched on t t in n infinite cuent-cing wie. The mgnetic vecto potentil t pependicul distnce fom the wie is given (fo time t / c ) b () K c c t c t ct d / (b) ct K t d / ct Solution: K c ct ct d / ct t / K t R c A d d R R ct A d K ct / c ct (d) K c t c t d d t R P / Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

17 . A cuent i p flows though the pim coil of tnsfome. The gph of function of time t is shown in the figue below. i p t i p t s t Which of the following gphs epesents the cuent i S in the second coil? () (b) is t is t (d) t t Solution: i is s t dip dt t. f the electosttic potentil in spheicl pol coodintes is / e whee nd e constnts, then the chge densit t distnce will be is t t () e e (b) e (d) e Solution: e e / / e e / / e e / / Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

18 At distnce, e e e e e. f A i j k nd C is the cicle of unit dius in the plne defined b, with the cente on the - is, then the vlue of the integl Ad is C () (b) (d) i j k Solution: A i j k Ad Ad Since C S. Conside n electomgnetic wve t the intefce between two homogenous dielectic medi of dielectic constnts nd. Assuming nd no chges on the sufce, the electic field vecto E nd the displcement vecto D in the two medi stisf the following inequlities () E E nd D D (b) E E nd D D E E nd D D (d) E E nd D D. A chge e is plced in vcuum t the point,, d, whee d. The egion d is filled unifoml with metl. The electic field t the point,, is e e (),, (b),, 9 d 9 d e d,, e d (d),, Solution: e d d P d E E e Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

19 E e e e e E d / 9d nd d / d Thus esultnt electic field t point P is e e e e e E E E E 9d d 9d 9 d 9 d 5. A bem of light of fequenc is eflected fom dielectic-metl intefce t noml incidence. The efctive inde of the dielectic medium is n nd tht of the metl is n n i. f the bem is polised pllel to the intefce, then the phse chnge epeienced b the light upon eflection is () tn / (b) tn / tn / (d) tn Solution: Since E R E whee v c/ n i v c/ n i i / i e i/ E R E E e E whee tn. i i e Thus phse chnge / tn cot tn 6. A thin, infinitel long solenoid plced long the - is contins mgnetic flu. Which of the following vecto potentils coesponds to the mgnetic field t n bit point,,? () A, A, A,, (b) A, A, A,, A, A, A,, (d) A, A, A,, Solution: BA Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

20 7 7. An electomgneticll-shielded oom is designed so tht t fequenc d/s the intensit of the etenl dition tht penettes the oom is % of the incident m is the conductivit of the shielding mteil, its dition. f 6 minimum thickness should be (given tht ln. ) ().6 mm (b). mm. mm (d).6 mm Solution: e ln whee 6 7 7, ln. 8. A chged pticle is t distnce d fom n infinite conducting plne mintined t eo potentil. When elesed fom est, the pticle eches speed u t distnce d / fom the plne. At wht distnce fom the plne will the pticle ech the speed u? Solution: d q mm dt d d A dt whee q A 6 m. dv A dv A d d d v v A dt dt dt dt dt v A C A t d, vc v A d d. P q d d q Thus A u A d / d d then d u A d 5 Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

21 9. A chged pticle moves in helicl pth unde the influence of constnt mgnetic field. The initil velocit is such tht the component long the mgnetic field is twice the component in the plne noml to the mgnetic field. The tio / R of the pitch to the dius R of the helicl pth is () / (b) (d) l R Solution: v v R R l Pitch of the heli l vt v v R v v R 5. A pllel bem of light of wvelength is incident nomll on thin polme film with i on both sides. f the film hs efctive inde n, then second-ode bight finges cn be obseved in eflection when the thickness of the film is () / n (b) / n / n (d) / n cos Solution: o constuctive intefeence: nd m o noml incidence nd second odem nd cos d n 5. A solid sphee of dius R hs chge densit, given b R whee is the dil coodinte nd nd R e positive constnts. f the mgnitude of the electic field t R / is.5 times tht t R is () (b) / (d) /,, then the vlue of Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

22 Solution: Ed S Q. enc R E d E d E R R R E R /.5E R R / R /.5 R R R R The electosttic lines of foce due to sstem of fou point chges is sketched hee. At lge distnce, the leding smptotic behviou of the electosttic potentil is popotionl to () (b) (d) Solution: The given electosttic line of foce is due to qudupole. So V. 5. A plne electomgnetic wve incident nomll on the sufce of mteil is ptill eflected. Mesuements on the stnding wve in the egion in font of the intefce such tht the tio of the electic field mplitude t the mim nd the minim is 5. The tio of the eflected intensit to the incident intensit is () / 9 (b) / / 5 (d) / 5 E E E 5 E E 5 E E 6E E E E E Solution: R R R R R R R R E E 9 Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

23 5. A non-eltivistic pticle of mss m nd chge e, moving with velocit v cceletion, emits dition of intensit. Wht is the intensit of the dition emitted b pticle of mss m /, chge e, velocit v / nd cceletion? () 6 (b) 8 (d) q sin q e Solution: 6 6 q e 55. A Plne electomgnetic wve is tvelling long the positive -diection. The mimum electic field long the - diection is V / m. The ppoimte mimum vlues of the powe pe unit e nd the mgnetic induction B, espectivel, e 7 (). wtts / m nd tesl 7 (b). wtts / m nd. 8 tesl.65 wtts / m nd tesl (d).65 wtts / m nd. 8 tesl P E V / m, c E W / m A Solution: B 8 E. c 8 8 Tesl 56. Which of the following tnsfomtions V, A V ', A' V nd the vecto potentil A is guge tnsfomtion? () VV, A At k (b) VV, A At k VV, A At i (d) VV, A At i of the electosttic potentil Solution: V V t c t t ti. Thus, A At Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

24 57. Suppose the -plne foms chgeless bound between two medi of pemittiviti left nd ight whee left: ight :, if the unifom electic field on the left is E c i jk left () c i j k (whee c is constnt), then the electic field on the ight (b) ci j k c i j k Solution: E c jk E (d) ci j k D D E E E E E ci E c i j k 58. A poton moves with speed of m/ s in cicul obit in the -pln in mgnetic field tesl long the positive - diection. When n electic field of V / m is pplied long the positive -diection, the cente of the cicul obit () emins sttion (b) moves t m/ s long the negtive diection moves t m/ s long the positive diection (d) moves t m/ s long the positive diection Solution: chnge pticle will deflect in E v m / s. B -diection with 59. Conside ectngul wve guide with tnsvese dimensions m m diven with n ngul fequenc in this wve guide? 9 d / s. Which tnsvese electic () TE, TE nd TE (b) TE, TE nd TE TE, TE nd TE (d) TE, TE nd TE E B ight E is TE modes will popgte Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

25 Solution: mn m n C b 8 c. 8.7 od / sec 8 c. b c b c 8 9. od / sec 8.5 od/ sec od / sec c b,, 8.5 / sec Since 6. The electic nd mgnetic fields in the chge fee egion e given b k E, t Ee cos k t j E k B t, e ksink ti kcosk tk whee,k nd k e positive constnts. The vege eneg flow in the -diection is Ek () e k Ek (b) e k Ee Solution: k Ek e k (d) c Ee S EB k cos sin k kcos i, whee k t k k Ee Ek k S e 6. A unifom mgnetic field in the positive -diection psses though cicul wie loop of dius cm nd esistnce ling in the -plne. The field stength is educed fom tesl to 9 tesl in s. The chge tnsfeed coss n point in the wie is ppoimtel (). coulomb (b). coulomb k. coulomb (d) 5. coulomb Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

26 d dq d Solution: A dq db db dt dt R R dt R R. dq. coulomb 6. A od of length L cies totl chge Q distibuted unifoml. f this is obseved in fme moving with speed v long the od, the chge pe unit length (s mesued b the moving obseve) is () Q v L c (b) Q L v c L Q v c Q (d) v L c Q Solution: v v L c 6. A hollow metllic sphee of dius, which is kept t potentil V hs chge Q t its cente. The potentil t point outside the sphee, t distnce fom the cente, is Q V () V (b) Q V V (d) Q Solution: Let chge on conducto is Q, then V Q V Now V V 6. Conside chge Q t the oigin of - dimensionl coodinte sstem. The flu of the electic field though the cuved sufce of cone tht hs height h nd cicul bse of dius R (s shown in the figue) is Q () (b) Q hq R (d) QR h R h Q Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

27 65. Given unifom mgnetic field B Bk (whee B is constnt), possible choice fo the mgnetic vecto potentil A is () B i (b) B i B j i (d) B i j Solution: () A Bk (b) A B k A (d) A 66. A bem of unpolied light in medium with dielectic constnt is eflected fom plne intefce fomed with nothe medium of dielectic constnt. The two medi hve identicl mgnetic pemebilit. f the ngle of incidence is 6, then the eflected light () is plne polied pependicul to the plne of incidence (b) is plne polied pllel to the plne of incidence is cicull polied (d) hs the sme polition s the incident light n Solution: B tn n tn tn B 6 (hence eflected light is plne polied pependicul to plne of incidence)) B 67. A smll mgnetic needle is kept t, with its moment long the -is. Anothe smll mgnetic needle is t the point, nd is fee to otte in the - plne. n equilibium the ngle between thei mgnetic moments is such tht () tn (b) tn tn (d) tn Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

28 Solution: U m m m m sin cos sin tn so, option is coect. 68. A dipole of moment p, oscillting t fequenc, dites spheicl wves. The vecto potentil t lge distnce is m mm U cos cos 5 cos 5 o stble position eneg is minimum i.e. U mm m sin sin 5 5 To ode ik e A i p the mgnetic field B t point n is ik e () np ik e n (b) n p C C ik e ik e (d) p k n p p C Solution: Let Check p p, then B must be in diection. n p. So, coect option is (b). 69. The fequenc dependent dielectic constnt of mteil is given b A i whee A is positive constnt, is the esonnt fequenc nd is the dmping coefficient. o n electomgnetic wve of ngul fequenc, which of the following is tue? (Assume tht ). () Thee is negligible bsoption of the wve (b) The wve popgtion is highl dispesive Thee is stong bsoption of the electomgnetic wve (d) The goup velocit nd the phse velocit will hve opposite sign Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

29 Solution: When, thee is negligible bsoption of the wve. 7. ou equl chges of Q, ech e kept t the vetices of sque of side R. A pticle of mss m nd chge Q is plced in the plne of the sque t shot distnce R fom the cente. f the motion of the pticle is confined to the plne, it will undego smll oscilltions with n ngul fequenc () Q R m (b) Q R m Q R m (d) Q R m kq Q Q Solution: E E R R E E Resultnt field E, E cos R/ kq R kq R E, R R R Q R/ Q E kq R R, kq Simill; E E R R Q R/ R E E Q kq R Resultnt E, E cos R R Q Q Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

30 E kq R R, kq R R 8 kq Resultnt E R R 8 Q E Q E R R Q QE R Q mr 7. Two pllel plte cpcitos, septed b distnces nd. espectivel, hve dielectic mteil of dielectic constnt. inseted between the pltes nd e connected to btte of voltge V. The diffeence in chge on the second cpcito comped to the fist is () 66% (b) %.% (d) % A A Solution: Q CV V, Q CV V. A V Q Q. % 9% Q A V 7. The hlf spce egion nd e filled with dielectic medi of dielectic constnts nd espectivel. Thee is unifom electic field in ech pt. n the ight hlf, the electic field mkes n ngle to the intefce. The coesponding ngle in E the left hlf stisfies () sin sin tn tn (b) tn tn (d) sin sin E Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

31 Solution: tn tn E E E E E E E E E D D E E tn tn tn E tn 7. The - nd -components of sttic mgnetic field in egion e B B nd B, espectivel. Which of the following solutions fo its -component is consistent with the Mwell equtions? () B B (b) B B (d) B B B B Solution: B B, B B B B B B B B B B 7. A mgnetic field B is B in the egion nd eo elsewhee. A ectngul loop, in the -plne, of sides l (long the -diection) nd h (long the - diection) is inseted into the egion fom the egion t constnt velocit v v the following vlues of l nd h will genete the lgest EM? () l 8, h (b) l, h 6 l 6, h (d) l, h. Which of Solution: m Bh d dt m Bvh h l v h Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

32 75. Conside sphee S of dius R which cies unifom chge of densit. A smlle sphee S of dius R is cut out nd emoved fom it. The centes of the two sphees e septed b the vecto b nr, s shown in the figue. The electic field t S b S P point P inside S is () R n R n (b) R n 6 (d) R Solution: Electic field t P due to S is E S S Electic field t P due to S (ssume ) is E Thus E E E b P ; b b R E b n b The vlue of the electic nd mgnetic fields in pticul efeence fme (in Gussin units) e E nd B espectivel. An inetil obseve moving with espect to this fme mesues the mgnitude of the electic field to be E. The mgnitude of the mgnetic field B mesued b him is () 5 (b) 9 (d) Solution: B E B E B constnt B 77. A loop of dius, cing cuent, is plced in unifom mgnetic field B. f the noml to the loop is denoted b n, the foce nd the toque T on the loop e () nd T n B B nd T n B (b) B (d) ndt B Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

33 Solution: n unifom field Toque T mb n B 78. A wveguide hs sque coss-section of side. o the TM modes of wve vecto k, the tnsvese electomgnetic modes e obtined in tems of function, obes the eqution c k, with the bound condition mode is given b which,,. The fequenc of the lowest () c k (b) c k c k (d) c k Solution: ck ck mn mn m n mn c b c c c c k Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

34 79. A sceen hs two slits, ech of width w with thei centes t distnce w pt. t is illuminted b monochomtic plne wve tvelling long the -is. The intensit of the intefeence ptten, mesued on distnt sceen, t n ngle n to the -is is w () eo fo n,,... (b) mimum fo n,,... 5 mimum fo n,,... (d) eo fo n onl w w w Solution: mimum fo n nd eo fo n,, The electic field of n electomgnetic wve is E, t EcosktiEsin kt j whee nd k e positive constnts. This epesents () linel polised wve tvelling in the positive -diection (b) cicull polised wve tvelling in the negtive -diection n ellipticll polised wve tvelling in the negtive -diection (d) n unpolised wve tvelling in the positive -diection Solution: Amplitude long î is E nd long ĵ is E. So esultnt wve is ellipticll polised Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

35 8. A conducting cicul disc of dius nd esistivit ottes with n ngul velocit in mgnetic field B pependicul to it. A voltmete is connected s shown in the figue below. Assuming its intenl esistnce to be infinite, the eding on the voltmete () depends on, B, nd (b) depends on, B nd but not on B is eo becuse the flu though the loop is not chnging (d) is eo becuse cuent the flows in the diection of B V Solution: oce epeienced b chge is q v B nd v 8. The chge pe unit length of cicul wie of dius in the -plne, with its cente t the oigin, is cos, whee is constnt nd the ngle is mesued fom the positive -is. The electic field t the cente of the cicle is () E i (b) E i E (d) E k Solution: At centeo, diection of field is. So best option is () o Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

36 8. A pi of pllel glss pltes septed b distnce d is illuminted b white light s shown in the figue below. Also shown in the gph of the intensit of the eflected light s function of the wvelength ecoded b spectomete. ptill eflecting mio d spectomete incident white light i gp glss pltes Assuming tht the intefeence tkes plce onl between light eflected b the bottom sufce of the top plte nd the top sufce of bottom plte, the distnce d is closest to () m (b) m 6 m (d) m ntensit m Solution: o constuctive intefeence of eflected light, dcos n. 95 m ist mim occus t 95 m, nd n. Thus, d m 8. Suppose tht fee chges e pesent in mteil of dielectic constnt nd esistivit m. Using Ohm s lw nd the eqution of continuit fo chge, the time equied fo the chge densit inside the mteil to dec b e is closest to () 6 S (b) 6 S S (d) S t f f e 8.8 ;, sec, 85. A pticle with chge q moves with unifom ngul velocit in cicul obit of Solution: t dius in the - plne, ound fied chge q, which is t the cente of the obit t,,. Let the intensit of dition t the point,, R be nd t R,, be The tio fo R, is Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

37 Solution: R R A pllel plte cpcito is fomed b two cicul conducting pltes of dius septed b distnce d, whee d. t is being slowl chged b cuent tht is nel constnt. At n instnt when the cuent is, the mgnetic induction between the pltes t distnce fom the cente of the plte, is () (b) (d) Solution: B B t 87. Two unifoml chged insulting solid sphees A nd B, both of dius, c totl chges Q nd Q, espectivel. The sphees e plced touching ech othe s shown P in the figue. f the potentil t the cente of the sphee A is V A nd tht t the cente of B is V B then the diffeence VA VB is A B () Q (b) Q Q (d) Q Solution: V V V B A A Q Q Q 8 Q Q Q 8 V B Q Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

38 88. Two long hollow co-il conducting clindes of dii R nd R R in vcuum s shown in the figue below. R e plced R R The inne clinde cies chge pe unit length nd the oute clinde cies chge pe unit length. The electosttic eneg pe unit length of this sstem is () ln R / R (b) R / R ln R / R (d) ln R / R Solution: R, E ; R R, E R, E R W E d ld ll spce R W l R R d ln R R 89. A set of N concentic cicul loops of wie, ech cing sted cuent in the sme diection, is nged in plne. The dius of the fist loop is nd the dius of the th n loop is given b n nn. The mgnitude B of the mgnetic field t the cente of the cicles in the limit N, is () e / e (b) e /8 / (d) e / Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

39 Solution: B... n n n n... B N B n n n e e e n n n n n n n n N lim e B e N nl n 9. An electomgnetic wve (of wvelength in fee spce) tvels though n bsobing medium with dielectic pemittivit given b R i whee. f the skin depth is, the tio of the mplitude of electic field E to tht of the mgnetic field B, in the medium (in ohms) is () (b) 77 (d) R Solution: d, R / Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

40 K E B k / K / c / c E c 8 8 H 7 8 E H 9. t The vecto potentil A ke (whee nd k e constnts) coesponding to n t electomgnetic field is chnged to A ke. This will be guge tnsfomtion if the coesponding chnge in the scl potentil is t () k e t (b) k e t k e (d) k e t Solution: Guge Tnsfomtion A A, t ' t A A ke ke t ke t ' ke t t t 9. An electon is deceleted t constnt te stting fom n initil velocit u (whee u c ) to u / duing which it tvels distnce s. The mount of eneg lost to dition is () eu mc s (b) eu 6 mc s eu 8 mcs eu (d) 6 mcs Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

41 Solution: Totl powe dited q P 6 c Totl eneg dited in time t is u u vut ut t E c eu e e u E P t t 6c 6c E E ction of initil KE.. lost due to dition mu mu eu e mu c 6mcu u u u u u u s ut t u 8 8 8s e u e 6mcu 8s 6mcs 9. The figue below descibes the ngement of slits nd sceens in Young s double slit epeiment. The width of the slit in S is nd the slits in S e of negligible width. S S b sceen d f the wvelength of the light is, the vlue of d fo which the sceen would be dk is () b (b) b b (d) b Solution: f the pth diffeence Op Op Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

42 The minim of the intefeence ptten poduced b O will fll on the mim poduced b O Now / b b OP d d d P / b b OP d d d b OP OP db, d b b Thus d d 9. A constnt cuent is flowing in piece of wie tht is bent into loop s shown in the figue. b / / O O d P b b b O b b The mgnitude of the mgnetic field t the point O is () ln 5 b 5 (b) 5 b (d) 5b d Solution: B sin sin Mgnetic field due to left nd ight segment of B 5 ield due to uppe segment of 5 5 d Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /

43 Net field B 5 5 B (inwd) 5 simill, B b b 5 (outwd) Net field B B Bb 5 b 95. The chge distibution inside mteil of conductivit nd pemittivit t initil time t is,, constnt. At subsequent times t, () ep t t (b) ep is given b (d) t cosh t ep f f Solution: J f E,. E,. J f E f f. E f t t ep f t f ep f t t Admission ee : TNSET Coching Clss, Rsipum, Nmkkl D.t. Phone : 8755 /