UnitI( 2 marks) 1.

1.State stokes theorem.The line integral of a vector around a closed path is equal to the surface integral of the

normal component of its curl over any surface bounded by the path ∫ H.dl = ∫ curlH.nds

2.State the condition for the vector F to be solenoidal.If divergence of a vector F is zero then the vector F is solenoidal vector .ie ▼.F =0

3.State the condition for the vector F to be irrotational.If curl of a vector F is zero then the vector F is irrotational vector .ie ▼xF =0

4.What is the physical significance of div D?The divergence of a vector flux density is electric flux per unit volume leaving a small

volume. If divergence of a vector F is zero then the vector F is solenoidal vector 5.State Divergence Theorem.The volume integral of the divergence of a vector over a volume v is equal to the surface integral o f the normal component of the vector over the surface bounded by the volume.

∫ divFdv = ∫ F.nds 6.Define divergence.The divergence of a vector F at any point is defined as the limit of its surface integral per unit volume as the volume enclosed by the surface around the point shrinks to zero.

7. Give practical examples for diverging and curling fields. ANS: Diverging fields examples: 1.The air velocity going out from punctured tube and gas velocity going out from a hole in a gas balloon. Curling fields examples: 1.The water velocity in a river.2.Velocity of rigid body rotating about a fixed axis 8. Mention the criteria for choosing an appropriate coordinate system for solving a field problem easily. ANS: For point charges and line charge analysis Cartesian system is proper choice. For cylindrical conductors and cylindrical surfaces, cables analysis cylindrical coordinate system is preferred. For electromagnetic field analysis in all directions, spherical conductors, a spherical coordinate system is much easier than other systems

9.What are the various sources of electric and magnetic fields? Refer CAT exam answer key10.Define Curl Refer CAT exam answer key11.Define gradient Refer CAT exam answer key12.Define divergence Refer CAT exam answer key13.What is the physical significance of curl?

The Curl of a vector represents it rotational property. If Curl of a vector F is zero then the vector F is Irrotational vector . 2.

14.Define coordinate system? List different types of coordinate system. Refer CAT exam answer key15.What are the +ve and –ve effects of Electromagnetic field.? Refer CAT exam answer key16.How to reduce the effects of EM field?

By providing proper shielding the effects of EM field is reduced. 17.When two vectors are parallel to each other and perpendicular to each other?

If dot product of two vectors is zero the two vectors are perpendicular to each otherIf cross product of two vectors is zero the two vectors are parallel to each other

18.Define unit vectorRefer CAT exam answer key

Unit II (2 marks)1.Write the poisson’s and laplace equation.          Poisson’s equation is                          ▼2V = - ρ/ Є        ∂ 2V/ ∂x2  + ∂ 2V/∂y2  + ∂ 2V /∂z2          = - ρ/ Є , Where        ρ – volume charge density,  Є – permittivity of the medium,   ▼2 –  laplacian operator         Laplace equation is  ▼2V = 0  ∂ 2V/ ∂x2  + ∂ 2V/∂y2  + ∂ 2V /∂z2  = 0 2.     Obtain Poisson’s equation from Gauss’s law?     Gauss law in point form is          ▼.D = ρ      where ,  D – electric flux density,  ρ  - volume charge density          but  D = Є E          therefore Є  ▼.E = ρ                              ▼. E = ρ/ Є          but E = - ▼V                 - ▼ . ▼V  = ρ/ Є                  ▼2V = - ρ/ Є  This is poisson’s equation 3.     What is a capacitor?              A capacitor is an electric device which consists of two conductors separated by a dielectric medium which can store equal and opposite charges.4. Express laplace equation in Cartesian coordinate system[ april 2003]  Laplace equation  ▼2V = 0  In Cartesian coordinate system∂ 2V/∂x2  + ∂ 2V/∂y2  + ∂ 2V /∂z2  = 05.What is the capacitance of  a parallel plate capacitor?     The capacitance of a parallel plate capacitor is C = Є0 Єr  A     farad                             d                   Where  A – plate area of the capacitor,d – distance between the parallel plates

36.  State the boundary conditions at the interface  between two perfect dielectricsa)      The tangential component of electric field is continuous                 Et1 = Et2

b)The normal component of electric flux density is continuous.                 Dn1 = Dn2

 7.  Define Boundary conditions.The conditions existing at the boundary of the two media when field passes from one medium to other are called boundary conditions.8.Define Polarization             The product of charge Q and length L between dipole is dipole moment.Dipole moment per unit volume is called polarization, a vector field directed from –Q to +Q  .  P = Ql/Al = Q/A ul    where ul  is unit vector directed –Q to +Q.9.Write the point form of ohm’s law               J α E ,ie    J = σE9.Give the expression for capacitance of parallel plate capacitor with 2 dielectrics medium                Capacitor of a capacitor with 2 dielectrics is                C =    A Є0

                                    d1      +     d2

                                       Єr1             Єr2

 10) Write down the capacitance for two concentric spheres.  The capacitance fro two concentric spheres of radius a and b is  C = 4 π Є ab b-a  11) Write the capacitance for 2 wire parallel transmission line             The capacitance for 2 wire parallel transmission line of radius a is             C =        π Є                        ln (d/a)             where  d  - distance between two transmission line12)    A parallel plate capacitor with d = 1m and plate area 0.8 m2 and a dielectric relative permittivity of 2.8.  A dc volt of 500 v is applied between the plates.  Find the capacitance and energy stored. d = 1m,   A = 0.8 m2 , Єr = 2.8 , V =500            Capacitance C = Є0 Єr  A  /  d = 8.854x10-12x2.8x0.8/1 C = 19.833 pF             Energy stored E = ½ CV2 =½ 19.833x10-9x5002

  E          =  2.48 x 10—6 J. 13. Define energy and energy density in an Capacitor or electrostatic field.

Energy in capacitor = ½ CV2 Joules Energy density = Energy per unit volume

= ½ DE joules/m3

14.What is dielectric break down?

The minimum voltage at which the dielectric material losses its insulation property and starts to conduct is known as dielectric breakdown.15. What is dielectric break down strength ? 4 The maximum voltage that can be withstand by a dielectric material without losing its losses its insulation property is known as dielectric breakdown strength .16.Define electric potential and potential difference. Electric potential = Work done per unit positive charge is known as Electric potential. potential difference = Difference in potential between two points in an electric field is known as potential difference17. State coulombs law.

Coulombs law states that the force between any two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. F=Q1Q2 / 4πεr2

18.Define electric field intensity. Electric field intensity is defined as the force per unit positive charge. E =F/ Q =Q/4πεr2 V/m

18.State Gauss law for electric fieldsThe total electric flux passing through any closed surface is equal to the total charge

enclosed by that surface. ∫ D.ds = Q

19. Name few applications of Gauss law in electrostatics.Gauss law is applied to find the electric field intensity from a closed surface.e.g) Electric

field can be determined for shell, two concentric shell or cylinders etc.20. What is a point charge?

Point charge is one whose maximum dimension is very small in comparison with any other length. 21. What are equipotential surfaces?An equipotential surface is a surface where the potential energy at every point is same value.22. When is method of images used?

Method of images is used in solving problems of one or more point charges in the presence of boundary surfaces.

UNIT 3 (2 marks)1.  Define Magnetic dipole  [ nov 2003]              When equal and opposite magnetic poles are separated by a small distance it forms a magnetic dipole2.  What is magnetic dipole moment (m)?

               It is the product of magnetic pole strength and distance between dipoles  3.Define magnetization

magnetic dipole moment to unit volume is known as magnetization. magnetization (M)= Magnetic dipole moment /  Volume                        4. Define magnetic susceptibility.             It is the ratio of magnetization to magnetic field intensity.                Xm =   M/H                        

5. What is the relation between relative permeability and susceptibility.                          μr  = 1  +  Xm where    μr -   relative permeability, Xm  -  susceptibility6. What are the different types  of magnetic materials 5. According to their behavior , magnetic materials are classified as diamagnetic ,paramagnetic and ferromagnetic materials. 7. Define magnetic flux?It is define das ratio of magnetomotive force to reluctance of magnetic circuit.  Magnetic flux = mmf/ reluctance            8.  Define mmf?          Magneto motive force of a magnetic circuit is equal to the line integral of magnetic field H around the closed circuit.     Mmf = ∫ H.dl = NI amp-turns. 9.  Define Reluctance  and pemeance?               It is defined as ratio of total  mmf of magnetic circuit to flux through it. Reluctance (R) =  mmf/ Magnetic flux Permeance is the  revesal of reluctance.        P = 1/R= Magnetic flux/mmf 10.Write down the magnetic boundary conditions

a)The normal components of magnetic flux density B is continuous across the boundary.   Bn1 = Bn2

b)The tangential component of magnetic field intensity H is continuous across the boundary          Ht1 =  Ht2

 11) Give the inductance of solenoid.       The inductance of solenoid                               L =  μN2A H/ l , where   l – length, N -  number of turns, A  -  area of cross section   12) Give inductance of toroid.               The inductance of toroid  is  L =   μN2r2   Henry                                                        2R       where N – number of turns, R – radius of the toroid, r  -  radius of the ring.

        13) Define energy and energy density in an inductor or Magnetic field. Energy in inductor = ½ LI2 Joules

Energy density = Energy per unit volume = ½ BH joules/m3

14)    Define self inductance.          The self induction of a coil is defined as ratio of total magnetic flux linkage to the coil to current thro’ the same coil 15)    Define Mutual inductance.          The mutual inductance between two coils is defined as the ratio of induced magnetic flux linkage in one coil to current through in other coil.

              16)    Give the relation between mutual inductance and self inductance.         K = M √L1L2

where M -  Mutual inductance , L1- Self inductance of coil 1,   L2 -  Self inductance of coil 2,  K -  Coupling coefficient. 17).   Define Hysteresis: (April / 2003)

            The phenomenon which causes magnetic flux density (B)  to lag behind magnetic field intensity is called Hysteresis.

  18)    Two coils of self inductances of 0.5 H and 0.8 H with negligible resistance are 6 connected in series. If their mutual inductance is 0.2H.  Determine the effective inductance of the combination.

L1 = 0.5 H       L2 = 0.8 H      M = 0.2 H.  L = L1 + L2

L(aiding)    = 0.5 + 0.8                   = 1.7 H.  L (opposing)    = 0.5  + 0.8  - 2 x 0.219.Define Biot –Savart Law?             dH = IdLsinθ A/m

4πd2             where, dH is magnetic field intensity by a small current element         I dl  is the current element, d is the distance between point and current element.

20.State Ampere’s Law     Magnetic field Intensity around a closed path is equal to the current enclosed by the path ∫ H.dl = I enclosed

21.What is the relation between magnetic flux density B and magnetic field Intensity H.            B         = µH =µ0 µr H wb/m2

22.Define Magnetic Flux Density            It is flux per unit area ie B =Φ/A   Wb/m2 or Tesla.                         23. Give Lorentz force Equation           It is expressed as follows. F= q(E+ vxB)

Where F   -  Lorentz force  , q    - Charge of the moving charge v   -Velocity of charge , B -Magnetic field.

  24.What is the expression for the torque experienced by a current carrying loop, placed in a magnetic field. [April 2003]      Torque experienced by a current carrying loop, placed in a magnetic field is given by            T = BIA sinθ N-m25.What is the difference between scalar and vector magnetic potential.[Nov 2003]      Magnetic scalar potential (V) is a quantity whose negative gives the magnetic field intensity (H). ie H = -▼V Magnetic Vector potential (A) is a quantity whose curl gives the magnetic flux density(B)

ie B = ▼xA26.Can a magnetic field exist in a good conductor if it is static or time varying? Explain   Yes, magnetic field exist in a good conductor if the field is static or Time Varying.  For a good conductor, conductivity is high and current exists. But Static or time varying Magnetic field exists.

27.Give the force between two parallel conductors  F12 = µ0I1I2 L

2πd Where,  F  - Force between two conductors, I1  - Current flowing in 1st conductor, I2  - Current flowing in2nd conductor, d - Distance between two conductors. L –length of conductor

28.State Gauss Law for Magnetic field. 7            The total magnetic flux passing through any closed surface is equal to zero.

∫ B.ds = 0UNIT 4 (2 marks)

1. What is the significance of displacement current density?ANS: Current through the capacitor is known as displacement current .This current is due to the displacement of charges and vanishes with in fraction of time periods.

2. State Faraday’s law of electromagnetic induction with a mathematical expression.ANS: Whenever flux linking with conductor changes, an EMF is induced in the conductor and is directly proportion to rate of change of flux linking with that conductor. EMF =-N dФ/dt , where N is no. of turns.

3.What is displacement current? Compare displacement current with current due to flow of charges?

ANS: Current through the capacitor is known as displacement current .This current is due to the displacement of charges and vanishes with in fraction of time periods. But current through resistor is known as conduction current and this is due to the movement of free electronics.

3. Explain the significance of displacement current and eddy current.ANS: Displacement current: Current through the capacitor is known as displacement current .This current is due to the displacement of charges and vanishes with in fraction of time periods. EDDY current: The current through short circuited conducting material is known as eddy current. Eddy current is produced by eddy emf and eddy current is dissipated as heat.

4. Define Lenz’s Law.ANS: Lenz’s law states that the induced emf as per the Faraday’s law opposes the causes of producing that emf. EMF =-dФ/dt where the negative sign is due to the Lenz’s Law.

5. Define and explain the use of vector potential in time varying field.

ANS: Vector magnetic potential is given by where J is current

density, V is electric potential. Using the of Vector magnetic field , we can determine the magnetic flux

density B and Electric field intensity E for the time varying fields as follows(1)B= (2) E=

6. A conductor of length 0.5 m moves in a uniform magnetic field of density 1.1 T at a velocity of 30 m/s. Calculate the induced voltage in the conductor when the direction of motion is perpendicular to the field. ANS: Induced emf e= BLvsinӨ 8

= 1.1x0.5x30xsin90 = 16.5 volts7. In a time varying situation how do you define a good conductor and a lossy

dielectric materials?

ANS: If

If

If

8. Explain the existence of eddy current and displacement current with example. ANS: Displacement current: current due to the displacement of charges is known as displacement current and vanishes with in fraction of time periods. Example Current through the capacitor . EDDY current: The current through short circuited conducting material is known as eddy current. Eddy current is produced by eddy emf and eddy current is dissipated as heat. Example : Current in the core part of transformer and generator.

9. Write down the expression for the emf induced in the moving loop in static B field.ANS: If the velocity of loop is and magnetic flux density is B and length of loop is L

then emf induced in the loop e = BLv sin90 = BLv

10.How a dielectric medium can be identified as a lossless and lossy for a given frequency?

If

If

11. Compare transformer EMF(Statically induced) and s motional EMF(dynamically )?

S.no transformer EMF motional EMF

1.

2.

Here conductor position is stationary but magnetic flux is changing with respect to timeExample : Emf induced in transformer

Here magnetic field is constant but conductor position is changing with respect to timeExample : Emf induced in generator

12.Calculate the EMF induced in a circuit having an inductance of 700 µH if the current through it various at a rate of 5000A per second.ANS: di/dt =5000A per sec, L= 700x10-6 H Emf e = Ldi/dt = 5000x700x10-6= 3.5 Volts

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15.In a material for which σ = 5.0S/m and E= 250 sin1010t (V/m).Find the displacement and conduction current densities.

Ans : Conduction current density Jc = σ E A/m2 = 5.0x 250 sin1010t = 1250 sin1010t A/m2 Displacement Jd = Є0 Єr ƏE/Ət = 8.854x10-12x1x250x1010cos1010t

16.Explain why ▼.B =0 If there is no magnetic charges then the net magnetic flux from any closed surface is 0 17. Explain why ▼x E =0 As per Maxwell equation, ▼x E = -dB/dt

If there is no time changing flux ,the voltage induced around the closed loop is would be 0 18. Explain why ▼.D =0 In a free space if there is no electric charges enclosed by the medium, then the volume charge density is 0.Therefore ▼.D =0

19. Explain the conservative property of electric field.The work done in moving a point charge around a closed path in a electric field is zero.

Such a field is said to be conservative. ∫ E.dl = 0

20.Compare circuit theory and field theory Refer CAT exam answer key

UNIT V(2 Marks)1.Define a wave.

If a physical phenomenon that occurs at one place at a given time is reproduced at other places with time delay , the time delay being proportional to the distance between two places,then the group of phenomena constitutes a wave.

2.Mention the properties of uniform plane wave.i) At every point in space, the electric field E and magnetic field H are perpendicular to

each other.ii)The fields vary harmonically with time and at the same frequency everywhere in space.

3.Write down the wave equation for E and H in free space.∂ 2H– μ0ε0∂ 2H / ∂t 2 =0.

4.Define intrinsic impedance or characteristic impedance.It is the ratio of electric field to magnetic field. or . It is the ratio of square root of permeability to permittivity of medium.

5.Give the characteristic impedance of free space.377ohms

6.Define propagation constant.Propagation constant is a complex number γ =α +jβwhere α is attenuation constant ,β is phase angle constant stant

γ 2 = jωµ ( σ +jωε)7.Define skin depth 10

It is defined as that depth in which the wave has been attenuated to 1/e or approximately 37% of its original value.

skin depth = 1/α 8.Define Poynting vector.

The pointing vector (P ) is defined as the cross product of E and H. P =E X H It gives the energy associated with the electromagnetic waves.

9.State Poyntings Theorem.The net power flowing out of a given volume is equal to the time rate of decrease of

the energy stored in Electromagnetic field within the volume- conduction losses.10. Define loss tangent.Loss tangent is the ratio of the magnitude of conduction current density to displacement cuurrent density of the medium.

Tan δ = σ / ωε11.Defie reflection and transmission coefficients.Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that of the incident field.12.Define transmission coefficients.

Transmission coefficient is defined as the ratio of the magnitude of the transmitted field to that of incident field.13.What will happen when the wave is incident obliquely over dielectric –dielectric boundary?When a plane wave is incident obliquely on the surface of a perfect dielectric part of the energy is transmitted and part of it is reflected .But in this case the transmitted wave will be refracted, that is the direction of propagation is altered.14.What are uniform plane waves?Electromagnetic waves which consist of electric and magnetic fields that are perpendicular to each other and to the direction of propagation and are uniform in plane perpendicular to the direction of propagation are known as uniform plane waves.15.Write short notes on imperfect dielectrics.

A material is classified as an imperfect dielectrics for σ <<ωε, that is conduction currentdensity is small in magnitude compared to the displacement current density.16.Define standing wave ratio(SWR) (Refer CAT Answe key)17.What is Brewster angle. (Refer CAT Answer key)18.Write Helmholtz equation. (Refer CAT Answer key)19.Write one dimensional wave equation. (Refer CAT Answer key)20.What is Homogeneous and isotropic medium(Refer CAT Answer key)21.What is skin effect. The non uniform distribution current through the cross section of conductor is known as skin effect.

UNIT 1 (16 Marks) - question no 11. a and 11.b PART B 111. i) State and prove Divergence theorem. (8) ii) State and prove Stokes theorem.(8)

2.Define Divergence, Gradient, curl and laplacian and write their equation in Cartesian, cylindrical and Spherical Systems with expression (16) .3. i) What are the major sources of Electromagnetic fields (any five)?

ii) What are the positive and negative effects of EM fields on living things? iii) What are the E and H field limits for public exposure? iv)Give any one example to reduce the effect of EM field.

4. Explain three coordinate systems (or) Write short notes on (16) i) Cartesian system ii) Cylindrical system iii) Spherical system Problems 1 .Determine divergence and Curl of the following vector fields. i) P= x2yz ax + xz az. ii) Q = ρsinΦaρ + ρ2z aΦ + zcosΦ az

iii) T = 1 / r2 cosθ ar + r sinθ cosθ aθ+ cosθ aΦ

2. Find the gradient of the following scalar fields i) V = e-z sin2x coshy ii) U = ρ2z cos 2Φ iii) W = 10r sin2θ cosΦ.

3.Find the value of the constant a, b, c so that the vector E = (x + 2y + az) ax + (bx – 3y –2) ay + (4x + cy + 2z) az is irrotational.

4. (i) Determine the constant c such that the vector F = (x + ay)i + (y + bz)j + (x + cz)k will be solenoidal. (ii) Given in cylindrical co-ordinate. For the contour shown in Fig.Q-32, verify Stoke’s theorm.

Fig.Q-32.

4. Verify Stoke’s theorem for a vector field F = ρ2cos2 Φaρ+zsinΦaz around the path L defined by 0≤ ρ ≤ 3, 0≤ Φ ≤ 45o and z = 0.

5. Verify the divergence theorem for a vector field A = xy2 ax+y3 ay+y2z az and the surface is a cuboid defined by 0<x<1, 0<y<1, 0<z<1. 6. Given that F = x2 y ax - yay. Find ∫ F. dl for the closed path shown in figure and also verify Stoke’s theorem.

7. i) Given A = 5ax and B = 4ax + t ay ; Find ‘t’ such that the angle between A and B is 45˚ 12 ii) Using the Divergence theorem, evaluate ∫∫ A.dS = 2xy ax + y2 ay + 4yz az over the cube bounded by x = 0; x = 1; y = 0; y = 1; z = 0; z = 1. 8. i) Determine divergence and curl of the vector A = x2 ax + y2 ay + y2 az.

ii) Determine the gradient of the scalar field at P (√2, π / 2, 5) defined in cylindrical co-ordinate system as A= 25ρ sinφ.

UNIT 2 (16 Marks) - question no 12. a and 12.b PART B1.Define coulombs law in vector form. (6)2.Derive boundary conditions for electrostatic field (10)3.Derive capacitance of (16) i) Parallel plate capacitor ii) Coaxial cable iii)Concentric Sphere iv) Isolated sphere4.Derive Energy stored and energy density in a capacitor (or ) in an electrostatic field 5.Derive Poisson’s and Laplace equations. (10)5.. (i) A circular disc of radius ‘a’, m is charged uniformly with a charge density of σ C/m2

Find the electric field intensity at a point ‘h’, m from the disc along its axis. (10) (ii) A circular disc of 10 cm radius is charged uniformly with a total charge of 10-6c.

Find the electric intensity at a point 30 cm away from the disc along the axis. (6)UNIT 3 (16 Marks) - question no 13. a and 13.b PART B

1.Use Biot – Savart’s law to find magnetic field intensity for (i)finite length of conductor (ii)finite length of conductor at a point P on Y – axis.

2. (i)A steady current of ‘I’ flows in a conductor bent in the form of a square loop of side ‘a’. Find the magnetic field intensity at the centre of the current loop. ii) Find the magnetic field intensity at the centre of a square of sides equal to 5m and carrying 10 A current. 3. Derive H at (i) any point along the axis of circular loop (ii)at the centre of circular loop

4.Derive H due to a circular current loop and extend the same to compute H due to a

long solenoid. 5.(i)Derive an expression for the inductance of solenoid.

(ii)Derive an expression for the inductance of toroid. 6.Derive energy stored and energy density in magnetic field or Inductor 7.Derive the boundary conditions at an interface between two magnetic media.

8.Two wires carrying currents in the same direction of 5000 A and 10000 A are placed with their axes 5 cm apart. Calculate the force between them. 7. (i) Find the field intensity at a point due to a straight conductor carrying current I as shown in Fig.Q-7.

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Fig.Q-7 (ii) Find H at the centre of an equilateral triangular loop of side 4 m carrying current of 5 A.

8.(ii) An iron ring with a cross sectional area of 3 cm2 and a mean circumference of 15 cm is wound with 250 turns wire carrying a current of 0.3 A. The relative permeability of the ring is 1500. Calculate the flux established in the ring. UNIT 4 (16 Marks) - question no 14. a and 14.b

1. Define the Faraday’s laws. What are the different ways of e.m.f generation? Explain with the governing equations and suitable example for each. (16)

(OR)Write short notes on Faradays law of electromagnetic induction. (8) (OR)State and explain faraday’s and Lentz’s Laws of induction using a simple network. (8)

2. Derive Maxwell’s equation in point and integral form (16) (OR)Derive general field relations for time varying electric and magnetic fields using Maxwell’s equations. (16)

(OR)Derive Maxwell’s equations from Ampere’s law and Faradays law .Express the equations in phasor form for time varying fields. (16) (OR)From the fundamental laws derive the Maxwell’s equations and the need for the Maxwell’s contribution to electromagnetic theory. State the equations in both differential and integral form. (16)

(OR)State and explain Maxwell’s equations and give their physical significance. (10)3. Derive the Maxwell’s equations for fields varying harmonically with time. (16)4. In free space E (z,t)=100cos(ωt-βz)ax (V/m).calculate H and plot E and H waveforms at

time t=0 (16)

5. Differentiate conduction and displacement current and derive the same. Explain the need of displacement current in Maxwell’s equations. (16)(OR)What do you mean by displacement current? Write down the expression for total current density. (8)(OR)Derive equation for conduction and displacement current density. (16)

6. Compare circuit theory and field theory (10)

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UNIT 5 (16 Marks) - question no 15. a and 15.b1.Derive wave equation in general form for electric and magnetic fields (16)2.Derive phasor form or frequency form of wave equations (16) (or) Explain wave propagation for the following

i)Lossy dielectric ii)Lossless dielectrics iii)Free space iv)Perfect conductors (or) Derive equation for wave parameters ά,β, ή, γ3. What is skin effect? What is skin depth? What is its relation with Attenuation constant, conductivity and frequency? (8) (or) What is skin depth(depth of penetration)? Derive skin depth.4. Define pointing vector. State and prove Poynting theorem (16)5.What is Brewster angle? Derive Brewster angle. (16)6. Define and derive skin depth. Calculate skin depth for a medium with conductivity 100 mho/m, µr=2, εr=3 at 50Hz, 1MHz and 1 GHz.7. A plane wave propagating through a medium with µr=2, εr=8 has E = 0.5 sin (108 t-βz)az (V/m). Determine (i) β (ii) The loss tangent (iii) wave Impedance (iv) wave velocity (v) H field 8.Calculate intrinsic impedance η, propagation constant γ and wave velocity υ for a conducting medium in which σ = 58 S / m, µr=1, εr=1 at a frequency of 100 MHz.