s.k.p. engineering college, tiruvannamalai iii sem skp...

S.K.P. Engineering College, Tiruvannamalai III SEM

Department of EEE 1 EE8391 Electromagnetic Theory

SKP Engineering College

Tiruvannamalai – 606611

Department Of Electrical and Electronics Engineering

Question Bank

on

EE 8391 ELECTROMAGNETIC THEORY

2018



Unit I ELECTROSTATIC FIELD

Part - A Questions & Answers

1.Mention the sources of electromagnetic fields. .(Apr/May-2017,May/June-2016,Nov/Dec-14)

The sources of EMF are electrical lighting and appliances, computer monitors, microwave

ovens, radios, TV, Cellular phones, broadcast stations, overhead lines and communication satellites.

2.How are the unit vectors defined in cylindrical coordinate systems? ?(Nov/Dec-2013)

In cylindrical coordinate system the unit vectors are represented as ar , a and az

3. Define Curl.

The curl of a vector field, denoted or [the notation used in this work], is defined as

the vector field having magnitude equal to the maximum "circulation" at each point and to be

oriented perpendicularly to this plane of circulation for each point. More precisely, themagnitude of

is the limiting value of circulation per unit area. Written explicitly

4.State the physical significance of curl of a vector field. (Nov/Dec-2011)

The physical significance of the curl of a vector field is the amount of "rotation" or angular

momentum of the contents of given region of space. It arises in fluid mechanics and elasticity theory.

It is also fundamental in the theory of electromagnetism, where it arises in two of the four Maxwell

equations.

5.What is the physical significance of divergence of a vector field? May/Jun-2013)

Divergence of a vector field at a given point is a measure of how much the field represented by

divergence of a vector field A converges or diverges from that point.Diverging-Field is spreading

from point P[positive] Converging-Field converges at point P[negative].

6.Give practical examples for diverging and curling fields.

Diverging Field

Air velocity flowing out from punctured tube and gas velocity going out from ma hole in a gas

balloon are the examples of diverging fields.

Curling field

A body rotating about fixed axis, the water velocity in a river are the examples of curling field.

7.State the conditions for a vector A to be [a] solenoidal [b] irrotational.

A vector is said to be solenoidal if its divergence is zero.

A = 0

A vector is said to be irrotational if its curl is zero.

A = 0

8.State Stoke’s theorem.(Apr/May-2017,Nov/Dec-2016,13,May/June-2014).

The line integral of a vector A around a closed path L is equal to the integral of curl of A over

the open surface S enclosed by the closed path L.

http://mathworld.wolfram.com/Area.html

http://mathworld.wolfram.com/VectorField.html



( H )N =

H.d L

S → 1

S

N = Normal to ΔS according to Right hand rule.

d LS = Perimeter of the incremental surface

Curl of H in the normal direction is the dot product of curl of with an

This theorem is applicable only when A and A are continuous.

9.Define Divergence. (May/June-2016,Nov/Dec-2014,10)

Divergence: The divergence of a vector „A‟ at any point is defined as the limit of its surface

integrated per unit volume as the volume enclosed by the surface shrinks to zero.

.A = Lt 1

A.nds

V

v→0 S

.A =div A

Divergence of a vector is scalar quantity.

10.State Coulomb’s law of electrostatic charges. Nov/Dec-2017)

The force of attraction or repulsion between the two point charges will be

Acts along the line joining the two point charges

Directly proportional to the point charges Inversely proportional to the square of the distance between them and

F = Q1Q2 a12

4R122

11.State the properties of electric flux lines. (Apr/May-2018)

Electric field lines start from positive charge and terminate on negative charge.

If negative charge is absent then flux lines terminate at infinity

The lines are parallel and never cross each other.

The lines are independent of the medium in which charges are placed.

The lines always enter or leave the charged surface normally.

12.What is meant by equipotential surface?

An equipotential surface is a surface on which the electrostatic potential is constant. In

electrostatics, a conductor has to be equipotential, because if it weren't, the free charges therein

would get pushed around until the potential were equalized. Outside the sphere, the potential is NOT

generally constant.



13.Electric field is conservative field. Justify. (Apr/May-2017)

A gravitational field is proportional to 1/r^2 with a unit vector pointing in the negative

direction of r at all times. Using the definition of curl in spherical coordinates (see this in any calculus textbook) you will find that it will be zero. For a field to be conservative, the line integral of

it from one point to another should be independent of the path. This has the implication that the line

integral over a closed path is zero or, using the stoke

14.What is the use of Gauss -law? (May/June-2016)

Gauss law can be used to find Electric flux density or Electric field intensity for symmetrical

charge distributions, such as point charge, an infinite line charge, infinite sheet of charge and a

spherical distribution of charge. Gauss law can be used to find the charge enclosed or the flux

passing through the closed surface.

15.Define vector and scalar field. Give an example.

A scalar field is specified by a single number at each point.

Eg.Temperature and pressure of a gas.

A vector field is specified by both magnitude and direction at each point in space.

Eg Velocity and acceleration of a field.

16.Why Gauss law cannot be applied to determine the electric field due to finite line charge?

Gauss law cannot be applied on non Gaussian surface. It can be applied if the surfaces enclose the

volume completely. Therefore Gauss law cannot be applied to determine electric field due to finite

line charge s theorem, the curl of the field is zero. In physics, the line integral of a force field (e.g.

gravitational or electric field) is the energy that it will take to move an object from one point to

another.

17.List the properties of gradient of a scalar.

1. The gradient W gives the maximum rate of change of W per unit distance.

2.The gradient W always indicate the direction of maximum rate of change of W

3.The gradient W at any point is perpendicular to the constant surface.

18. What is Electric field intensity?

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

Gauss's law states that the net flux of an electric field through a closed surface is proportional to the

enclosed electric charge. The electric flux is defined as the electric field passing through a given area

multiplied by the area of the surface in a plane perpendicular to the field.

19.Points P and Q are located at (0,2,4) and (-3,1,5). Calculate the distance vector from P

and Q.

|RPQ|= SQRT(32+1

2+(-1)

2)

=SQRT(11)

20.Find the unit vector extending from the origin towards the point P(2,-2,1).

IPO=2IX-2IY+IZ/(3)

=0.66IX-0.66IY+0.33IZ



21.Obtain the Cartesian coordinate system the gradient of the function:

f(r,Ɵ,z)=5r4z

3sinƟ.

=

=20

=5

22.What is gradient.(Nov/Dec-2017)

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

function .If scalar V represents electric potential gradiant

V= grad V

PART-B

1.Determine curl of these vector fields.(Apr/May-2010,2013)

P = x2 yzax + xzaz

Q = sina + 2 za + z cosaz

T = 1/r2 cos ar + r sin cos a + cos a

2.Find the gradient of the following scalar fields(Apr/May-2010,2013)

V= e−z sin 2x cosh y

U= 2 z cos 2

W =10r sin2 cos

3.Determine the electric field intensity at P[-0.2, 0, - 2.3] due to a point charge of + 5nC at Q[0.2,

0.1, -2.5] in air. All dimensions are in meters.(Apr/May-2010,Nov/Dec-2016)

4.Given point P [–1, 4, 3] and vector A = yax + (x + z)ay express P and A in

cylindrical and spherical coordinates. Evaluate A at P in the Cartesian and spherical systems.

(Apr/May-2011)

5. Determine divergence and curl of the vector A = x2 ax+ y 2 ay+ z 2 az (Apr/May-2011,2015,

Nov/Dec-2013)

6.Write short notes on the following 1.Gradient 2.Divergence 3.Curl (Apr/May-

2010,2013,2017,Nov/Dec-2013,2014,May/June-2016,2014)

7. Transform the vector A = 4ax − 2ay − 4az at P[x=+2,y=+3,z=4] to spherical coordinate.(Nov/Dec-2010,2012)

8. Given point P(-2,6,3) and A = yi + (x + z) j express P and A in cylindrical coordinates (Nov/Dec-2012,May/June-2015)



9. Using Divergence theorem, evaluate F.nds where F = 2xyi + y 2 j + 4 yzk and S is the

surface of the cube bounded by x=0,x=1,y=0,y=1 and z=0,z=1(Apr/May-2010, 2013)

10. Verify divergence theorem for the following case A = xy 2 a+ y3 a+ y 2 za and the surface is

cuboid defined by 0<x<1,0<y<1,0<z<1.(Nov/Dec-2011,2012)

11.Three concentrated charges of .25µC are located at the vertices of an equilateral triangle of 10cm

side.Find the magnitude and direction of the force on one charge due to other two charges

12.Derive Electric field intensity by applying Gauss‟s law to an [i] infinite line charge and [ii]

infinite sheet of charge(Nov/Dec-2016)

13.Three point charges in free space are located as follows: 50nC at (0,0) m: 40nC at(3,0) m; -60 nC

at (0,4) m. Find the electric field intensity at (3,4) m.(May/June-2016)

14.A circular ring of radius „a‟ carries a uniform charge L C/M and is placed on the XY plane with

the axis same as Z axis. Find the electric field intensity.(Nov/Dec-2014)

15.Find Electric field intensity of a Uniformly charged sphere using Gauss law.(Nov/Dec- 2016)

16.Find the force on a charge Q1 of 20 µC at (0,1,2) m due to Q2 of 300 µC at (2,0,0) (Nov/Dec-

2016)

17.Transform the vector A=3i-2j-4k at p(x=2,y=3,z=3) to cylindrical coordinate. (May/June- 2014)

18.Describe the classification of vector fields. (May/June-2013)

19.Explain the coulomb‟s law of force.(Nov/Dec-2014)

20.Describe how the different elements in length, area, and volume are defined in various orthogonal

coordinate systems.(Apr/May-2015)

21. Using Divergence theorem, evaluate F.nds where F = 2xyi + y 2 j + 4 yzk and S is the

s is the surface of the cube bounded by x=0,x=1,y=0,y=1 and z=0,z=1 (Apr/May-2015)

22.Derive the laplace‟s equation.obtain the laplacians operator in the cylindrical coordination

system. (May/June-2014)

23.State and prove gauss divergence theorem. (Apr/May-2017,Nov/Dec-2016).

24.with neat diagrams ,explain the spherical system with co-ordinates (R,ɵ,ɸ)(Apr/May-2018)

25.By mean of gauss Law to find the electric field indensity at any point P due to a straight ,

uniformly charged wire of linear wire of linear charge density +LC\m . the point p is at a distance of

‘h’ m above the wire.(Apr/May-2018)

26.State gauss law and give any two application (Nov/Dec-2017,May/June-2016)

27.State and prove stoke’s theorem(Nov/Dec-2011)



Unit – II

ELECTROSTATICS – II

PART – A

1. Define Electric Potential. .(May/June-2016)

Potential at any point is defined as the work done in moving a unit positive charge from infinity to that point in an electric field.

It can be expressed as

V = Q / 4πεor

Where Q is the charge

εo is the permittivity of free space

r is the radius.

2.What are the significant physical differences between Poisson’s and laplace’s equations.

(Nov/Dec-2011)

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.

3.Define electric field.

Electric field due to a charge at a point in space is defined as the force experienced by a unit

positive charge placed at that point. Electric field is a vector quantity. The direction of electric field

due to a point positive charge is Radially outward and the direction of electric field due to a point

negative charge is Radially inward. S.I. unit of electric field is newton per coulomb [NC-1]

4.Mention any two properties of electric field lines. (Apr/May-2018,2013)

• The electric lines of force are imaginary lines.

• Electric field lines start from a positive charge and end on a negative charge.

• Electric field lines do not intersect each other

5. Give the relationship between potential gradient and electric field.

The relationship between potential gradient and electric field can be given

E=-V

E= -[ + + ]V

6.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 of a dielectric are tightly bound to their nucleus. Examples

for dielectric are air, water, mica, etc.,



7. What is an equipotential surface?

An equipotential surface is an imaginary surface in an electric field of a given charge distribution, in which all points on the surface are at the same electric potential.

8. What is an electric flux and define electric flux density.

The total number of lines of force in any particular electric field is called electric flux. It is

represented by the symbol. Similar to the charge, unit of electric flux is also Coulomb.

The net flux passing normal through the unit surface area is called electric fluxdensity. It is denoted as D . It has a specified direction which is normal to the surface area under consideration hence it is a vector field.

9.State the applications of Poisson’s equation and Laplace’s equation.

• To obtain potential distribution over the region.

• To obtain E in the region.

• To check whether given region is free of charge or not.

• To obtain the charge induced on the surface of the region.

10.Define Polarization in dielectric material.(Nov/Dec-2011)

The applied field E shifts the charges inside the dielectric to induce the electric dipoles. This process is called Polarization. It can also be said as dipole moment/ unit volume.

11.Write the expression for the energy density in electrostatic field.

The expression for the energy density in electrostatic field can be

stated as

= ½

= ½ DE 12. Define equipotential lines.

Equipotential lines are like contour lines on a map which trace lines of equal altitude. In this case the “altitude” is electric potential or voltage in equipotential lines is always perpendicular to the

electric field. Equipotential lines and field lines are always orthogonal to each other.

13.What is polarization? State the expression for polarization.

Polarization is a characteristic of the waves which specifies the direction of the electric field

“vector” in a relation to the direction of the travel. Plane containing the electric field that is the plane

in which the electric field is oscillating is called as the plane of polarization. It is also defined as the

dipole moment/ unit volume. The relation of polarization in terms of the

applied and internal fields is given by

P = C/m2



14. What is dielectric polarization?( May/June-2016)

The alignment of the dipole moments of the permanent or induced dipoles in the direction of applied electric field is called polarisation or electric polarisation. The magnitude of the induced dipole moment p is directly proportional to the external electric field E.

p = α E,

where α is the constant of proportionality and is called molecular polarisability.

15.Write the expression for the energy density in electrostatic field and capacitance for coaxial

cable.

The expression for the energy density in electrostatic field can be stated as

= ½

= ½ DE

The expression for the capacitance for coaxial cable can be stated as C=2 0 r /

ln[b/a]

Where b is the outer radius of the cable and a is the inner radius of the cable

16.Obtain Poisson’s equation from Gauss’s law.

Gauss‟s law in point form is given by

.D= v

where D is the electric flux density and v is the volume charge density.

But, D= E /

.D= v

But, E = - v

v = - v/

v = - v/

Hence the Poisson‟s equation.

17.Write Poisson’s equation in vector notation for simple medium.

v = - v/

Where V is the potential

v is the volume charge density,

is the dielectric constant or permittivity of the medium.

18. Why is the electrostatic potential continuous at the boundary?

The electrostatic potential is continuous at the boundary because the tangential component of the electric field is continuous across the boundary.



19.Distinguish between conductor and dielectric.

Conductor:

• Conductor has free charges.

• Conduction current flows in conductor. Dielectric

• Dielectric does not have free charges

• Displacement current flows in a dielectric.

20. Define Dielectric strength. (Nov/Dec-2017)

Dielectric Strength is a measure of the electrical strength of a material as an insulator. Dielectric strength is defined as the maximum voltage required to produce a dielectric breakdown

through the material and is expressed as Volts per unit thickness. The higher the dielectric strength of

a material the better its quality as an insulator.

20.Give some examples for uniform and non uniform electric fields.

In uniform field, the lines are parallel and equipotential lines a parallel orthogonal of

lines. Actually equipotential are plane surface perpendicular to E and for a fixed voltage increment

v are spaced uniformly. In non-uniform field, the lines diverge in going from astronger to a weaker

field region. Further mode, for field voltage increments such as 10v.

The equipotential surfaces become more widely spaced in the weaker field regions.

22.State expression the electric field intensity due to infinite line charge.

E = ar V/m

Where is the line charge density,

r is the perpendicular distance of point p from the line charge.

ar is the unit vector in direction of the perpendicular distance of point p from the line charge

23. Draw the equipotential lines and electric fields for a parallel plat capacitor?(Apr/May-

2008,10)



24. Define electric dipole and dipole moment.

Electric dipole or dipole is nothing but two equal and opposite point charges are separated by a very small distance.

Electric dipole moment is defined as the product of electric charge and distance n in it. It is denoted by m

m = Q * L

Where Q is the charge and L is the length.

25. State Poisson’s equation and Laplace equation for simple medium. .(Nov/Dec-2017

,May/June-2014)

Poisson‟s equation v = - /

Laplace equation v = 0

Where is the volume charge density,

is the dielectric constant or permittivity of the medium.

is the laplacian operator

V is the electric potential

26.What is the potential at a point p due to parallel line charges which are equal and opposite?

(Nov/Dec-2008)

Potential at a point p due to parallel line charges which are equal and opposite is given as E= .

27.What is a conservative field?(Apr/May-2017)

Conservative vector fields have the property that the line integral is path independent, i.e., the

choice of any path between two points does not change the value of the line integral. Path

independence of the line integral is equivalent to the vector field beingconservative.

28.What is capacitor and capacitance?

A capacitor is a passive electronic component that stores energy in the form of an electrostatic field. In its simplest form, a capacitor consists of two conducting plates separated by an insulating

material called the dielectric.

29.Find the capacitance of an isolated spherical shell of radius a.

The capacitance of spherical or cylindrical conductors can be obtained be evaluating the voltage difference between the conductors for a given charge on each.

31.Define electric potential and potential different difference.

Potential difference, or voltage, is the difference in electric potential energy between two

points. It is denoted by ∆V and has units of volts, or joules per Coulomb



PART – B

1.Conducting spherical shells with radii a = 10cm and b = 30 cm are maintained at a potential

difference of 100V such that V[r = b] = 0 and V[r = a] =100. Determine V and E in the region

between the shells.(Apr/May-2010,2013)

2.State how the capacitance of a parallel plate capacitor is related to the plate area

and plate separation. Determine the capacitance for plates of area 20 cm2 and separation 8.854 mm.

Calculate the electric potential between the plates, the electric field in the region between the plates

and the energy stored when the charge of the capacitor is 44.27 nC. (Apr/May-2014,Nov/Dec-

2012,May/June-2016)

3.Two parallel plate capacitors with uniform surface densities equal and opposite to

each other have an area of 2m2 and distance of separation of 2.5 mm, in free space. A steady

potential of 200 volts is applied across the capacitor formed. If a dielectric of width 1 mm is inverted

into this arrangement what is the new capacitance if the dielectric is a perfect non-

conductor.(May/June-2009)

4.Derive expression for electric field intensity between two infinitely conducting plane. (Nov/Dec-

2015)

5.Derive the boundary conditions at the interface of two dielectric media .(Apr/May-2007,Apr/May-

2008, Nov/Dec-2008, Apr/May-2010, 2015,Nov/Dec-2014,2013, Apr/May-2017)

6.Determine the capacitance of concentric cylinders with mixed dielectrics. (Nov/Dec-2008,

Apr/May-2017)

7.Derive Poisson‟s and Laplace equation.(Nov/Dec-2009,2016,Apr/May-18)

8.Derive expression for capacitance of a parallel plate capacitor having three dielectric media.

(Nov/Dec-2010, 2014, Apr/May-2017)

9.Derive the expression for energy density in electrostatic fields.(Apr/May-2010,Nov/Dec- 2013)

10.Derive expression for electric field intensity and potential at any point due to a charged circular

disc. (Nov/Dec-2015,Apr/May-2009)

11.Using Gauss‟s law, obtain an expression for the electric field due to an infinitely long straight

uniformly charged conductor. (May/June-2016,Apr/May-2017) 12.Using Gauss‟s law, obtain an expression for the electric field due to uniformly charged circular

disc of col/m2.

(Nov/Dec-2016) Obtain the electric potential due to electric dipole.(Apr/May-2017)

13.Explain the potential at a point in an electric field. Derive the electric field intensity at any point

in a field due to a point charge.(May /June-2016)

14.Calculate the potential at a point P(0,0) m due to point charges Q1 and Q2. Q1=10-12

Coulomb is

located at(0..5,0) m and Q2=-10-11

Coulumb is located at (-0.5,0)m.(May/June- 2016).

15.Find the potential at rA=5 m with respect to rB=15 m due to point charge Q=500pC at the origin

and zero reference at infinity.(Nov/Dec-2016).

16.Find the capacitance between two parallel conductor. The radius of conductor is „r‟ separated by

a distance „d‟ mtrs. Both wire are carrying the current in opposite direction. (May/June-

2014,Nov/Dec-2016)

17.Explain briefly the polarization in dielectrics(Apr/May-2018,Nov/Dec-2017)



Unit – III

MAGNETOSTATICS

PART - A

1.What is the force on a charge, moving in a uniform magnetic field?

The force on a charge Q moving in a uniform magnetic field B with velocity v is given by

F = Q(v B) N

F = BQv sin

where, Q is the charge.

v is the velocity with which the charge moves in the field.

B is the magnetic flux density

is the angle between the direction of B and the direction in which the charge moves

2.What is the force experienced by a current carrying element in a uniform magnetic field?

The force experienced by a current carrying element Idl in a uniform magnetic field B is given by

F = I (dl B N

F = BIl sin N

where, Q is the charge.

v is the velocity with which the charge moves in the field.

B is the magnetic flux density

is the angle between the direction of B and the direction of current in the conductor.

3.Give the relation between Magnetic flux and Flux density.

The relation between Magnetic flux and flux density is obtained through the property of

medium and permeability µ . The relation can be given as given as,

B =µH .

Where,B is the magnetic flux density

µ is the permeability

H is the magnetic field intensity.

4.State Lorentz’s law of force. (Nov/Dec-2011,2013)

If a charged particle is moving with velocity „v‟ in the presence of both an electric field „E‟

and a magnetic field „B‟, then the total electromagnetic force acting on it is

F = Q[E+v*B]

This is called Lorentz‟s law or Lorentz‟s force.

Where, F is the force



v is thevelocity

B is the magnetic flux density E is the electric field

Q is the charge.

5. Define Magnetic flux density.

The total magnetic lines of force i.e. magnetic flux crossing a unit area in a plane at right angles to the direction of flux is called magnetic flux density. It is denoted as B

B = A 2 Wb/m [or] Tesla

Where, B is the magnetic flux density

is the permeability

is the total flux

is the magnetic field intensity.

6.State Biot-Savart’s law. (Apr/May-2017,May/June-2016,Nov/Dec-2014)

The Biot-Savart law states that the magnetic flux density produced by a current element at any point in a magnetic field is proportional to the current element and is inversely proportional to

the square of the distance between them.

B =

Idl sin

Wb/m2

4r 2


is the permeability r is the distance

7.State Ampere’s law for a magnetic field. (Nov/Dec-2016,May/June-2016,14)

The Ampere‟s law states that the line integral of H around a single closed path is equal to the current enclosed.

It can also be stated as the line integral of B around a single closed path is equal to the

permeability of the medium times the current enclosed.

H dl = I

B dl = I Where, B is the magnetic flux density

µ is the permeability

H is the magnetic field intensity

8.What is the force between two current carrying conductors?

The force between the two conductors carrying current I1 and I2 separated by a distance r is given by



F =

0 I1I2

N

2r

Where, F is the force

µ0 is the permeability

I1 and I2 are the current passing through the conductor.

r is the distance

9. Give the relation between B and magnetic vector potential.

B = CurlA

10.What is the magnetic field at any point due to a infinitely long conductor carrying current?

B = Wb/m2

2d


µ0 is the permeability of the medium


d is distance between the conductor and the point where the field is required.

11.What is the magnetic field at the centre of the circular coil carrying current?

B = 0 I Wb/m2

2a


µ0 is the permeability of the medium

I is the current in the coil.


12.Write down the equation for general form, integral form and point form of the ampere’s

law.

General form of ampere‟s law can be given as

= I

Integral form of ampere‟s law can be given as

=

Point form of ampere‟s law can be given as



* H = J.

13.Give the similarities between Electrostatic field and Magnetic field.

Electroststic field Magnetic field

1.charges are rest 1.charges are in motion

2.energy stored in ½ cv^2 2.energy stored in ½ LI^2

3.Electric flux density D= cm^2 3.Magnetic flux density B=HWeb/m^2

4.Electric field indensity E volts/m 4.Magnetic field indensity HA/m

14. State Ampere’s Circuital law. Must the path of integration be circular?(Nov/Dec-2017)

Ampere‟s Circuits law states that the line integral of the H about any closed path is exactly equal to the direct current enclosed by the path.

= I

Where H is the magnetic field intensity and I is the current in the closed path

The path of integration must be enclosed one. It could be any shape and it need not be

circular alone.

15.List the applications of Ampere’s circuital law.

due to infinitely long straight conductor.

due to co axial cable.

due to infinite sheet of current.

16.State the expression for H due to infinite sheet of current.(Apr/May-2008)

Expression for H due to infinite sheet of current can be given as

= *

Where is the Current density A/m.

17. State the expression for [i] energy stored in magnetic density and [ii] energy density in

magnetic field.

[i] Energy stored in magnetic density Energy stored in magnetic density, W = ½ LI^2

Where L is the inductance

I is the current

[ii] Energy density in magnetic field

Energy density, w = 1/2 BH or

[iii] Energy density, w =1/2µH



18. Define magnetic moment. (Nov/Dec-2014)

Magnetic moment is defined as the maximum torque per magnetic induction[flux density]. m =T/B

Where T is the maximum torque

B is the magnetic flux density.

19.Give torque on closed circuits.

The torque on closed circuit in a magneticfield is T=BIA sinθ

T=mBsinθ where m is magnetic moment

T=m*B.

20.Give torque on a solenoid.

Torque on a solenoid in a magnetic field is

T=n/2.2IAB

=nBIA

=mB where m=nIA.

21.A circular coil of radius 2m carries a current of 4A what is the value of magnetic field

intensity at the centre.

I = 4A a=2m

H=I/2a=4/2*2 = 1A/m.

22.A flux density vector in air of1 web/m2 is emerging normally magnetic material with μr= 1000.What is the value of flux density in magnetic material.

According to boundary condition, the normal component of magnetic flux density is continuous. So magnetic flux density is in air is same as in any material. B = 1 web/m2.

23.Find the maximum torque on an 100 turn rectangular coil,0.2m by0.3m,carrying a current of 2A in the field of flux density 5 Wb/m2.

Solution:

N = 100

A = 0.2*0.3=0.06 m2

I = 2A

B = 5 web/m2

Tmax = NIAB

= 100*2*0.06*5=60 Newton-metre. 24.Determine the force per unit length between two long parallel wires separated by 5cm in air

and carrying currents of 40A in same direction. Force/length = μ0 I1 I2 / 2πD

= [40*40 / 2π*5*10-2]*4π*10-7

= 6.4*10-3 N/m.



25.State Gauss’s law for magnetic field.

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

∮a B.da = 0.

26. Define magnetic dipole.

A small bar magnet with pole strength Qm and length l may be treated as magnetic dipole whose magnetic moment is Qml.

27. Define magnetic susceptibility.

Magnetic susceptibility is defined as the ratio of magnetization to the magnetic field intensity. It is dimensionless quantity.

Χm = M/H

28.Write down the magnetic boundary condition.

Similar to the boundary conditions in the electro static fields, here we will consider the

behavior of and at the interface of two different media. In particular, we determine how the

tangential and normal components of magnetic fields behave at the boundary of two regions having

different permeabilities.

29.What is the total force acting on a moving charge Q in the presence of both electric and

magnetic fields?

Mangnitic filed

Magnitic force

Total force will be

30.Compare magnetic scalar potential and vector potential.(May/June-2016,Apr/May-

2018,Nov/Dec-2014

Magnetic scalar potential Magnetic vector potential

It is defined as dead quantity whose

negative gradient gives the magnetic

indensity if there is no current source

present

H=- Vm

it is defined as that quantity whose curl

gives the magnetic flux density

B=×A



PART – B

1.Determine the force between two long parallel wires of 200m length separated by 5 cm in air and

carrying currents of 40A in same direction and in opposite direction.(Apr/May-2014)

2.Two narrow circular coils A and B have the common axis and are placed 15cm apart coil has 10

turns of radius 5cm with a current of 2A passing through it. Coil B has a single turn of radius 8cm. If

the magnetic field at the centre of the coil A is to be zero what current must be passed through the

coil B. (Nov/Dec-2012)

3.State and Explain BiotSavart‟s law.(Nov/Dec-2014,2013,Apr/May-2015).

4.Give the statement for Ampere‟s circuital law and give the expression for it. (Apr/May-

2015,May/June-2016,Nov/Dec-2013)

5.Establish the force between the current carrying parallel conductors. (Nov/Dec-2013)

6.Obtain the magnetic flux density on the axis of the circular coil carrying current.(Apr/May-

2016,April-May-

2018,Nov/Dec-2017).

7.Derive the expression for magnetic field intensity at any point due to infinite straight

conductor.(Nov/Dec-2014,Nov,Dec-2016)

8.State and explain Ampere‟s law and show that the field strength at the end of a long solenoid is

one half of that at the centre. (Nov/Dec-2010, Apr/May-2017)

9.Give short notes on the following. (Nov/Dec-2013,2012)

1.lorentz‟s law of force.

2.Magnetic energy density.

10.Derive an expression for the inductance of solenoid. (April/May-2010)

11.Obtain the expression for inductance of a toroid. (May/Jun-2010)

12.Derive an expression for the inductance of a transmission line having conductors of radius ‘a’ and

‘b’. (Nov/Dec-2015)

13.Define Self Inductance and Mutual Inductance and show that M= k √L1 L2. (Nov/Dec-2011)

14.Consider the boundary between two media .show that the angles between the normal to the

boundary and the magnetic flux densities on either side of the boundary satisfy the relation:

tanϴ1 /tanϴ2 = µ1 /µ2. Where µ1 and µ2 are the permeabilities of the respective media and ϴ1 and ϴ2

are the angles.(May/Jun-2014, Apr/May-2017) . 15.Obtain the expression for energy stored in magnetic field and also derive an expression for

magnetic energy density. (Nov/Dec-2013)

16.Describe the classification and magnetization of magnetic materials.(Nov/Dec-2014)

17.Determine the torque on a rectangular loop (am×bm) carrying current I and placed in a uniform

magnetic field.(May/Jun-2016)

18.Calculate the inductance of a ring shaped coil of mean diameter 20 cm, wound on a wooden core

of 2 cm diameter containing 200 turns.(Nov/Dec-2016)

19.Determine H for a solid cylindrical conductor of radius a, where the current I is uniformly

distributed over the cross section.(Nov/Dec-2016)

20.Derive the expression for the magnetic vector potential in the cases of an infinitely long, strainght

conductor in free space. (May/Jun-2014)

21.Explain the classification and magnetization of magnetic materials. (Apr/May-2015,Nov/Dec-

2014)

22.Find the pull exerted on the plunger of an electromagnet, when the total flux uniformly distributed

is 500 micro-weber and the diameter of the plunger is 2.54 cm. (Apr/May-2015)

23.Find the self-inductance of a solenoid?(Nov/Dec-2014)



24.Find the maximum torque on 85 turn rectangular coil 0.2m by 0.3m carrying current of 2.0A in a

field B=6.5T?(Nov/Dec-2012)

25.A circular loop conductor having a radius of 0.15m is placed in X-Y plane.this loop consists of a

resistance of 20 ohms. If the magnetic flux density is 0.5 sin 3 ax tsla, Find the current through the

loop.(Apr/May-2017)

26.Two parallel circular loops of radii, r1 and r2(r1>>r2) are coaxially located and carry currents I1

and I2 respectively. The axial distance between the centres of loops is „z‟. find approximately the

force between the loops.(May/June-2016)

27. State and prove magnetostatic boundry conditions.(Nov/Dec-2017,Apr/May-2017)

28. Develop an expression for a magnetic field indensity at any point on the line through the centre at

a distance ‘h’ m from the centre and a perpendicular to the plane of a circular loop (in xy plane)of

radius ‘a’m and carrying a current I ampere in anti-clockwise direction.(May/June-2016)

29. Determine the self inductance of a coaxial cable. (May/Jun-2011)



Unit – IV

ELECTRODYNAMIC FIELDS

PART – A

1.State Maxwell’s equation I and II. (Nov/Dec-2010)

xH = J + ӘD/Әt

xE = - ӘB/Әt

2.State Faraday’s law of electromagnetic induction. .(Nov/Dec-2016,May/June-

2016,Nov/dec-2010) Faraday‟s law states that” the electromotive force [mmf] induced in a circuit is equal to the rate of decrease of the magnetic flux linkage in the magnetic circuit”.

i.e., V = - dϕ /dt

3.Mention the Maxwell’s equation in phasor form.

(i) × E = - jωB = - jωµH

(ii) × H = J + jωD = ζE + jω [ԑE]

= E [ζ+jωԑ] (iii) . D = ρv

6.Explain why .B=0.

States that there are no magnetic charges. The net magnetic flux emerging through

any closed surface is zero.

7. Explain whyXE=0?

In a region in which there is no time changing magnetic flux, the voltage around the loop would be zero. By Maxwell‟s equation

8. Explain Why .D=0.?

In a free-space there is no charge enclosed by the medium. The volume charge density is zero.

By Maxwell‟s equation

9.Mention the significance of displacement current. Write the Maxwell’s equation in which it is

used.



The displacement current ID through a specified surface is obtained by integration of the normal

component of ID over the surface.

= .ds

s

This is a current which directly passes through the capacitor,

Maxwell‟s equation

= [differential form]

H .dl

[J+

ds

[integral form]


Department of EEE 23 EE8391 ELECTROMAGNETIC THEORY

10. In a material for which find the

conduction and displacement current densities.

Conduction current density,

=1250

Displacement current density,

11. Find the total current in a circular conductor of radius 4mm if the current density

varies according to J= A/ .

J=

Current I=

=

=

=



=

=

=80

12.Differntiate transformer and motional emf. (Apr/may-2017,May/June-2016,Nov/Dec-

2013)

Induced emf'' is the more general term. By Faraday's Law, you get an induced emf

whenever there's a changing magnetic flux through a loop. If the changing emf is due to some

kind motion of a conductor in a magnetic field, you would call it a ``motional emf''. For

example, if a loop moves into or out of a region of field, or rotates, or a bar rolls along a rail,

you'd get a ``motional'' induced emf. But if the changing magnetic flux were due to, say, an

increasing current in a wire, you wouldn't call it a ``motional'' emf.

13.What is meant by displacement current? (Nov/Dec-2017,May/June-2016)

In electromagnetism, displacement current is a quantity appearing in Maxwell's equations

that is defined in terms of the rate of change of electric displacementfield. Displacement current

has the units of electric current density, and it has an associated magnetic field just as actual

currents do. 14.What is dissipation factor?( May/June-2016)

In physics, the dissipation factor (DF) is a measure of loss-rate of energy of a mode of

oscillation (mechanical, electrical, or electromechanical) in a dissipative system. It is the

reciprocal of quality factor, which represents the "quality" or durability of oscillation.

15.How does displacement current differ form conventional current?(Apr/May-2018)

conduction current: current in conductors due to flow of electron under applied electric potential. This is usually the case where the surface charge density is small.

Displacement Current: current b/w two plates of capacitors, due to electric field". This is true for the space between two capacitor plates if the flux tubes connecting the source charges on the plates (displacement field) is varying in time. Of course, the displacement current is non-zero under all time varying displacement fields.

16.Give the important equation that provide a connection b/w field and cicurit theory?

(Nov/Dec-2014,Nov/Dec-2012,Nov/Dec-2013)

A theory is a contemplative and rational type of abstract or generalizing thinking, or the results such thinking. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several different related meanings.

https://en.wikipedia.org/wiki/Contemplation

https://en.wikipedia.org/wiki/Reason

https://en.wikipedia.org/wiki/Abstraction

https://en.wikipedia.org/wiki/Nature_(philosophy)

https://en.wikipedia.org/wiki/Ancient_Greek



17.What are the significant displacement current? (Nov/Dec-2014,Nov/Dec-2012,Nov/Dec-

2013)

Displacement current has the same units as electric current, and it is a source of the

magnetic field just as actual current.

18.Write the relation showing the energy required to establish a magnetic field by a quasi-

stationary current system.

It is shown that the time averaged magnetic forces produced in a system excited by quasi-stationary current may be expressed in terms of derivatives of effective inductance parameters in a manner similar to that magnatostatics. Practical application of the theorem include electromagnetic levitation, the absolute calibaration of electrical measuring instruments, and the assessment of mechanical stresses in magnet assemblies.

19.Define ‘dynamic emf’ or ‘motional emf’(Nov/Dec-2011)

The emf induced due to the movement of conductor in a magnetic field is called

motional or dynamic induced emf.

Ex:Generator

20.State any major difference between circuit theory and field theory.(Nov/Dec-

2017,May/June-2006)

Circuit theory:

This analysis originated by its own

Laplace transform is employed

Z,Y and H parameters are used

Two dimensional analysis

Lumped components are involved

Field theory:

Evolved from transmission theory

Maxwell induction is employed

S parameter is used

Three dimensional analysis

Distributed components are used



PART – B

1.Derive Maxwell‟s equation from Fundamental laws . [OR] Derive Maxwell‟s equation from

Ampere‟s law, Faraday‟s law and Gauss law. (Nov/Dec-2014,May/June-2015)

2.Derive Maxwell‟s Equation in Point form and Integral form. (May/June-2016,2014,Apr/May-

2017,Nov/Dec-2016,2013,2014)

3.Derive Maxwell‟s Equation for Free Space and for Conductor. (May/June-2015)

4.Derive Maxwell‟s equation for Time Varying Fields in Phasor form. (May/June-2013)

5. Discuss the relation between Circuit Theory and Field Theory. (May/June-

2016,2014,Apr/May-2017)

6. Explain the concept of emf induction in static and time varying magnetic field.(Nov/Dec

2016)

7.Derive the differential form of time harmonic Maxwell equation?(May/June-2013)

8.Write the down and explain the Maxwell equation intragal and differential form for the

following cases (Apr/May-2015)

(i)general case (ii)free

space (iii)harmonic

variation (iv)static case

(v)steady case

9.Explain briefly about transformer and motional EMFs. (Apr/June-2015)

10.Explain how the circuit equation for a series RLC circuit is derived from the field relations.

(Nov/Dec-2014)

11.Show that the total displacement current between the condenser plates connected to an

alternating current voltage source is exactly same as the value of charging current flowing in the

leads. (May/June-2013)

12.A rectangular T-turn coil with mean length „l‟ and which „w‟ is wound on a cylindrical

drum. If the drum rotates in a uniform field with a flux density B everywhere in the positive X-

direction at a constant speed of N rpm, the axis being in alignment with Z-axis, develop an

expression for induced emf in the coil. (May/June-2013).

13.An iron ring with a cross sectional area 3cm^2 and a mean circumfrance of 15cm^2 is wound

with 250 turns of wire carrying a current of 0.3 A.the relative permeability of the ring is 1500.

Calculate the flux established in the ring.(Apr/May-2018)

14. Describe the applications where circuit theory and field theory is used and applications,where

field theory is used.(Nov/Dec-2017)

15.Explain and detail about the difference between the conduction and displacement

currents(Nov/Dec-2015)



Unit – V

ELECTROMAGNETIC WAVES

PART – A

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 constitutes a wave.

2.Mention the properties of uniform plane wave.( Nov /Dec -2013, Nov /Dec -2014,Nov/Dec

2016)

The properties of uniform plane wave are as follows

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 vary harmonically with time and at the same frequency, everywhere 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.

3.Write down the wave equations for E and H in a non-dissipative[free space] medium.

2E- µ0ϵ0 ∂2E/∂t2=0

2H - µ0ϵ0 ∂2 H/∂t2=0

4.Write down the wave equations for E and H in a conducting medium.

2E - µϵ∂2E/∂t2 - µζ∂E/∂t =0

2H - µϵ∂2H/∂t2 - µζ∂H/∂t =0

5.Define intrinsic impedance or characteristic impedance.( Nov /Dec -2008,Nov/Dec 2017,

Apr/May-2018)

It is the ratio of the electric field to magnetic field. or It is the ratio of the square root of permeability to permittivity of the medium.



ɳ=E/H = √µ/ϵ ohms.

6.Calculate the characteristic impedance of free space.

ɳ=E/H = √µ/ϵ ohms.

=√[[4π*10-7]/1]/[36π*109]

= 120π=377 ohms.

7.Define propagation constant.

The propagation constant [γ] is a complex number, and it is given by

=α+jβ

where α is attenuation constant. is phase constant.

√jωµ[ζ+jωϵ].

8.Define skin depth or depth of penetration. (Nov/Dec 2017, Apr/May-2018)

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

δ = 1/α =√2/jωζ for good conductor.

9.Define polarization.

Polarization of a uniform plane wave refers to the time varying nature of the electric field vector to some fixed point in space.

10.Define linear polarization.

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

resultant electric field has a direction at angle of tan-1

Ey/E x and if this angle is constant with

time, the wave is said to be linearly polarized.

Ey

tanϴ = Ey/Ex

ϴ E=√Ex2+Ey

2.



11.Define circular polarization.

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

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

polarized.

12.Define elliptical polarization.

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

phase difference , the locus of the resultant electric field E is a ellipse and the wave is said to be

elliptically polarized.

13.Find the velocity of a plane wave in a lossless medium having a relative permittivity of 5

and relative permeability of unity. (April/May -2017)

v =1/√µϵ =1/√µ0µrϵ0ϵr

= 1/√µ0 ϵ0 1/√µr ϵr

= 3*108/√5 =1.34*10

8 m/sec.

14.Find the skin depth at a frequency of 2MHZ is Aluminium where σ=38.2s/m and µr=1.

ζ =38.2*106s/m

µr=1

ω=2πf=2π*2*106

for good conductor, the skin depth δ =√2/ωµζ

δ =√2/[2π*2*106*1*4π*10

-

7*38.2*10

6] = 5.758*10

-5 m.

15.At what frequencies may earth be considered a perfect, if σ = 6*10-3

s/m, µr =1 and

ϵr=10.

ζ/ωϵ=1

This is the boundary line between dielectric and conductor ζ/ωϵ<1

ζ/ωϵ=6*10-3

/ ω.[1/[36π*109]]=6*36π*109*10

-3/2πf = 108*10

6/f

ζ/ωϵ=1, 108*106/f = 1

f = 108*106

If frequency is greater than 108 MHZ, it acts as dielectric.



16.A uniform plane wave in free space in described by = 100e-[πz/3]

ax- determine the

frequency and wavelength.

E=100e-[πz/3]

ax-

β = 2π/λ= π/3 λ = 6m

f = e/λ = 3*108/6 =50 MHz.

f= 50 MHz.

17.The velocity of uniform plane wave in a loss-less dielectric is 1*108 m/sec. Find the

dielectric constant.

For loss-less dielectric µr=1

v =1/√µϵ =1/√µ0µrϵ0ϵr

= 1/√µ0 ϵ0√µr

ϵr 1*10 8 =

3*108/√ϵr

√ϵr = 3, ϵr = 9.

18.Write Helmholtz’s equation.

2 E – γ2E =0

Where γ = √jωµ[ζ+jωϵ]

19.Define poynting vector?( Nov /Dec -2008,May /June -2016)

The poynting vector is defined as rate of flow of energy of a wave as it propagates. It is the vector product of electric field and magnetic field.

P =E*H.

20.Write down the expression for instantaneous power flow in electromagnetic field and

instantaneous pointing vector.

Instantaneous power

w =|V| |I| cos[ωt+ϴv] cos[ωt+ϴi]

Instantaneous poynting vector P=E*H



21.Write down the expression for average power flow in electromagnetic field and average

poynting vector.

Wav= |V||I| cosϴ/2.

Pav= ½ Real part of [E*H *]

22.What is complex poynting vector.

The complex poynting vector is P= ½ [E*H *]

Where, H* complex conjugate of H.

23.Write down the complex poynting vector in rectangular co-ordinates.

Px= ½ [EyHz *- EzHy* ]

24.State Slepian vector.

Slepian vector is a vector which defined at every point such that its flux coming out of any

volume is zero. [ .s =0 ] . slepian vector is given by

S = * [VH]

Where , V is electric potential

H is magnetic field intensity.

25.State poynting theorem. (Nov /Dec -2013)

The vector product of electric field intensity and magnetic field intensity at any point is a measure of the rate of the rate of energy flow per unit area at that point.

P=E*H

26.State snell’s law.

When a wave is travelling from one medium to another medium, the angle of incidence is related to angle of reflection as follows.

Sinϴi/Sinϴt=√ɳ1/ɳ2=√ϵ2/ ϵ1[µ1=µ2=µ0]

Where, ϴi is angle of incidence

ϴt is angle of refraction



ϵ1 is dielectric constant of medium 1

ϵ2 is dielectric constant of medium 2

27.Define Brewster angle.

Brewster angle is an incident angle at which there is no reflected wave for parallel polarized

wave.

ϴ=tan-1 √ϵ2/ ϵ1

28.Define surface impedance.

Surface impedance is defined as the ratio of tangential component of electric field at the surface of a conductor to the linear current density.

Zs = Etan/Js = γ/ζ

Where, γ is propagation constant.

ζ is conductivity medium.

29.Mention the expression for plane electromagnetic waves propagating in a dielectric

media in a direction x with respect to origin [0,0,0].

The equation for plane electromagnetic waves propagating in a electric medium is given by

∂2Ey/∂t2 = 1/µϵ ∂2Ey/∂x2

Or ∂2Hy/∂t2 = 1/µϵ ∂2Hy/∂x2

30.Define skin depth and its significance at low frequency and at very high frequency

applications to conductors. (Nov/Dec-2015,Apr/May-2018)

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

approximately 37% of its original value.For good conductor

δ= 1/α = √2/ωµζ

= √1/

πfµζ Δα

1/√f



For low frequency, the skin depth δ is large.

For very high frequency, the skin depth δ is very small.

31.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

good conductor, conductivity ζ is high and current exists.

But * H=J [from amperes law]

Static magnetic field and time varying magnetic field are exist.

32.In a time varying situation how do you define a good conductor and lossy dielectric?

For good conductor ζ/ωϵ >> 1

α= β= √ωµζ/2

= √πfµζ

α and β are large i.e, the wave is attenuated greatly as it progresses through the conductor.

33.Define standing wave ratio. ( Apr/May-2018)

In radio engineering and telecommunications,standing wave ratio (SWR) is a measure of

impedance matching of loads to the characteristic impedance of a transmission line or waveguide

34.What is loss tangent? (Nov /Dec -2014, Apr/May-2015)

The loss tangent is then defined as the ratio (or angle in a complex plane) of the lossy reaction to the electric field E in the curl equation to the lossless reaction: . For dielectrics with small loss, this angle is ≪ 1 and tan δ ≈ δ.

35.If a plane wave is incident normally from medium 1 to medium 2, write the reflection

and transmission coefficients. (Nov /Dec -2014)

The coefficient of reflection, , is defined as the ratio of the intensities of the reflected and

incident waves:



PART-B

1.Derive the electromagnetic wave equation.(Nov/Dec-2011, Nov/Dec-2016)

2.Derive the wave equation for magnetic field in phasor form. [OR]Derive the Helmholtz wave

equation.(May/June-2016,Apr/May-2015)

3.Deduce the equation of propagation of the plane electromagnetic waves in free space,

conductors and dielectrics. (May/June-2014, May/June-2016,Apr/May-2017, Nov/Dec-2015,

Nov/Dec-2017,Apr/May-2018)

4.Derive the Poynting theorem and give its significance.(Nov/Dec-2012, Nov/Dec-2015,

Apr/May-2017, Apr/May-2018)

5.Briefly explain about the wave incidence normally on perfect conductor. (May/June-2016)

6.Explain about the wave incidence obliquely on perfect conductor. (Nov/Dec-2011)

7.Describe briefly about reflection coefficient. (Nov/Dec-2012)

8.Describe briefly about transmission coefficient. (Nov/Dec-2012)

9.Derive the expression for Brewster angle. (Nov/Dec-2013)

10.Write short notes on standing waves.( Apr/May-2015, May/June-2016, )

11.Discuss phase velocity and propagation constant of electromagnetic waves.(May/June-2016)

12.A 6580 MHz uniform plane wave is propagating in a material medium of 2.25. If the

amplitude of electric field intensity of lossless medium is 500 V/m.Calculate the phase constant

,propagation constant , velocity , wavelength and intrincic impedance. (Nov/Dec- 2016)

13.Derive the expression for an intrinsic impedence, propagation constant and velocity of a plane

Electromagnetic wave when propagated in a perfect medium conducting media and good

conductor. (May/June-2014, May/June-2016)

14.A transmission line having a characteristic impedence of 75 ohms is terminated in an

impedence of 200+200j ohms. If the line is 2.1 lambda long and lossless, determine its input

impedence. (May/June-2014, May/June-2016)

15.Derive the relationship between electric field and magnetic field. Derive the wave equation

for the magnetic field in phasor form. (Nov/Dec-2013)

16.Describe the concept of electromagnetic wave propagation in a linear, isotropic,

homogeneous, lossy dielectric medium.(Nov/Dec-2014,April/May-2018)

17.Derive the EM wave equation in frequency domain and obtain the expressions for intrinsic

impedence and propagation constants for free space , conductor and dielectric

medium.(May/June-2013).

18.Derive Poynting vector and state its significance.(Nov/Dec-2017)

19.The electric field intensity associated with a plane wave travelling in a perfect dielectric

medium is given by Ex(z,t)=10cos(2x107t-0.1z)V/m.What is the velocity propagation?

(April/May-2018)

s.k.p. engineering college, tiruvannamalai iii sem skp...

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