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ELECTROMAGNETIC FIELDS

B.KALAIMATHI

AP/ECE

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UNIT-1

Two mark questions

1. Define electromagnetic field.

The electric charges such as positive and negative charges produce a field around it which is

called an electric field.

If the field produced is due to magnetic effects, it is called magnetic field.

The electric and magnetic fields are related to each other. Such a field is called electromagnetic

field.

2. Define scalar and vector.

A quantity that is characterized only by magnitude is called a scalar.

A quantity that is characterized both by magnitude and direction is called a vector.3. Define gradient.

The gradient of any scalar function is the maximum space rate of change of that function. If

scalar V represents electric potential, V represents potential gradient.

V = V/x ax+V/x ay+z/xaz This operation is called gradient.

4. Define divergence.

The divergence of a vector A at any point is defined as the limit of its surface integrated per unitvolume as the volume enclosed by the surface shrinks to zero.

.V = limv01vSA.nds .A = Axx +Ayx +Azx 5. Define curl.

The curl of a vector A at any point is defined as the limit of its surface integral of its cross

product with normal over a closed surface per unit volume shrinks to zero.

|curl A| = limv01vSnXAds 6. Define divergence theorem.

The volume integral of the divergence of a vector field over a volume is equal to the surface

integral of the normal component of this vector over the surface bounding the volume.

7. 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

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H.dldl = ( x H) ds

8. 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. It is directed along the line joining the two charges.

F=Q1Q2 / 4r 2 ar9. State Gauss law for electric fields

The total electric flux passing through any closed surface is equal to the total charge enclosed by

that surface.

10. Define electric flux.

The lines of electric force are electric flux.

11. Define electric flux density.Electric flux density is defined as electric flux per unit area.

12. Define electric field intensity.

Electric field intensity is defined as the electric force per unit positive charge.

E =F/ Q =Q/4r 2 V/m13. Name few applications of Gauss law in electrostatics.

Gauss law is applied to find the electric field intensity from a closed surface. e.g)Electricfield can be determined for shell, two concentric shell or cylinders etc.

14. What is a point charge?

Point charge is one whose maximum dimension is very small in comparison with any other

length.

15. Define linear charge density.

It is the charge per unit length.

16. Define potential difference.

Potential difference is defined as the work done in moving a unit positive charge from one point

to another point in an electric field.

17. What is the difference between absolute potential and potential difference.

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26. Give the transformations of scalar co-ordinates from the spherical co-ordinates to

rectangular co ordinate.

Fx = FR xx2+y2+z2 + F xz(x2+y2)(x2+y2+z2) - F y(x2+y2)

Fy = FR yx2+y2+z2 + F yz(x2+y2)(x2+y2+z2) + F x(x2+y2)

Fx = FR zx2+y2+z2 - F x2+y2(x2+y2)(x2+y2+z2)

27. State the principle of superposition with respect to Electric field.

The principle of superposition of fields states that the electric field at a point due to n number of

charges is the algebraic sum of the individual field intensities produced by the various charges

at that point.

In vector superposition, the resultant field at P is given by, E =14k=1Nqkrkp2 ukP Where q k =k th charge, r kp = distance of k th charge.

Ukp = unit vector directed from kth charge to P.28. Find the gradient of scalar system t= x 2 y + e z at point P(1, 5, -2)

2 = (xi +yj +zk) (x2 y + ez)=2xyi +x2 j + ezk = 10i + j + e-2k

29. Define volume charge density.

Volume charge density is defined as, the charge per unit volume.

Pe =Total charge in columbTotal volume in cubic metres(Cm3)

30. State the nature of conservative field.Any field where the closed line integral of the field is zero said to be conservative field.

BIG QUESTIONS:

1. State and explain (i)Divergence Theorem (ii) Stokes theorem

(iii) The electric flux density is given as D =r/4 1r nc/m2 in free space. Calculate: 1) the

electric field intensity at r = 0.25 m 2) the total charge within a sphere of r = 0.25 m and the

total flux leaving the space of r = 0.35 m. (Nov/Dec 2008)

2. Define Divergence, Gradient, Curl and Laplacian in cylindrical and spherical Coordinate

system with mathematical expressions. (April /May 2004)

3. State the principle of superposition as applied to electric potential and derive a general

expression for the resultant potential due to point, line, surface and volume charges

composing the systems. (April /May 2004)

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4. (i) Derive an expression for the electric field due to a straight uniformly charged wire of

length L metres and with a charge density of + c/m at the point P which lies along perpendicular bisector of wire.

(ii) Given A = (Y cosax) ax + (Y +ex) az. Find V X A at the origin. (Nov/Dec 2006)

5. (i) A circular disc of radius am is charged uniformly with a charge density of c/2.Find the electric field intensity at a point h m from the disc along its axis.

(May/June 2009) & (Nov/Dec 2007)

(ii) If V = 60 sinr2 volts, Find V and E at P(3, 600 , 250) where V = electric potential andE = electric field intensity. (Nov/Dec 2007)

6. (i) State and prove Gausss law. (May/June 2009)

(ii)Describe any two applications of Gausss law. (Nov/Dec 2006)

a. (i) Determine the variation of filed from point to point due to (1) A singlespherical shell of charge with radius R 1 (2) Two concentric spherical shells of

charge of radii R 1 (inner) and R 2 (outer). (Nov/Dec 2007)

(ii) Derive the expression for electric field intensity due to an array of point charges.

(Nov/Dec 2007)

7. Verify Stokes theorem for a vector field, F =r 2 cos ar +z sin az around the path Ldefined by 0

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12. (i) State super position theorem in relevance to field theory and derive the equation for

total electric field intensity. (Nov/Dec 2006)

(ii) Consider two point charges Q1 =80 coulombs and Q2= -4 0 coulombs situated at(-1, 0, 0) m respectively. Find the electric field intensity at the point (0, 0, 1). Draw the

phasor diagram. (Nov/Dec 2006)

13. (i) Let, A =5ax, and B = 4 ax+By ay, Find by such that, angle between , A and , B is 450.

If, B also has a term Bz az, what relationship must exist between by By and Bz.

(ii) A uniform line charge L = 25nC/m lies on the line, x= -3m and y= 4m, in free space.Find the electric field intensity at a point (2, 3, 15) m. (May/June 2006)

14. (i) If two vectors are expressed in cylindrical coordinates as A = 2ax + ay +azB = -ax+3/2 ay -2azCompute a unit vector perpendicular to the plane containing A and B.

(ii) A regular tetrahedron has vertices at P1 (2, 0, 0) . P2(-1, 3, 0), P3(-1, -3, 0) , P4(0, 0,22). Charges of 1mC are located at each of the four vertices. If the configurationlocated in free space, find the magnitude of force on each charge. (May/June 2007)

UNIT-II

Two mark questions:

1. What is the fundamental difference between static electric and magnetic field

lines?

There is a fundamental difference between static electric and magnetic field lines. The

tubes of electric flux originate and terminates on charges, whereas magnetic flux tubes

are continuous.

2. State Biot Savarts law.

It states that the magnetic flux density at any point due to current element is proportional

to the current element and sine of the angle between the elemental length and inversely

proportional to the square of the distance between them

dB= 0Idl sin / 4r 2

3. State amperes circuital law.

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The line integral of magnetic field intensity around a closed path is equal to the direct

current enclosed by the path. H.dl=I

4. Define magnetic scalar potential.

It is defined as dead quantity whose negative gradient gives the magnetic intensity if there

is no current source present. H = - Vm Where Vm is the magnetic vector potential.

5. Define magnetic vector potential.

It is defined as that quantity whose curl gives the magnetic flux density.

B= x A = / 4 vJrdr web/m2

6. Define magnetic field strength.

The magnetic field strength (H) is a vector having the same direction as magnetic flux

density. H=B/ 7. State Gauss law for magnetic field.

The total magnetic flux passing through any closed surface is equal to zero.

B.ds =0

8. Write down the equation for general, integral and point form of Amperes law.

General form: H.dl=I

Integral form: H.dl= sJ.dl

Point form : x H = J 9. Define magnetic flux density.

Magnetic flux density(B) = Magnetic fluxarea =A webers /m2(Tesla)10. Give the formula to find the force between two parallel current carrying conductors.

F=I1 I2 / 2D Nw 11. Give the expression for torque experienced by a current carrying loop situated in

a magnetic field. T = IABsin12. What is torque on a solenoid? T = NIABsin 13. Write down the expression for magnetic field at the centre of the circular coil.

H = I/2a.

14. Give the relation between magnetic flux density and magnetic field intensity. B = H 15. What is Lorentz force?

Lorentz force is the force experienced by the test charge .It is maximum if the direction

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of movement of charge is perpendicular to the orientation of field lines.

16. Define magnetic moment.

Magnetic moment is defined as the maximum torque on the loop per unit magnetic

Induction of flux density. m=IA

17. Give the force on a current element. dF = BIdlsin 18. Describe what are the sources of electric field and magnetic field ?

Stationary charges produce electric field that are constant in time, hence the term

electrostatics. Moving charges produce magnetic fields hence the term magneto statics.

19. A long conductor with current 5A is in coincident with positive z direction. If

B =4i +4j. Find the force per unit length.

F = BI l sin => F/ l = IBsin = I XB = 5k * (4i+4j) =20j-25i N/m

20. A steady current of I flows in a conductor bent in the form of a square loop of sidea meteres. Find the magnetic field intensity at the centre of the loop.

H =I4d( cos -cos) = I4a/2( cos45 -cos135)

= I2a (12+12) = 12 1a

21. Define magnetic dipole.

A small bar magnet with pole strength Qm and length l may be treated as magnetic dipole

whose magnetic moment is Qm l.

22. Define magnetization.

Magnetization is defined as the ratio of magnetic dipole moment to unit volume.

M = Magnetic dipole / volume = Qm / A a/m

23. Define magnetic susceptibility.

Magnetic susceptibility is defined as the ratio of magnetization to the magnetic field

intensity. It is dimensionless quantity.

m =M /H

BIG QUESTIONS:

1. (i) State and prove Amperes law.

(ii) Find the magnetic field intensity at the centre O of a square of sides equal to 5 m

and carrying 10 amperes of current. (May/June 2009)

2. (i) Obtain an expression for magnetic vector potential.

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(ii) At a point P(x, y, z) the components of magnetic vector potential A are given as

Ax =(4x +3y +2z); Ay = (5x +6y +3z); Az = (2x +3y +5z); Determine B at point P.

(May/June 2009)

3. (i) State Biot -Savarts law in vector form.

(ii)Obtain the expression for magnetic field intensity due to a circular loop of wire

carrying a current I, placed with its centre at origin. (Nov/Dec 2008)

4. (i) Derive an expression for Magnetic Gauss law in point form and integral form.

(ii) Explain the magnetic field intensity due to a straight wire. (April /May 2008)

5. Obtain an expression for the magnetic field intensity due to infinitely long current

carrying conductor.

6. (i) Find the force exerted between current carrying conductors kept in 1 meter distance

and carries the current in the same direction. (April /May 2008)(ii) Find the magnetic field intensity at theorigin due to a current element IdL = 3 (ux +2uy +3uz) A. m, at the point P (3, 4, 5) in free space. (May/June 2007)

7. (i) Consider a conductor of rectangular loop abcd situated in a uniform magnetic field of

B wb/m2. Derive the expression for torque and magnetic moment. (Nov/Dec 2006)

(ii) A single phase circuit comprises two parallel conductors A and B, 1cm diameter and

spaced 1 metre apart. The conductors carry currents of +100 and -100 amps respectively.

Determine the field intensity at the surface of each conductor and also in the space

exactly midway between A and B. (Nov/Dec 2006)

8. (i) Consider a solenoid in a uniform magnetic field of flux density B wb/m2. Obtain the

expression for the torque on the solenoid.

(ii) A conductor located at x =0.4 m; y =0 and 0< z

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(ii) Find the magnetic flux density around infinitely long straight conductor by magnetic

vector potential. (Nov/Dec 2005)

11. (i) Explain the constructional features of solenoid.

(ii) Derive expressions for a magnetic flux density (B) at any point along the axis of the

solenoid.

(iii) Draw the variations of flux density (B) along the axis. (April /May 2005)

12. (i)Define a magnetic circuit with a sketch and hence obtain the expression for its

reluctance.

(ii) A magnetic circuit employs an air core toroid with 500 turns, cross sectional area

6cm2 mean radius 15cm and coil current 4A. Determine the reluctance of the circuit, flux

density and magnetic field intensity. (Nov/Dec 2004)

13. A rectangular loop in the loop in the xy plane with sides b1 and b2 carrying a current I liesin a uniform magnetic field B = ax Bx + ay By + az Bz . Determine the force and torque on

the loop. (Nov/Dec 2003)

UNIT-III

Two mark questions:

1. Write poissons and laplace s equations.

Poisson s equation: 2V= - v /

Laplace s equation: 2V= 0

2. Define current density.

Current density is defined as the current per unit area. J= I/A Amp/m2

3. What is the expression for energy stored in a magnetic field? W = LI2 4. What is energy density in magnetic field? W = H2

5. Write the point form of continuity equation and explain its significance.

J= - v / t 6. 20.Write the expression for energy density in electrostatic field.

W=1 / 2 E2

7. 21.Write the boundary conditions at the interface between two perfect dielectrics.

i)The tangential component of electric field is continuous i.e) Et1=Et2

ii)The normal component of electric flux density is continuous i.e) Dn1=Dn2

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8. Write down the expression for capacitance between two parallel plates.

C=A / d 9. .State point form of ohms law.

Point form of ohms law states that the field strength within a conductor is

proportional to the current density. J=E 10. What is polarization?

The product of electric charge and distance n know as dipole moment. It is denoted by m

where Q is the charge l is the length.

m=Q.l

Dipole moment per unit volume is called Polarization. P = Q/A

11. Write down the magnetic boundary conditions.

i) The normal components of flux density B is continuous across the boundary.ii) The tangential component of field intensity is continuous across the boundary.

12. Write he expression for field intensity due to a toroid carrying a filamentary

current I. H=NI / 2R 13. What are equipotential surfaces?

An equipotential surface is a surface in which the potential energy at every point is of the

same vale.

14. Distinguish between solenoid and toroid.

Solenoid is a cylindrically shaped coil consisting of a large number of closely spaced

turns of insulated wire wound usually on a non magnetic frame.

If a long slender solenoid is bent into the form of a ring and there by closed on itself it

becomes a toroid.

15. State Lenz law.

Lenzs law states that the induced emf in a circuit produces a current which opposes the

change in magnetic flux producing it.

16. What is the effect of permittivity on the force between two charges?

Increase in permittivity of the medium tends to decrease the force between two

charges and decrease in permittivity of the medium tends to increase the force between

two charges.

17. What are the significant physical differences between Poisson s and laplace s

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equations.

Poisson s and Laplace s equations are useful for determining the electrostatic potential

V in regions whose boundaries are known.

When the region of interest contains charges poissons equation can be used to find the

potential.

When the region is free from charge laplace equation is used to find the potential.

18. How is electric energy stored in a capacitor?

In a capacitor, the work done in charging a capacitor is stored in the form of electric

energy.

19. What are dielectrics?

Dielectrics are materials that may not conduct electricity through it but on applying

electric field induced charges are produced on its faces .The valence electron in atoms ofa dielectric are tightly bound to their nucleus.

20. What is a capacitor?

A capacitor is an electrical device composed of two conductors which are separated

through a dielectric medium and which can store equal and opposite charges ,independent

of whether other conductors in the system are charged or not.

21. Define dielectric strength.

The dielectric strength of a dielectric is defined as the maximum value of electric field

that can b applied to the dielectric without its electric breakdown.

22. What is meant by dielectric breakdown?

As the electric field applied to dielectric increases sufficiently, due to the force exerted on

the molecules, the electrons in the dielectric become free. Under such large electric field,

the dielectric becomes conducting due to presence of large number of free electrons. This

condition is called dielectric breakdown.

23. What meaning would you give to the capacitance of a single conductor?

A single conductor also possess capacitance. It is a capacitor whose one plate is at

infinity.

24. Why water has much greater dielectric constant than mica.?

Water has a much greater dielectric constant than mica .because water ha a permanent

dipole moment, while mica does not have.

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25. Define inductance.

The inductance of a conductor is defined as the ratio of the linking magnetic flux to the

current producing the flux. L = N / I 26. Define self inductance.

Self inductance is defined as the rate of total magnetic flux linkage to the current

through the coil. L = / i where, = magnetic flux.i =current.

27. Define mutual inductance.

The mutual inductance between two coils is defined as the ratio of induced magnetic flux

linkage in one coil to the current through the other coil. M = N2 12 / i1Where, N2 = no of turns in coil 2

12 = magnetic flux links coil 2I1 = the current through coil 1

28. Define mmf.

Magnetic motive force (mmf) =is given by mmf = flux X reluctance = . R Amp turn 29. Define reluctance.

Reluctance is the ratio of mmf of magnetic circuit to the flux through it.

R = mmf / flux() 30. What is main cause of eddy current?

The main cause of eddy current is that it produces ohmic power loss and causes local

heating.

31. How can the eddy current losses be eliminated?

The eddy current losses can be eliminated by providing laminations. It can be proved

that the total eddy current power loss decreases as the number of laminations increases.

32. Distinguish between diamagnetic, paramagnetic and ferromagnetic materials.

Diamagnetic: In diamagnetic materials magnetization is opposed to the applied field. It

has weak magnetic field.

Paramagnetic: In paramagnetic materials magnetization is in the same direction as the

applied field. It has weak magnetic field.

Ferromagnetic: In ferromagnetic materials magnetization is in the same direction as the

applied field. It has strong magnetic field.

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33. A ferrite material has R = 50, operate with sufficiently low flux densities and B =

0.05T and H.

The magnetic field intensity H =B /0 R = 796 amperes/m

BIG QUESTIONS:

1. (i) Derive an expression for the capacitance of a spherical capacitor with conducting

shells of radius a and b.

(ii) Obtain the expressions for the energy stored and energy density in a capacitor.

(May/June 2009)

2. (i) Derive the boundary conditions between two magnetic media.

(ii) A solenoid has an inductance of 20mH. If the length of the solenoid is increased by

two times and the radius is decreased to half of its original value, find the newinductance. (May/June 2009)

3. (i) An air core toroid has a mean radius of 40mm and is wound with 4000 turns of wire.

The circular cross section of the toroid has a radius of 4mm. A current of 10A is passed in

the wire. Find the inductance and the energy stored.

(ii) Calculate the inductance of a 10m long co-axial cable filled with a material for which

r = 80 and radii of inner and outer conductors are 1mm and 4mm respectively.(Nov/Dec 2008)

4. (i) Derive the boundary relations at the boundary between a conductor and a dielectric.

(Nov/Dec 2008)

(ii) Parallel plate capacitor is of area 1m2 and has a separation of 1mm. The space

between the plates is filled with dielectric of n =25. If 1000V is applied, find the forcesqueezing the plates together. (April /May 2008)

5. (i) Three point charges 1, 2, 3 coulombs are situated in free space at the corners of an

equilateral triangle of side 1m. Find the energy stored in the system.

(ii) Show that the inductance of the cable L= l2lnbaH. (April /May 2008)6. (i) Derive an expression for the capacitance of a parallel plate capacitor with two

dielectric media.

(ii) A parallel plate capacitor with a separation of 1cm has 29kV applied, when air was

the dielectric used. Assume that the dielectric strength of air as 39kV/cm. A thin piece of

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glass with r =6.5 with a dielectric strength of 290kV/cm with thickness 0.2 cm isinserted. Find whether glass or air will break. (Nov/Dec 2007)

7. (i) Derive an expression for inductance of a solenoid with N turns and l meters length

carrying a current of I amperes.

(ii) Calculate the inductance of solenoid of 200 turns wound tightly on a cylindrical tube

of 6cm diameter.The length of the tube is 60cm and the solenoid is in air.(Nov/Dec 2007)

8. (i)A parallel plate capacitor has a plate separation t. The capacitance with air only

between the plates is C. When a slap of thickness t and relative permittivity r is placedon one of the plates, the capacitance is C. Show that C/C = r t/(t +r (t-t)).

(Nov/Dec 2007)

(ii) Obtain the expression for the inductance of a toroid. (May/June 2007)

9. (i) A dielectric slab of flat surface with relative permittivity 4 is disposed with its surfacenormal to a uniform field with flux density 1.5C/m2. The slab occupies a volume of

0.08m3 and is normally polarized. Determine (1) The polarization in the slab and (2) The

total dipole moment of the slab.

(ii) Capacitance of coaxial cable with two dielectrics 1 and 2. (May/June 2007)10. (i) Discuss briefly about nature of dielectric materials.

(ii) Given the potential field, V = 50 sinr2V, in free space, determine whether V satisLaplaces equation. (May/June 2007)

11. (i) Explain and derive the polarization of a dielectric material.

(ii) Draw and explain the magnetization curve and hysteresis loop of a toroid with

ferromagnetic core. List out any five ferro magnetic material. (Nov/Dec 2006)

12. A solenoid 25cm long, 1cm mean dianeter of the coil turns a uniformly distributed

windings of 2000 turns. The solenoid is placed in uniform field of 2 tesla flux density. A

current of 5A is passed through the winding. Detertmine the (1) maximum force on the

solenoid (2) maximum torque on the solenoid and (3) compute the magnetic moment on

the solenoid. (Nov/Dec 2004)

13. Evalauate the capacitance of (i) a spherical satellite 1.5m diameter in free space.

(ii) a co-axial cable 1.5m long filled with polyethylene (r =2.26) with inner conductor ofradius 0.6 mm and inner radius of outer conductor 3.5 mm.

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(iii) an infintely long conductor with 1.5 mm radius and suspended horizontally at a

height of 15 m above a conducting plane and parallel to it in air. (April /May 2004)

14. (i) Calulate the inductance of a ring shaped coil having a mean diameter of 20 cm. Wound

on a wooden core of 2 cm diameter. The winding is uniformly distributedand contains

200 turns.

(ii) A coil has a self inductance of 1H and a resistance of 4 ohms if it is connected to a 40

volts DC supply,estimate the energy stored in the magnetic field whrn the current has

attained its final steady value. (April /May 2004)

UNIT-IV

Two mark questions:

1. Define Poynting vector?The cross product of electric field and magnetic intensity vector is defined as pointing

vector P = E x H (or)

Poynting vector gives the magnitude as well as the direction in which power flows in

time varying electromagnetic fields.

2. Determine emf developed about the path r = 0.5, z = 0 and t = 0. If B = 0.01 sin 377 t.

e = - d / dt =- d / dt (B.A)

= -A d / dt (0.01 sin 377 t)

e t=0 = -2.96V

3. Write down Maxwells equation derived from Faradays law?

E. dl =- (B / t ) ds---- Integral form

Del cross E = - B / t --- Differential form

4. What is displacement current and conduction current?

The current through a capacitor is called displacement current. It is denoted as ID.

ID = dQ / dt

The current through a conductor is called conduction current. It is denoted as IC.

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IC = V / R

5. Brief about the amperes circuital law for a in integral form.

Amperes law states that the line integral of magnetic field intensity H on any closed path

is equal to the current enclosed by the path

H. dl = I

H. dl = {J + D / t} ds

6. State Faradays law for a moving charge in a constant magnetic field.

Faradays law states that the electromagnetic force (mmf) induced in a circuit is equal to

the rate of decrease of the magnetic flux linkage the circuit.

v = - d / dt

7. Write down Maxwells equation in integral form?

(i) H. dl = {J + D / t} ds (ii) E. dl =- (B / t ) ds (iii) D. ds = . Dv (iv) B. ds = 0

8. Write Stokes theorem and Divergence theorem. Mention it uses?

Stokes theorem:

The line integral of a vector around a closed path is equal to the surface integral of the

normal component of its equal to the integral of the normal of its curl over any closed

surface. H. dl = x H ds Divergence theorem:

The integral of the normal component of ant vector field over a closed surface is

equal to the integral of the divergence of this vector field over a volume enclosed by the

closed surface. D. ds = .D dv These above theorems are used to determine the Maxwells equation from fundamental

laws.

9. State Poynting Theorem?

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Poynting Theorem states that the net power flowing out of a volume v is equal to the time

rate of decrease in the energy stored within a volume v minus the conduction losses.

(E x H). ds =- / t ( E2 + H2) dv - E2 dv.

10. Mention significance of displacement current density?

Displacement current density = JD =D / t =E / t

For Maxwells equation for free space x H = JD =D / t

11. Discuss the condition under which conduction current is equal to displacement

current?

In a conductor conductivity goes to zero means it act as a dielectric and corresponding

current is displacement current

12. Brief about complex Poynting vector?

The complex Poynting vector is given by, P = (E x H)

The product of E and H is vector product. The mutually perpendicular components E and

H, contribute to the power flow. This power flow is directed along the normal to the plane

containing E and H.

13. Write Helmholtzs equation.2E 2E =0

Where =[ j ( + j )]1/2

14. What is meant by displacement current?

Displacement current is nothing but the current flowing through capacitor. J= D / t

15. State Maxwells fourth equation.

The net magnetic flux emerging through any closed surface is zero.

16. State Maxwells Third equation.

The total electric displacement through the surface enclosing a volume is equal to the

total charge within the volume.

17. State electric displacement .

The electric flux or electric displacement through a closed surface is equal to the charge

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enclosed by the surface.

18. What is displacement flux density?

The electric displacement per unit area is known as electric displacement density or

electric flux density.

19. What is the significance of displacement current?

The concept of displacement current was introduced to justify the production of

magnetic field in empty space. It signifies that a changing electric field induces a

magnetic field .In empty space the conduction current is zero and the magnetic fields are

entirely due to displacement current.

20. Distinguish between conduction and displacement currents.

The current through a resistive element is termed as conduction current whereas the

current through a capacitive element is termed as displacement current.

BIG QUESTIONS:

1. Write down the Maxwells equation in integral and point form and give their physical

interpretation.

2. Derive the poynting vector from Maxwells equation and explain.

3. Derive the Maxwells curl equation from amperes law and faradays law. Explain the

equations in phasor form for time harmonic fields.

4. A circular loop of N turns of conducting wire lies in the x-y plane with its center at the

origin of a magnetic field specified by B = az B0 cos(r/2b)sint, where b is the radius ofthe loop and is the angular frequency. Find the emf induced in the loop.

(Nov/Dec 2003)

5. Define poynting vector and deduce the poyntings theorem neatly. (April/May 2004)

6. State and prove Poynting theorem. (Nov/Dec 2006)

7. Prove that x E =-B /t. (May/June 2007)8. Discuss about Poynting vector and power flow. (May/June 2007)

9. Obtain the expression for instantaneous power flow /unit area. (May/June 2007)

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10. From the fundamental law, derive the generalized Maxwells equations in integral form.

(Nov/dec 2004)

11. Define poynting vector and prove that the electromagnetic power flow is the product of

electric and magnetic field intensities. (Nov/dec 2004)

12. If D = 20x aX -15y ay+ kz aZ C/m2, find the value of k to satisfy the Maxwells equation

for region =0 and v= 0. (May/June 2006)

13. A conductor 1 cm in length is parallel to z axis and rotates at radius of 25 cm at 1200

rpm. Find induced voltage, if the radial field is given by B = 0.5ar T. (May/June 2006)

14. If the magnetic field H = (3x cos +6y sin )az, find current density J if the fields areinvariant with time. (May/June 2006)

15. Derive the expression for total power flow in a coaxial cable. (May/June 2006)

16. A conducting cylinder of radius 5 cms, height 20cm , rotates at 600 rps in a radial field

B =0.5 tesla. The sliding contacts at the top and bottom are connected to a voltmeter.

What is the reading of voltmeter? (May/June 2006)

17. The conduction current flowing through a wire with conductivity = 3 x 107 s/m andrelative permittivity r = 1 is given by Ic = 3 sint (mA). If =108 rad/s, Find thedisplacement current? (May/June 2006)

18. A material for which = 4.5 mho/m and r =1, electric field intensity is E = 300 sin109tux V/m. Determine the conduction and displacement current densities and the frequency

at which they equal magnitude. (Nov/Dec 2006)

19. Explain about displacement current and displacement current density. Also find

displacement current density for the field E = 300 sin109t V/m. (Nov/Dec 2006)

20. Find the frequency at which conduction current density and displacement current density

are equal in (1) distilled water, for which r =81 and = 2.0 x 10-4 mho/m.

(2) sea water, for which r =1 and = 4.0 mho/m. (May/June 2007)

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21. Given the conduction current density in a lossy dielectric as Jc =(0.02 sin109t) A/m2. Find

the displacement current density if = 103 mho/m and r =6.5 (Nov/Dec 2006)

UNIT-V

Two mark questions:1. Define a wave?

If a physical phenomenon that occurs at one place at a given time is reproduced at other

places at later times, the time delay being proportional to the space separation from the

first location, then the group of phenomena constitute a wave.

2. Find the velocity of a plane wave in a lossless medium having a relative permittivity

of 5 and relative permeability of 2.

v =1 / = 1/ (0 r 0 r) =

3. Define the term intrinsic impedance of free space with its value?

It is the ratio of electric field to magnetic field or It is the ratio of square root of

permeability to permittivity of the medium. = E /H = (0 / 0) =377 ohms4. What is homogeneous material?

The medium is called homogeneous when the physical characteristics of the medium do

not vary from point to point but remain same everywhere throughout the medium.

5. Mention properties of uniform plane wave?

1. At every point in space, the electric field E and magnetic field H are perpendicular to

each other and to the direction of the travel.

2. The fields are vary harmonically with time and at the same frequency, every where in

space.

3.

Each field has the same direction, magnitude and phase at every point in any plane perpendicular to the direction of wave travel.

6. What is meant by skin effect or skin depth or depth of penetration?

Skin depth is defined as that of depth in which the wave has been attenuated to 1/e or

37% of its original value.

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=1/ =2/(j) = for good conductor.

7. Brief about the intrinsic impedance for a perfect dielectric medium?

= /(1+j/2)

8. What is Polarization?

Polarization is defined as the Polarization of a uniform plane wave refers to the time

varying nature of the electric field vector at some fixed point in space.

9. What is meant by linear polarization?

If x and y component of electric field Ex and Ey are present and are in phase, the resultant

field has a direction at an angle of tan-1(Ey/Ex) and if the phase angle is constant with

time, the wave is to be linearly polarized.

10. What is meant by circular polarization?

If x and y component of electric field Ex and Ey have different amplitude and 90 phase

difference, the locus of the resultant electric field E is a circle and wave is to be circularly

polarized.

11. What is meant by elliptical polarization?

If x and y component of electric field Ex and Ey have different amplitude and 90 phase

difference, the locus of the resultant electric field E is a ellipse and wave is to beelliptically polarized.

12. What is Brewster Angle?

Brewster Angle is an incident angle at which there is no reflected wave for parallely

polarized wave.

= tan-1 2/1where, 1 = dielectric constant of medium 1, 2 = dielectric constant of medium 2

13. Write down the wave equation for E and H in free space.2H 2Ht2=0 2E 2Et2=0

14. Define propagation constant.

Propagation constant is a complex number = +j where is attenuation constant

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is phase constant = j (+j) 15. Define loss tangent.

Loss tangent is the ratio of the magnitude of conduction current density to displacement

current density of the medium.

16. Define reflection and transmission coefficients .

Reflection coefficient is defined as the ratio of the magnitude of the reflected field to that

of the incident field.

17. Define transmission coefficients.

Transmission coefficient is defined as the ratio of the magnitude of the transmitted field

to that of incident field.

18. 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.

19. 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.

20. Write short notes on imperfect dielectrics .

A material is classified as an imperfect dielectrics for

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( ii )obliquely to the surface of perfect conductor. (April/May 2008)

3. Derive the wave equations in phasor form and also derive for ,,and . (Nov/Dec2007 4. Explain in detail the wave incident normally on perfect dielectric. (May/June 2007)

5. (i)Explain about the propagation of EM waves in good conductor.(ii) A uniform plane wave is travelling at a velocity of 2.5 x 105 m/s having wavelength

= 0.25mm in a good conductor. Calculate the frequency of wave and the conductivitthe medium. (Nov/Dec 2007)

6. Derive the wave equations for plane waves in

( i) free space ( ii) homogeneous materials (iii)conducting medium. (April/May 2008)

7. (i) Describe about linear and circular polarization.

(ii) Describe about reflection of plane waves by a perfect dielectric. (May/June 2007)8. (i) Calculate the attenuation constant and phase constant for a uniform plane wave with

frequency of 10 GHz in a medium for which = 0 , r =2.3 and =2.56 x 10-4mho/m(ii) Derive the expressions for the attenuation constant, phase constant and intrinsic

impedance for a uniform plane in a good conductor. (May/June 2006)

9. (i) Assume that E and H waves, travelling in free space, are normally incident on the

interface with a perfect dielectric with r =3. Calculate the magnitudes of incident,reflected and transmitted E and H waves at the interface.

(ii) A uniform plane wave of 200MHz, travelling in a free space impings normally on a

large block of material having r = 4, r = 9, = 0. Calculate transmission and reflectioncoefficients at the interface. (May/June 2006)

10. Derive the expression for total field when a horizontally polarized EM wave is incident

obliquely on a perfect conductor.

11. Derive the expression for total field when a vertically polarized EM wave is incident

obliquely on a perfect conductor.

12. Determine the reflection coefficient of oblique incidence in perfect dielectric for

perpendicular polarization.

13. Determine the reflection coefficient of oblique incidence in perfect dielectric for parallel

polarization.

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14. A lossy dielectric is characterized by r = 2.5, r = 4 and = 10-3 mho/m at 10MHz. LetE =10e-Vz ax V/m. Find (i) (ii) (iii) (iv) V p (v) ?

15. Given two dielectric media, medium 1 is free space and medium 2 has 2 = 4 0 and 2 =0 . Determine reflection coefficient for oblique incidence 1 =30 for a) perpendicular polarization and b) parallel polarization.

16. For a lossy dielectric material having r = 48, r = 1, = 20 s/m. Calculate the propagation constant at a frequency of 16 GHz.

17. Find the depth of penetration of plane wave in copper at a power frequency of 60Hz and

at microwave frequency 1010 Hz. Given = 5.8 x 107 mho/m18. (i)Derive the wave equation starting from maxwell equation for free space

(ii)Explain reflection of uniform plane waves with normal nicidence at a plane dielectric

boundary. (May/June 2009)19. Explain the types of polarization of uniform plane wave.

(May/June 2009)

20. (i)Derive wave equation for E and H in conducting medium

(ii)Write briefly on total internal reflection (Nov/Dec 2009)