ELECTROMAGNETIC THEORY SOLUTIONS GATE- Q. An insulating sphee of adius a aies a hage density a os ; a. The leading ode tem fo the eleti field at a distane d, fa away fom the hage distibution, is popotional to (A) d - (B) d - (C) d - (D) d -4 Ans: (b) V d osd V, a zeo V E I st tem, d a os sinddd. Q. Two magneti dipoles of magnitude m eah ae plaed in a plane as shown The enegy of inteation is given by m (A) Zeo (B) 4d m (C) d Ans: (d) U 4 m m m m Sine m m m m, m (D) 8d U mos 45 mos 45 m U. 8 d 4d m o 45 d o 45 m fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om
Statement fo Linked Answe Questions and 4: Conside the popagation of eletomagneti waves in a linea, homogenous and isotopi mateial medium with eleti pemittivity ε and magneti pemeability μ. Q. Fo a plane wave of angula fequeny ω and popagation veto k popagating in the medium Mawell s equations edue to (A) (B) (C) (D) k E ; k H ; k E H; k H E k E ; k H ; k E H; k H E k E ; k H ; k E H; k H E k E ; k H ; k E H; k H E Ans: (d) Q4. If ε and μ assume negative values in a etain fequeny ange, then the dietions of the popagation veto k and the Poynting veto S in that fequeny ange ae elated as (A) k and S ae paallel (B) k and S ae anti-paallel (C) k and S ae pependiula to eah othe (D) k and S makes an angle that depends on the magnitude of ε and μ fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om
Q5. Conside a onduting loop of adius a and total loop esistane R plaed in a egion with a magneti field B theeby enlosing a flu. The loop is onneted to an eletoni iuit as shown, the apaito being initially unhaged C V out If the loop is pulled out of the egion of the magneti field at a onstant speed u, the final output voltage V out is independent of (A) (B) u (C) R (D) C fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om
GATE- Q6. If a foe F is deivable fom a potential funtion V(), whee is the distane fom the oigin of the oodinate system, it follows that (A) F (B) F (C) V (D) V Q7. Tow hages q and q ae plaed along the -ais in font of a gounded, infinite onduting plane, as shown in the figue. They ae loated espetively at a distane of.5 m and.5 m fom the plane. The foe ating on the hage q is (A) 4 7q (B) 4 q.5m q q.5m (C) q 4 (D) 4 q Using method of Images we an daw equivalent figue as shown below: q q.5m.5m.5m q q.5m q q q q q 7q 7q F 4 8 4 Q8. A unifom sufae uent is flowing in the positive y-dietion ove an infinite sheet lying in -y plane. The dietion of the magneti field is (A) along î fo z > and along (B) along k fo z > and along (C) along (D) along î fo z < k fo z < î fo z > and along î fo z < k fo z > and along k fo z < fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om 4
Q9. A magneti dipole of dipole moment m is plaed in a non-unifom magneti field B. If the position veto of the dipole is, the toque ating on the dipole about the oigin is (A) m B (B) m B (C) m B (D) m B m B Ans: () Q. A spheial onduto of adius a is plaed in a unifom eleti field E E k. The potential at a point P(, θ) fo > a, is given by Ea Φ(, θ) = onstant E os os whee is the distane of P fom the ente O of the sphee and θ is the angle OP makes with the z-ais P The hage density on the sphee at θ = o is (A) / (B) / E E (C) / (D)) / E E O k V a E Ea os os a. E os E os E os E os E Q. Whih of the following epessions fo a veto potential A DOES NOT epesent a unifom magneti field of magnitude B along the z-dietion? (A) A, B, (B) A B y,, B B y B (C) A,, (D) y B A,, Ans: () B A fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om 5
Statement fo Linked Questions and : A plane eletomagneti wave has the magneti field given by whee k is the wave numbe and dietions espetively. B k, y, z, t B sin y t k i, j and k ae the Catesian unit vetos in, y and z Q. The eleti field E y, z, t, oesponding to the above wave is given by k (A) i j k B sin y t (B) i j B sin y t k (C) B sin y t i (D) B sin y t j E k k y y k B B sin E B sin y k k t y k tz k Q. The aveage Poynting veto is given by B i j (A) Ans: (d) B i j B i j (B) (C) B B y B S k y B i j (D) fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om 6
GATE- Q4. The spae-time dependene of the eleti field of a linealy polaized light in fee spae is given by E os t kz whee E, ω and k ae the amplitude, the angula fequeny and the waveveto, espetively. The time aveage enegy density assoiated with the eleti field is (a) E (b) E () 4 E (d) E u E E E os 4 wt kz u E E Q5. A plane eletomagneti wave taveling in fee spae is inident nomally on a glass plate of efative inde /. If thee is no absoption by the glass, its efletivity is (a) 4% (b) 6% () % (d) 5% n n R n n / / 4 4 5.4 o 4% Q6. The eleti and the magneti field E z, t and B z, t, espetively oesponding to the sala potential z, t and veto potential Az, t i tz ae (a) E iz and B -ĵt (b) E iz and B ĵt () E iz and B -ĵt (d) E iz and B -ĵt Ans: (d) A A E iz, t t B A j t. fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om 7
Q7. A plane polaized eletomagneti wave in fee spae at time t= is given E, y ep j i 6 8z B, z, t is given by by. The magneti field (a) B, z, t 6k 8 i ep i6 8z t (b) B, z, t 6k 8 i ep i6 8z t () B, z, t 6k 8 i ep i6 8z t (d) B, z, t 6k 8 i ep i6 8z t B B k i k k E E 8 6 ep j i k. t k 6k 8 i ep i6 8z t,. Q8. Two infinitely etended homogeneous isotopi dieleti media (medium-and medium- with dieleti onstant and 5, espetively) meet at the z = plane as shown in the figue. A unifom eleti field eists eveywhee. Fo z, the eleti field is given by E i j 5k. The intefae sepaating the two media is hage fee. The eleti displaement veto in the medium- is given by (a) D i j k 5 (b) D i j k 5 () D i j k 4 6 (d) D i j k 4 6 medium - medium - z = fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om 8
Ans: (b) E E E i j 5 and f D D E E k k E 5 D 5 E i j k. i j k fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om 9
GATE- Q9. At a sufae uent, whih one of the magnetostati bounday ondition is NOT CORRECT? (a) Nomal omponent of the magneti field is ontinuous. (b) Nomal omponent of the magneti veto potential is ontinuous. () Tangential omponent of the magneti veto potential is ontinuous. (d) Tangential omponent of the magneti veto potential is not ontinuous. Ans: (d) Q. Intefeene finges ae seen at an obsevation plane z, by the supeposition of two plane waves A i k ep t and A i k ep t, whee A and A ae eal amplitudes. The ondition fo intefeene maimum is (a) k k m (b) k k m () k k m (d) k k m Ans: (b) Q. Fo a sala funtion satisfying the Laplae equation, has (a) zeo ul and non-zeo divegene (b) non-zeo ul and zeo divegene () zeo ul and zeo divegene (d) non-zeo ul and non-zeo divegene Ans: (). and. fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om
Q. A iulaly polaized monohomati plane wave is inident on a dieleti intefae at Bewaste angle. Whih one of the following statements is oet? (a) The efleted light is plane polaized in the plane of inidene and the tansmitted light is iulaly polaized. (b) The efleted light is plane polaized pependiula to the plane of inidene and the tansmitted light is plane polaized in the plane of inidene. () The efleted light is plane polaized pependiula to the plane of inidene and the tansmitted light is elliptially polaized. (d) Thee will be no efleted light and the tansmitted light is iulaly polaized. Ans: () Q. A hage distibution has the hage density given by Q Fo this hage distibution the eleti field at,, Q (a) 9 Q (b) 4 Q () 4 Ans: ' ' ' a a a Potential V d d d... 4 a a a Fist tem, total hage Q T d Q d Q d Q Q Seond tem, dipole moment p. Q (d) 6 d Q d Q d Q Q Q Q V 4 V E 4Q 4 4Q 4 Q 8 fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om
Q4. A monohomati plane wave at oblique inidene undegoes efletion at a dieleti intefae. If k, k and n ae the unit vetos in the dietions of inident wave, i efleted wave and the nomal to the sufae espetively, whih one of the following epessions is oet? (a) k i k n (b) k i k n () k n k (d) k n k i Ans: () i Q5. In a onstant magneti field of.6 Tesla along the z dietion, find the value of the path integal A dl in the units of (Tesla m ) on a squae loop of side length / metes. The nomal to the loop makes an angle of figue. The answe should be up to two deimal plaes. 6 to the z-ais, as shown in the o 6 ẑ Ans: A dl S A. da B. da BA os 6.6.5T. m S fiziks, H.No., G.F, Jia Saai, Nea IIT, Hauz Khas, New Delhi-6 Phone: -6865455/+9-98745498 8-B/6, Jia Saai, Nea IIT Hauz Khas, New Delhi-6 Email: fiziks.physis@gmail.om