where k=constant of proportionality , are two point charges (C) r = distance between the charges (m)

Transcription

1 DMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINNERING EC6403 ELECTRO MAGNETIC FIELDS UNIT-I: STATIC ELECTRIC FIELD PART-A (2 Marks) 1. Conver he given recangular coordinae A(x=2, y=3, z=1) ino he corresponding cylindrical coordinae. (N-10) The Caresian (recangular) co-ordinaes (x, y, z) can be convered ino cylindrical coordinaes (r,,z). Given: x = 2, y = 3, z = 1 = Wha is an elecric dipole? Wrie down he poenial due o an elecric dipole. (N-10), (M-12) Dipole or elecric dipole is defined as wo equal and opposie poin charges are separaed by a very small disance. Poenial due o an elecric dipole 3. Sae Divergence heorem. (M-11),(N-12), (N-09), (M-09), [M/J 07], (M-13) The volume inegral of he divergence of a vecor field over a volume is equal o he surface inegral of he normal componen of his vecor over he surface bounding he volume. 4. Wha is he conservaive field? (N-10) The sign indicaes inegral over a closed pah. Such a field having propery of associaed wih i is called conservaive field or lamellar field.

2 5. Sae Coulomb s Law. (M-12), (N-12), (N-09) Coulomb s law saes ha he force beween wo very small charged objecs separaed by a large disance compared o heir size is proporional o he charge on each objec and inversely proporional o he square of he disance beween hem. 6. Wha is he physical significance of div D? (M-12) The Divergence of a vecor flux densiy is elecric flux per uni volume leaving a small volume. This is equal o he volume charge densiy. 7. Define -Sokes Theorem (N-12), (M-12) The line inegral of a vecor around a closed pah is equal o he surface inegral of he normal componen of is curl over any closed surface. 8. Wha are he feaures of Coulomb s law? (M-11) Coulomb s law saes ha here exiss a force beween charged bodies and i is: 1) Proporional o he produc of he wo charges, 2) Inversely proporional o he disance beween he charges. 3) The force also depends on he medium in which he charges are closed. Mahemaically, coulomb s law is given by, where k=consan of proporionaliy, are wo poin charges (C) r = disance beween he charges (m)

3 9. A vecor field is given by he expression in spherical coordinaes. Deermine F in Caresian form a a poin, x = 1, y = 1 & z = 1 uni. Soluion: (M-09) In general (in spherical coordinaes) In his example, he field varies only as a funcion of he radial disance of he poin from he origin. The poin assumed o lie on a sphere wih radius R. The componens and are, herefore nonexisen. A he poin x = 1, y = 1, z = 1 Hence, a (1, 1, 1), 10. Define Elecric Dipole (N-10) Dipole or elecric dipole is defined as wo equal and opposie poin charges are separaed by a very small disance. 11. Wha is elecric flux densiy? Elecric flux densiy or displacemen densiy is defined as he elecric flux per uni area.

4 12. Wrie he relaion beween poenial and elecric field. The relaion beween poenial and elecric field is given by: 13. Wha is elecric field inensiy? Elecric field inensiy is defined as he elecric force per uni posiive charge. I is denoed by E. 14. Sae Gauss s law. Gauss s law sae ha an elecric flux passing hrough any closed surface is equal o he oal charge enclosed by ha surface. 15. Define Elecric Poenial and Elecric Field (M-13) Elecric poenial: poenial a any poin as he work done in moving a uni posiion charge from infiniy o ha poin in an elecric field. Elecric field: Elecric field inensiy is defined as he elecric force per uni posiive charge. I is denoed by E.

5 Par B (16 Marks) 1. (i) A poin charge locaed a (1, 1, 3) m experiences a force. Due o poin charge a (3, 3, 2) m. Find he charge. (10) (ii) Given ha in spherical coordinaes, evaluae boh sides of divergence heorem for volume enclosed by r = 4 m and. (6) (M-12) 2. (i) Derive he expression for poenial due an elecric dipole a any poin P. Also find elecric field inensiy a he same poin. (10) (ii) Two poin charges, 1.5nC a (0, 0, 0.1) and 1.5nC a (0, 0, 0.1), are in free space. Trea wo charges as a dipole a he origin and find poenial a P (0.3, 0, 0.4). (6) (M-12) 3. (i) Find he elecric field inensiy a a poin P locaed a(0, 0, h)m due o charge of surface charge densiy uniformly disribued over he circular disc. (10) (ii) Deermine he divergence and curl of he given field a (1, 1, 0.2) and hence sae he naure of he field. (6) (N-12) 4. (i) Poin charges Q and Q are locaed a (0, 0, d 2) and (0, 0, d 2). Show ha he poenial a a poin ) is inversely proporional o nohing ha. (8) (ii) Given a field, find he poenial difference beween A ( 7, 2, 1) and B (4, 1, 2). (8) (N-12) 5. (i) Assume a sraigh line charge exending along he z axis in a cylindrical coordinae sysem from.deermine he elecric field inensiy a every poin resuling from a uniform line charge densiy. (8) (ii) Consider an infinie uniform line charge of parallel o z axis a x = 1, y = 6. Find he elecric field inensiy a he poin P (0, 0, 5) in free space. (8) (N-11) 6. (i) The flux densiy wihin he cylindrical volume bounded by r = 2m, z = 0 and z = 5m is given by.wha is he oal ouward flux crossing he surface of he cylinder. (8) (ii) Sae and prove Gauss s law for he elecric field. Also find he differenial form of Gauss law. (8) (N-11)

6 7. (i) Given poin P ( 1, 4, 3) and vecor express P and A in Cylindrical and Spherical coordinaes. Evaluae A a P in he Caresian and Spherical sysems. (8) (ii) Deermine D a (2, 0, 3) if here is a poin charge a (3, 0, 0) and a line charge along he y-axis. (8) (M-11) 8. (i) Deermine sokes heorem. (8) (ii) Show ha in Caresian coordinaes for any vecor A. (8) (M-11) 9. (i) Given he wo poins and.find he spherical Co-ordinaes of A and Caresian Co-ordinaes of B. (8) (ii) Find curl, if (8) (M-10) 10. (i) A circular disc of radius a m charged uniformly wih a charge of. Find he elecric field inensiy a a poin h meer from he disc along is axis. (8) (ii) If vols, find and a P(6, 2.5, 3). (8) (M-10)

7 UNIT- II: CONDUCTORS AND DIELECTRICS PART A (2 Marks) 1. Sae he Laplace s equaions in Caresian, cylindrical and spherical coordinaes. (N-09) The laplace s equaions in 1) Caresian form: 2) Cylindrical form: 3) Spherical form: 2. Sae ohms law a a poin. (M-13) Poin form of ohm s law saes ha he field srengh wihin a conducor is proporional o he curren densiy. Where is conduciviy of he maerial 3. Wrie he Poisson s and Laplace s equaion. (M-09) 1) Passion Equaion Where 2) Laplace equaion = Volume charge densiy ε = Permiiviy of he medium = Laplacian operaor

8 4. Classify he magneic maerials. (N-08) Magneic maerials can be classified ino hree groups according o heir behavior. There are 1) Diamagneic 2) Paramagneic 3) Ferromagneic 5. Define he erm capaciance beween wo conducors or capacior. (N-08) The capaciance of wo conducing planes is defined as he raio of magneic of charge on eiher of he conducor o he poenial difference beween conducors. I is given by The uni of capaciance is Coulombs/vol or Farad. 6. Find he capaciance of a parallel plae capacior having sored energy of wih a volage beween he plaes 0f 5V. Soluion: Given: Energy sored in a capacior Volage beween he plae V = 5V Capaciance of a parallel plae (N-08) 7. Wha are he boundary condiions beween wo dielecric media? (N-07) 1) The angenial componen of elecric field E is coninuous a he surface. Tha is E is he same jus ouside he surface as i is jus inside he surface. 2) The normal componen of elecric flux densiy is coninuous if here is no surface charge densiy. Oherwise D is disconinuous by an amoun equal o he surface charge densiy.

9 8. Wha is polarizaion? (N-07) Polarizaion of a uniform plane wave refers o he ime varying naural of he elecric field vecor a some fixed poin in space or Polarizaion is defined as dipole momen per uni volume. 9. Deermine he capaciance of he parallel plae capaciance composed of in foil shees, 25 cm square for plaes separaed hrough a glass dielecric 0.5 cm hick wih relaive permiiviy 6. (N-07), (M-13) Soluion: Subsiue in he above funcion 10. Wha is Displacemen curren densiy? (N-09) Displacemen curren is nohing bu he curren flow hrough he capacior. Displacemen curren densiy is given by 11. Wrie he coninuiy equaion. (N-08) The coninuiy equaion is (Inegral form) (Differenial form)

10 12. Wha is mean by Circular Polarizaion? If x and y componen of elecric field and have equal ampliude and phase difference, he locus of he resulan elecric field E is a circle and he wave is said o be circularly polarized. 13. Differeniae conducor and Dielecric. Conducor: If he valance band merges smoohly ino a conducion band, hen addiional kineic energy may be given o he valance elecrons by an exernal field, resuling in an elecro flow. The solid is called a meallic conducor. Dielecric: If he forbidden energy gap beween valence band and conducion band of a maerial is high, i requires large applied energy o conduc. The maerial is called a dielecric.

11 PART B (16 Marks) 1. Derive he boundary condiions of he normal and angenial componens of elecric field a he Iner face of wo media wih differen dielecrics. (16) (N-08), (M-14), (N-14) 2. Derive an expression for he energy sored and energy densiy in a capacior. (N-14), (M-09) 3. Drive an expression for energy sored and energy densiy in an Elecrosaic field (16) (N-14) 4. Derive an expression for he capaciance of wo wire ransmission line. (8) 5. Derive an expression for capaciance of co-axial cable. (8) (M-09), (N-06) 6. Find he expression for he cylindrical capaciance using Laplace equaion. (16) (N-14) 7. Derive he boundary condiions of he normal and angenial componens of magneic field a he iner face of wo media wih differen dielecrics. (16) (N-14) 8. Derive he expression for co-efficien of coupling. (8) 9. Prove Laplace s and Poisson s equaions. Also using he concep of magneic vecor poenial, derive Bio Savar s law and amperes law? (M-10), (M-12) 10. Derive he expression for co-efficien of coupling. (8) Also using he concep of magneic vecor poenial, derive Bio Savar s law and amperes law? (M-10), (M-12) 11. Derive an expression for he capaciance of a spherical capacior wih conducing shells of radius a and b. (M-09), (N-06) 12. Derive he expression for he coninuiy equaion of curren in differenial form and also derive he expression for inducance of a solenoid wih N urns and l mere lengh carrying a curren of I amperes. (N-11) 13. Derive he expression for he inducance of a oroidal coil (solenoid) wih N urns, carrying curren I and he radius of he oroid R. Also considering a oroidal coil derive an expression for energy densiy. (16) (N-12), (M-12), (M-09), (N-10) 14. A solenoid has an inducance of 20 mh If he lengh of he solenoid is increased by wo imes and he radius is decreased o half of is original value, find he new inducance (M-09) 15. Derive he expression for poenial energy sored in he sysem of n-poin charges. (16) (D - 09) 16. Derive an expression for Poisson and Laplace equaions and also Derive an expression for he inducance of solenoid (M-10), (N-10), (M-14) 17. Derive he boundary condiions a an inerface beween wo magneic Medias. (M-10), (M-09), (N-06) 18. A small loop wire lays a disance z above he cener of a large loop. The planes of he wo loops are parallel, and perpendicular o he common axis. Suppose curren I flows in he big loop. Find he flux hrough he lile loop. Find he muual inducance. (16) (M-14)

12 19. Solve he Laplace equaion for he poenial field in he homogenous region beween he wo concenric conducing spheres wih radius a and b and v=0 a r=b and v=vo a r=a; Find he capaciance beween he wo concenric spheres. (8) (M-11) 20. A meallic sphere of radius 10cm has a surface charge densiy of 10nc. Calculae he energy sored in he sysem. And also sae and explain he elecric boundary condiions beween wo dielecrics wih permiiviy s e1 and e2 (16) (N-11) 21. Derive he expression for he energy of a poin charge disribuion. Three poin charges -1nc, 4nc, 3nc are locaed a (0, 0, and 0) (0, 0, and 1) (1, 0, and 0) respecively, Find he energy in he sysem. (M-10) 22. Find he permeabiliy of he maerial whose magneic suscepibiliy is 49 also find, if he inner and ouer conducors of a co axial cable are having radii a and b respecively If he inner conducor is carrying curren I and ouer conducor is carrying he reurn curren I in he opposie direcion. Derive he expressions for he inernal and exernal inducance (16) (M-11)

13 UNIT- III: STATIC MAGNETIC FIELD PART A (2 Marks) 1. Wrie he Lorenz's force equaion for a moving charge. (N-10),(N-12) The force on a moving charge paricle arising from combined elecric and magneic fields is obained easily by superposiion This equaion is known as he Lorenz force equaion. 2. Find he magneic field inensiy a a poin P(0.01, 0, 0)m, if he curren a coaxial cable is 6A, which is along he z axis and a = 3mm, b = 9mm & c = 11mm. (N-10) Soln: Given poin is P (0.01, 0, 0) m = a = 3mm; b = 9mm & c = 11mm For he condiion, 3. Sae Ampere's circuial law. (N-12),(N-09),(N-09) Ampere s circuial law saes ha he line inegral of magneic field inensiy around a closed pah is exacly equal o he direc curren enclosed by ha pah. The mahemaical represenaion is 4. A loop wih magneic dipole momen B 0.2 a 0.4 a Wb / m x Soln: Given magneic dipole momen Magneic field Torque is z Am 3 a z 2, lies in a uniform magneic field. Calculae he orque. (M-11) T

14 5. Lis he applicaions of Ampere's circuial law. (N-10),(M-11) Ampere's circuial law is used 1) o deermine magneic field due o a sraigh conducor carrying curren. 2) o deermine magneic field due o a solenoid carrying curren. and 3) o deermine magneic field due o a curren in a oroid. 6. Disinguish beween diamagneic, paramagneic and ferromagneic maerials. (M-12) Diamagneic maerial 1) The magneic momen, inensiy of magneizaion and magneic suscepibiliy are all negaive while magneic permeabiliy has value less han1 2) Repelled by a srong magne 3) The magneic suscepibiliy is independen of emperaure Paramagneic maerial 1) The magneic momen, inensiy of magneizaion and magneic suscepibiliy are all posiive while magneic permeabiliy has value slighly greaer han1 2) Araced by a srong magne 3) The magneic suscepibiliy decreases wih rise of emperaure Ferromagneic maerial 1) The magneic momen, inensiy of magneizaion and magneic suscepibiliy are all posiive and quie large and magneic permeabiliy is of he order of hundreds and housands. 2) The magneic suscepibiliy decreases wih rise of emperaure 7. Define Magneic Flux Densiy (N-12) The oal magneic lines of force i.e. magneic flux crossing a uni area in a plane a righ angles o he direcion of flux is called magneic flux densiy. I is denoed as Uni Wb/m Sae Bio-Savar law. (N-09),(M-09),(M-13) The BioSavar law saes ha, The magneic field inensiy produced a a poin p due o a differenial curren elemen IdL is 1) Proporional o he produc of he curren I and differenial lengh dl 2) The sine of he angle beween he elemen and he line joining poin p o he elemen. 3) And inversely proporional o he square of he disance R beween poin p and he elemen

15 9. Wha is solenoid? (N-08) Solenoid is a cylindrically shaped coil consising of a large number of closely spaced urns of insulaed wire wound usually on a non magneic frame. 10. Menion he imporance of Lorenz s force equaion. [M/J 07] The Lorenz s force equaion find is imporance in 1) Deermining elecron orbis in he magneron 2) Proon pahs in he cycloron 3) Plasma characerisics in a magneohydrodynamic (MHD) generaor 4) Charged paricle moion in combined elecric and magneic fields. 11. A long conducor wih curren 5A is in coinciden wih posiive z direcion. If Find he force per uni lengh. [A/M 08] Soln: Given Curren I=5A Lengh L=1m Magneic field Force is

16 Par B (16 Marks) 1. (i) Find he magneic field inensiy due o a finie wire carrying a curren I and hence deduce an expression for magneic field inensiy a he cenre of a square loop. (8) (ii) Derive he magneic field inensiy in he differen regions of co-axial cable by applying Ampere s circuial law. (8) (M-12) 2. (i) Obain he expression for scalar and vecor magneic poenial. (8) (ii) The vecor magneic poenial in a cerain region of free space. 1. Show ha = 0. (3) 2. Find he magneic flux densiy and he magneic field inensiy a P (2, 1, 3). (5) (M-12) 3. (i) Derive an expression for magneic field inensiy due o a linear conducor of infinie lengh carrying curren I a a disance poin P. Assume R o be he disance beween conducor and poin P. Use Bio Savar s law. (8) (ii) Derive an expression for magneic field inensiy on he axis of a circular loop of radius a carrying curren I. (8)(N-12) 4. (i) A a poin P(x, y, z) he componens of vecor magneic poenial are given as, and. Deermine he magneic flux densiy a he poin P. (8) (ii) Given he magneic flux densiy, find he oal magneic flux crossing he srip defined by. (8)(N-12) 5. (i) Find he force on a wire carrying a curren of 2 ma placed in he xy plane bounded by x = 1, x = 3, y = 0 and y = 2 as shown in figure. The magneic field is due o a long conducor, locaed in y-axis, carrying a curren of 15A as shown. (8) (ii) A differenial curren elemen is locaed a he origin in free space. Obain he expression

17 for vecor magneic poenial due o he curren elemen and hence find he magneic field inensiy a he poin. (8)(N-11) 6. (i) Find he maximum orque on an 85 urns, recangular coil wih dimension ( )m, carrying a curren of 5 Amps in a field B = 6.5T. (8) (ii) A circular loop locaed on carries a direc curren of 7A along. Find he magneic field inensiy a (0, 0, 5). (4) (iii) Using Ampere s circuial law deermine he magneic field inensiy due o a infinie long wire carrying a curren I. (4) (N-11) 7. Two equal poin charges are placed on a line a disance a apar, This line joining he charges is parallel o he surface of an infinie conducing region which is a zero poenial. The specific line is a a disance from he surface of he conducing region. Show ha he force beween he charges is. Wha happens o he force when sign of one he charges is reversed. (16) (M-11) 8. Conducing spherical shells wih radii a = 8cm and b = 20cm are mainained a a poenial difference of 100 V such ha V(r = b) = 0 and V= (r = a) =70V. Deermine V and E in he region beween he shells. If in he region deermine he oal charge induced on shells and he capaciance of he capacior. (16) (M-11) 9. (i) Sae and explain Ampere s circuial law. (8) (ii) Find an expression for a any poin due o a long, sraigh conducor carrying I amperes. (8) (M-10) 10. A circular loop locaed on carries a direc curren of 10A along. Deermine H a (0, 0, 4) and (0, 0, 4). (16) (N-09)

18 UNIT IV: MAGNETIC FORCES AND MATERIALS PART A (2 Marks) 1. Wrie down he expression for he orque experienced by a curren carrying loop siuaed in a magneic field. (M-12) The expression for he orque experienced by a curren carrying loop in a magneic field is given by where I is he curren S is he area of curren carrying loop B is he magneic field 2. Wha is mean by magneic momen? (N-12)(N-09)(M-09) The Magneic momen of a curren loop is defined as he produc of curren hrough he loop and he area of he loop, direced normal o he curren loop. 3. Wha is mean by magneic field inensiy? (M-12) Magneic field inensiy a any poin in he magneic field is defined as he force experienced by a uni norh pole of one Weber srengh, when placed a ha poin. Uni: N/Wb (or) AT /m. I is denoed as. 4. Wha is Torque? (N-10) The Momen of a force or orque abou a specified poin is defined as he vecor produc of he momen arm and he force. I is measured in Nm. 5. Define muual inducance. (M-09), (N-08) The muual inducance beween wo coils is defined as he raio of induced magneic flux linkage in one coil o he curren hrough in oher coil. where = is number of urns in coil 2 =Magneic flux links in coil 2 = Curren hrough coil 1

19 6. Wrie he force on a curren elemen. The force on a curren elemen Idl is given by df = I x B dl = BI dl sinθ Newon 7. Define magneic vecor poenial I is defined as ha quaniy whose curl gives he magneic flux densiy. where A is he magneic vecor poenial A 4 V J dr r Web / m 8. Define self inducance The self inducion of a coil is defined as he raio of oal magneic flux linkage in he circui o he curren hrough he coil. where is magneic flux N is number of urns of coil i is he curren. 9. Define muual inducance The muual inducance beween wo coils is defined as he raio of induced magneic flux linkage in one coil o he curren hrough in oher coil. where N2 is number of urns in coil 2 12 is magneic flux links in coil 2 i1 is he curren hrough coil 1

20 10. Wha will be effecive inducance, if wo inducors are conneced in (a) series and(b) parallel? (a) For series L = L1 + L2 2 M + sign for aiding L L 1 2 M 2 (b) For Parallel L = L 1 L 2 2 M - sign for opposiion 11. Wrie he expression for inducance of a solenoid. where L o N N is number of urns A is area of cross-secion l is lengh of solenoid is free space permeabiliy l 2 A 12. Wrie he expression for inducance of a oroid. where L o 2 N N is number of urns r is radius of he coil R is radius of oroid is free space permeabiliy 2 R A N o 2 = 2 R r Wrie he expression for inducance per uni lengh of a co-axial ransmission line. Where L = a is he radius of inner conducor b is he radius of ouer conducor. 2 o ln b a H/m. 14. Wha is he muual inducance of wo inducively ighly coupled coils wih self inducance of 25mH and 100mH. L1 = 25 mh L2 = 100 mh M = K L L 1 2 = X = 50 mh

21 PART B (16 Marks) 1. Wrie down he Poisson s and Laplace s equaions. Sae heir significance in elecrosaic problems. (4) 2. Two parallel conducing plaes are separaed by disance d apar and filled wih dielecric medium having as relaive permiiviy. Using Laplace s equaion, derive an expression for capaciance per uni lengh of parallel plae capacior, if i is conneced o a DC source supplying V vols. (12) 3. Derive he expression for inducance of a oroidal coil carrying curren. (8) 4. A solenoid is 50 cm long, 2 cm in diameer and conains 1500 urns. The cylindrical core has a diameer of 2 cm and relaive permeabiliy of 75. This coil is co-axial wih second solenoid, also 50 cm long, bu 3 cm diameer and 1200 urns. Calculae L for he inner solenoid; and L for he ouer solenoid. (8) 5. Sae and derive Poisson s equaion and Laplace equaion. (16) 6. Obain he expression for energy sored in magneic field and also derive an expression for magneic energy densiy. (16) 7. Derive an expression for he capaciance of a parallel plae capacior wih wo dielecric media. (8) 8. A parallel plae capacior wih a separaion of 1 cm has 29 kv applied, when air was he dielecric used. Assume ha he dielecric srengh of air as 30kV/cm. A hin piece of glass wih wih a dielecric srengh of 290 kv/cm wih hickness 0.2 cm is insered. Find wheher glass or air will break. (8) 9. Derive an expression for inducance of a solenoid wih N urns and meer lengh carrying curren I amperes. (8) 10. Deermine wheher or no he following poenial fields saisfy he Laplace s equaion. (8) 11. Considering a oroidal coil, derive an expression for energy densiy. (8) 12. Derive he boundary condiions a an inerface beween wo magneic medias. (8) 13. A parallel plae capacior has an area of 0.8m 2, separaion of 0.1mm wih a dielecric for which and field of 10 6 V/m. Calculae C and V. (8) 14. A solenoid wih radius of 2 cms is wound wih 20 urns per cm and carries 10mA. Find H a he cenre of he solenoid if is lengh is 10cm. If all he urns of he solenoid were compressed o make a ring of radius 2 cms, wha would be H a he cenre of he ring? (8)

22 15. Find he permeabiliy of he maerial whose magneic suscepibiliy is 49. (4) 16. The inner and ouer conducors of a co-axial cable are having radii a and b respecively. I f he inner conducor is carrying curren I and ouer conducor is carrying he reurn curren I in he opposie direcion. Derive he expressions for he inernal inducance and he exernal inducance. (12) 17. Solve he Laplace s equaion for he poenial field in he homogeneous region beween he wo concenric conducing spheres wih radius a and b where b>a, V=0 a r = b, and V=V0 a r = a. Find he capaciance beween he wo concenric spheres. (8) 18. Calculae he inducance of a solenoid of 200 urns wound ighly on a cylindrical ube of 6 cm diameer. The lengh of he ube is 60 cm and he solenoid is in air. (8)

23 UNIT V TIME VARYING FIELD AND MAXWELL S EQUATIONS PART A (2 Marks) 1. Wrie down he Maxwell s equaions in inegralphasor form. (M-11) H. dl ( J j D ) ds ( j ) E. ds S S E. dl j Bds j H. ds S S S D. ds dv S B. ds 0 where E- elecric fieldinensiy, D-elecric flux densiy, B-magneic flux densiy, H-magneic field inensiy, µ-permeabiliy of medium, σ-conduciviy of medium, Ɛ -permiiviy of medium, J-curren densiy and ρ-resisiviy of medium 2. Wrie down he Maxwell s equaion in inegral form. (M 13) From Ampere s Law H. dl From Faraday s Law E. dl S S D ds B ds From Elecric Gauss s Law s D. ds From Magneic Gauss s Law s B. ds where D-elecric flux densiy, B-magneic flux densiy, E- elecric field inensiy, H-magneic field inensiy 0 0

24 3. Explain he significance of displacemen curren. Wrie he Maxwell s equaion in which i is used. (N-12) The displacemen curren idhrough a specified surface is obained by inegraion of he normal componen of JD over he surface. id = S id = S J. ds D D =. ds S E. ds This is a curren which direcly passes hrough he capacior. Maxwell s equaion C H = J C J D E E ( Differenial form ) D H. dl ( J ) ds ( Inegral form ) wheree- elecric field inensiy, D-elecric flux densiy, B-magneic flux densiy, H-magneic field inensiy, µ-permeabiliy of medium, σ-conduciviy of medium, Ɛ -permiiviy of medium, JC- conducion curren densiy, ρ-resisiviy of medium, JD-displacemen curren densiy S 4. Explain why.b 0 (N-12).B 0 saes ha here is no magneic charges. The ne magneic flux emerging hrough any closed surface is zero. 5. Wrie down he Maxwell s equaion in inegral form. (M 12) From Ampere s Law H. dl From Faraday s Law E. dl S S D J B ds From Elecric Gauss s Law ds

25 s D. ds v dv From Magneic Gauss s Law s B. ds 0 where E- elecric field inensiy, D-elecric flux densiy, B-magneic flux densiy, H-magneic field inensiy, J-curren densiy, ρ-resisiviy of medium. 6. Wrie he fundamenal posulae for elecromagneic inducion and explain how is leads o Faraday s Law. (N 11) A changing magneic flux (Φ) hrough a closed loop, produces anemf or volage a he erminals as given by v d d where he volage is he inegral of he elecric field E around he loop. he loop. For uniform magneic field Φ = B.A where B is he magneic flux densiy and A is he area of v E. dl B ds This is Faraday s law. I saes ha he line inegral of he elecric field around a saionary loop equals he surface inegral of he ime rae of change of he magneic flux densiy B inegraed over he loop area. 7. Wrie down he Maxwell s equaion in poin form. (M 10) From Ampere s Law H From Faraday s Law E From Elecric Gauss s Law.D 0 From Magneic Gauss s Law.B 0 wheree- elecric field inensiy, D-elecric flux densiy, B-magneic flux densiy, H-magneic field inensiy. D B

26 8. Wha is mean by Displacemen curren densiy? (M 09) Displacemen curren is he curren flowing hrough he Capacior. 9. Wrie down he general, inegral and poin form of Faraday s law. (N-10) d emf v ( General ) d B E. dl ds ( Inegral ) B E ( Poin form ) wheree- elecric field inensiy, B-magneic flux densiy, H-magneic flux inensiy, Φ-magneic flux 10. Wrie down he general, inegral and poin form of Faraday s law in phasor form. [A/M 09]. D.B H J j D ( j ) E E 0 wheree- elecric field inensiy, D-elecric flux densiy, B-magneic flux densiy, H-magneic flux inensiy, σ-conduciviy of medium, Ɛ -permiiviy of medium, J-curren densiy, ρ-charge densiy ω- angular frequency j B j H 11. Disinguish beween ransformer emf and moional emf. (N-09) The emf induced in a saionary conducor due o he change in flux linked wih i, is called ransformer emf or saic induced emf. B emf = -. ds eg. Transformer.

27 12. Wrie down he Maxwell s equaions in poin phasor forms. (M 10). D.B H J j D ( j ) E E wheree- elecric field inensiy, D-elecric flux densiy, B-magneic flux densiy, H-magneic field inensiy, µ-permeabiliy of medium, σ-conduciviy of medium, Ɛ -permiiviy of medium, J-curren densiy, ω- angular frequency, ρ-resisiviy of medium 0 j B j H 13. Explain why E 0. (N-11) In a region in which here is no ime changing magneic flux, he volage around he loop would be zero. By Maxwell s equaion B E =0 where E-elecric field inensiy, B-magneic flux densiy 14. Explain why. D 0 (M-09) In a free space here is no charge enclosed by medium. The volume charge densiyis zero. By Maxwell s equaion. D v where D-magneic flux densiy, v -volume charge densiy Sae Ampere s circuial law. Mus he pah of inegraion be circular? (M-11) The inegral of he angenial componen of he magneic field srengh around a closed pah is equal o he curren enclosed by he pah. H. dl I The pah of inegraion mus be enclosed one. I mus be any shape and i need no be circular alone.

28 PART- B (16 Marks) 1. Sae Maxwell s equaions and obain hem in differenial form. Also derive hem for harmonically varying field. (16) (N-13) 2. Sae Maxwell s equaions and obain hem in inegral and differenial form. (16) (N-13) 3. Sae and prove poining heorem. (8) (N-12) 4. Derive he expression for oal power flow in coaxial cable. (8) (N-12) 5. Sae and prove poining heorem. Wrie he expression for insananeous, average and complex poyning vecor. (16) (N-13) 6. Wrie he inconsisency of Ampere s law. Is i possible o consruc a generaor of EMF which is consan and does no vary wih ime by using EM inducion principle? Explain. (16) (M-13) 7. Derive and explain he Maxwell s equaions in poin and inegral form using Ampere s circuial law and Faraday s law. (16) (M-12) 8. Compare he field heory and circui heory. (8) (M-12) 9. The conducion curren flowing hrough a wire wih conduciviy σ=3x10 7 s/m and he relaive permeabiliy εr=1 is given by Ic=3sin ω (ma). If ω=10 8 rad/sec, find he displacemen curren. (8) (M-13) 10. An elecric field in a medium which is source free is given by E=1.5cos(10 8 -βz)ax V/m. Find magneic flux densiy,magneic field inensiy and elecric flux densiy. Assume εr=1, μr = 1, σ = 0. (8) (M-13)