bvrit hyderabad

College of Engineering for WomenDepartment of Electrical and Electronics Engineering

Subject Name: Electromagnetic Fields (EMF)

Prepared by (Faculty(s) Name): Dr.

Year and Sem, Department: IIYear

Important Points / Definitions:

BVRIT HYDERABAD College of Engineering for Women

Department of Electrical and Electronics Engineering

Hand Out

Electromagnetic Fields (EMF)

Dr. Chava Sunil Kumar, Professor, EEE

Year- I Sem, EEE

UNIT – I: Electrostatics

Fill in the blanks / choose the Best:

1. According to coulomb’s law, the force between two charges is

a) Along the line joining them

b) Directly proportional to product Q


According to coulomb’s law, the force between two charges is

ne joining them

b) Directly proportional to product Q1Q2

[ d ]

c) Inversely proportional to square of the distance

d) all

2. The potential due to dipole moment is [ c ]

a) Directly proportional to ‘P’

b) Inversely proportional to r2

c) Both directly proportional to ‘P’& inversely proportional to r2

d)N one

3. The net effect of dielectric on the electric field E is to [ a ]

a)Increase D value b)Decrease D value c)Constant d)none

4. The volume charge density ρv is measured in [ c ]

a)c/m b)c/m2 c)c/m

3 d)c-m

3

5. The electric flux density D Due to point charge at point ‘P’ is [ a ]

a) Q ar/ (4πr2) b) Q / (4πr) c) Q1Q2 ar / (4πr) d)none

6. Which of the following is relation between electric flux density & electric field intensity [ b ]

a)D=E / Є0 b)D= Є0E c)E= Є0D d)NONE

7. The relation between electric flux and electric flux density is ψ= ∫��.��

8. Integral form of Gauss’s law is ∫��.��= ∫��.��

9. Laplace equation for electrostatic field is ▼2V=0

10. Work done required to move a point charge in presence of electrostatic field is W= - Q ∫��.��.

11. Equipotential surfaces means surfaces which are having same potential.

Questions

1. State coulomb’s law of electric charge?

2. Derive an expression for field due to a hollow conducting sphere.

3. a).Find the electric field at a point (1,-2,1)m, if the potential is V=3x2y+2yz

2+2xyz.

b).derive an expression for EPI due to a sheet of charge.

4. a).state and explain Gauss’s law.

b).Derive an expression for electric field intensity in different region of a coaxial cable. Use Gauss

law.

5. State the expression for the force between one charge point to an array of charge points?

6. State and explain Gauss’s law.

7. Deduce the Expression for �� due to a electric dipole? A field is given in spherical co-ordinate

system P(r=5,Ɵ=30°, Φ=60°) as �� =(20�γ-30�Ɵ+60aΦ)v/m. Find the incremental work done in

moving a 10µC charge through a distance of 0.8 µm in the direction of a) �γ b) �Ɵ c) aΦ

8. a) Prove the expression ��=∇� V? Where E is the Electric Field Intensity and V is the scalar

Potential?

b) A uniform line of charge ρl=2.5µC/m lies along the z-axis and a circular cylinder of radius 3m

has a surface charge density of ρs = -0.12 µC/m2.Both the distributions are infinite in extent with

respect to z-axis .Using Gauss’s law. Find the �� in all regions. The region is free space?

9. Write the properties of potential function.

10. What is Maxwell’s first law?

11. a) State and prove Gauss’s law as applied to an electric filed and determine the field due to an

infinite line charge.

b) Derive poisson’s and Laplace equations starting from of Gauss’s law?

12. a).Show that the electric field intensity at any point inside a hollow charge Spherical conductor is

zero.

b).Three point charges each 5nC are located on the axis at points -1,0and +1m in free space. (i)

Find E at x=5. (ii) Determine the value and location of the equivalent single point charge that

would produce the same field at very large distance.

13. Define electric field intensity

14. Give the statement of Coulomb’s law.

15. a) State and explain Gauss’s law.

b) Four concentrated charges Q1=0.3µc, Q2=0.2µc, Q3= -0.3µc, Q4=0.2µc, are located at the

vertices of a plane rectangle. The length of rectangle is 5cm and breadth of the rectangle is 2cm.

Find the magnitude and direction of resultant force on Q1.

16. a) If D = [2y2+z]ax + 4xy ay + x az C/m

2 , find:

i) The volume charge density at (-1,0,3)

ii) the flux through the cube defined by 0≤x≤1, 0≤y≤1, 0≤z≤1.

iii) The total charge enclosed by the cube.

17. Show that div (D) = ρv.

18. b) Determine ρv at (0.3, 0.4, 0.5) due to �� = 20xy2 (z+1)��+20x

2y(z+1)��+10x

2y

2�� C/m2.

19. a) Derive Laplace’s and Poisson’s equations.

b) Define i) Potential ii) Dipole moment iii) Torque iv) Electric Dipole.

20. Write any two relations between E and V.

21. Plane z=10m carries charge 20 nC/m2 . Find the electric field intensity at the origin.

22. a) Derive the expression for work done in moving a point charge in an electrostatic field.

b) Let D=2y2z

2 ax + 3xy

2z

2 ay + 2xyz az p C/m

2 in free space. Find the total electric flux passing

through the surface x=2 , 0≤y≤2, 0≤z≤2 in a direction away from the origin.

23. a) Obtain the electric field intensity E at a point when an infinite line charge is placed along z-axis

by applying Gauss’s law.

b) Find the flux density D at a point A( 6,4,-5) caused by a point charge of 20m/c at the origin.

24. a) Obtain the expression for work done in moving a point charge in an electrostatic field.

b) The electric field intensity in free space is given by E=2xyz ax+x2y ay+x

2yaz V/m. Calculate the

amount of work necessary to move a 2µC charge from (2,1,-2) to (5,2,3).

25. a) Define Electric Dipole; also derive the expression for potential and Electrical Field Intensity due

to an electric dipole.

b) Two dipole with dipole moments -7az nC/m and 8az nC/m are located at points (0,0,5) and (0,0,-

4). Find the potential at the origin.

26. a) Define and deduce the coulomb’s law for the vector force between two point charges in free

space.

b) Show that the electric field due to an infinite straight line of uniform charge density λC/m along

the z-axis in free space is (λ/2πƐ0r)ar N/C using Gauss’s law.

27. a) Show that the torque on a physical dipole P in a uniform electric field E is given by PxE.

Extend this result to a pure dipole.

b) Two long metal plates of width 1m each held at an angle of 10° by an insulated hinge plates are

electrically separated. Using Laplace’s equation determines potential function.

28. Describe what are the source of electric field and magnetic fields?

29. What are the limitations of Gauss’s law?

30. a) Find the total electric field at the origin due to 10-8

C charge at P( 0,4,4) m and -0.5x10-8

C

charge at P(4,0,4)m

b) Find the electric field intensity of a straight uniformly charged wire of length ‘L’ m and having

a linear charge density of +q C/m at any point at a distance of ‘h’m . Hence deduce the expression

for infinitely long conductor.

31. a) Find the electric field intensity produced by a point charge distribution at P(1,1,1) caused by

four identical 3nC point charges located at P1(1,1,0) , P2(-1,1,0) , P3(-1,-1,0) , P4(1,-1,0).

b) A circular disc of radius ’a’m is charged with a charge density of �C/m2. Find the electric field

intensity at a point ‘h’m from the disc along its axis.

32. a) Derive an expression for electric field intensity due to a finite line charge of λc/m.

b) A uniform line charge of 20nc/m has on the z-axis between z=1 and z=3m.

No other charge is present .Find Ē at:

i) The origin

ii) P(4,0,0)

33. a) Derive Laplace’s and poisson’s equations.

b) A dipole at the origin in free space has

i) Find V at p(x,y,z) in Cartesian co

ii) Find Ē at p(x,y,z) in Cartesian co

34. a) Derive electrical potential. Show that the electric field intensity is negative gradient of potential.

b) Find �� at P(6,8,-10) cause due to

i) A uniform line charge �1= 40µc/m on the Z

ii) A uniform line charge �s= 57.2µc/m

35. a) Derive Poisson’s and Laplace’s equations.

b) What is dipole? Derive expression for torque experienced by a dipole in uniform electric field.

UNIT


a) Derive Laplace’s and poisson’s equations.

b) A dipole at the origin in free space has �̅ =95π∈o U c-m.

i) Find V at p(x,y,z) in Cartesian co-ordinates.

at p(x,y,z) in Cartesian co-ordinates.

a) Derive electrical potential. Show that the electric field intensity is negative gradient of potential.

10) cause due to

= 40µc/m on the Z-axis.

= 57.2µc/m2 on the plain x=9

a) Derive Poisson’s and Laplace’s equations.


UNIT – II: Dielectrics & Capacitance

a) Derive electrical potential. Show that the electric field intensity is negative gradient of potential.



1. The convection current density is

a)J=ρvu b)J=ρv/u c)J=ρ

2. Which of the following represents the continuity equation

a)J= −�ρv / �� b) J=�ρv /

3. For a copper material, having σa)1.53*10-9 sec b)1.53*10

4. If A is represented as susceptibility of any dielectric material then the

a) (1+A2) b)(1+A)

5. The conduction current density J equal to

6. The formation of a dipole in dielectric material due to electro static field is called as

7. Capacitance of co-axial cable is

8. Divergence theorem is relation between

Questions

1. Obtain Omh’s law in point form.

2. Define electric dipole and dipole moment?

3. a).Derive an expression for Capacitance of spherical capacitor.

b).Obtain boundary conditions between conductor and Dielectric interface.

4. a).What is the behavior of conductors in an electric field?


The convection current density is

c)J=ρv/u2 d) none

hich of the following represents the continuity equation

�� c) J=�ρ / �� d) none

having σ=5.8*10-7 s/m, the relaxation time is----------

b)1.53*10-19 sec c)1.35*10-19 sec d)1.35*10-9 sec

If A is represented as susceptibility of any dielectric material then the Єr value is

c) (1-A) d)(1-A2)

sity J equal to J=σE

The formation of a dipole in dielectric material due to electro static field is called as

axial cable is C = (2πЄ l) / (ln (b/a)).

Divergence theorem is relation between surface integral to volume integral of any vector field

Obtain Omh’s law in point form.

Define electric dipole and dipole moment?

a).Derive an expression for Capacitance of spherical capacitor.

b).Obtain boundary conditions between conductor and Dielectric interface.

).What is the behavior of conductors in an electric field?

[ a ]

[ a ]

-----------(Єr=1) [ b ]

9 sec

Єr value is [ b ]

The formation of a dipole in dielectric material due to electro static field is called as Polarization

integral of any vector field.

b).Deduce the expression for potential due to an electric dipole?

5. Give ohms law in point form.

6. Brief about the concept of polarization in materials.

7. Derive the expression for the Boundary conditions between two perfect dielectrics.

8. Prove that the convection current density is linearity proportional to the charge density and the

velocity with which the charge is transferred.

9. Define electric dipole.

10. Define Convection and conduction current densities.

11. a) Establish the electrostatic boundary conditions for the tangential components of electric field

and electric displacement at the boundary of two non dielectrics.

b) The relative permittivity of dielectric in a parallel plate capacitor varies linearly from 4 to 8. If

the distance of separation of plates is 1 cm and area of cross section of plates is 12cm2.Find the

capacitance .Derive the formula used.

12. a). A spherical capacitor with inner sphere of radius 1.5 cm and outer sphere of radius 3.8 cm has

an homogenous dielectrics of Ɛ=10. Ɛo. Calculate the capacitance of the capacitor. Derive the

formula used.

b).Prove that the derivative of the energy stored in an electrostatic field with respect to volume is

½ D.E, where D and E electric flux density and electric field intensity respectively.

13. Define polarization.

14. Define Electric dipole.

15. a) State and explain the continuity equation.

b) Parallel plate capacitor consists two square plate metals with 500mm side and separated by

10mm. A slab of sulphur (Ɛr=4) 6mm thick is placed on the lower plate and air gap of 4mm. Find

the capacitance of a capacitor.

16. a) Derive the boundary conditions between a conductor and a dielectric.

b) A parallel plate capacitor consists of two square metal plates of side 600mm and separated by a

12mm. A slab of Teflon with Ɛr = 3 and 5mm thickness is placed on the lower plate leaving an air

gap of 8mm thick between it and upper plate. If 200V is applied across the capacitor, find D, E and

V in Teflon and air.

17. a) Define and derive the expressions for conduction and convection current densities.

b) Obtain the expression for capacitance for a parallel plate capacitor with composite dielectrics.

18. Three point charges -2nC , 5 nC , 8 nC are located at (0,0,0) (0,0,1) and (1,0,0) respectively .

Determine energy in the system.

19. State Continuity Equation.

20. Define conduction and convection current densities.

21. a) Mention the applications of boundary conditions. Obtain the boundary conditions for conductor

–dielectric interface.

22. b) A homogeneous dielectric (Ɛr=2.5) fills region 1(x<0) while region 2(x>0) is free space. If

D1=12ax-10ay+4az nC/m2. Find D2.

23. Find the total current in a circular conductor of radius 4mm if the current density varies according

to J= 104/r A/m

2 .

24. a) Derive the expression for capacitance of the spherical condenser.

b) The permittivity of the electric of parallel plate capacitor increases uniformly from Ɛ1 at one

plate to Ɛ2 at the other. If A is the surface area of the plate and d is the thickness of dielectric,

derive an expression for capacitance.

25. a) Find the expression for the energy per unit volume of the dielectric due to electric field in a

charged capacitor.

b) What is the capacitance of a capacitor consisting of two parallel plates 30cm x 30cm, separated

by 5mm in air? What is the energy stored by the capacitor if it is charged to a potential difference

of 500Volts.

26. What are the boundary conditions of dielectrics?

27. Define polarization?

28. Obtain an expression for Ohm’s law in point form and integral form.

29. Derive an expression for energy stored and energy density in an Electrostatic field.

30. a) Derive the expression for capacitance of two concentric spherical shells.

b) Calculate the capacitance of parallel plate capacitor with the following details : plate area =

150cm2 ; Dielectric ∈r1=5 ; d1=3mm ; ; Dielectric ∈r2=4 ; d2=4mm. if 220V is applied across

plates , what will be the voltage gradient across each dielectric.?

31. a) Find the capacitance of a parallel plate capacitor , when the plates are of area 1m2 , distance

between the plates 1mm, voltage gradient is 105 V/m. and the charge �s= 2µc/m

2.

b) Explain about equation of continuity.

32. a) Derive the equation of continuity.

b) Given the vector current density J. =10ρ2zap -4ρcos

2Φ aΦ A/m2.

Determine the total current flowing outward through the Circular band ρ =3, 0<Φ<2π.2<z<2.8.

UNIT – III : Magneto Statics and Ampere’s Law & Applications


Magneto Statics and Ampere’s Law & Applications


Magneto Statics and Ampere’s Law & Applications


1. Magnetic Field Intensity due to infinite straight lon

A) 2I a∅ / (πρ) B) I a∅ / (πρ

2. Current densities are related as

A) IdS=Kdl=JdV B) IdL=KdS=JdV

3. Which of the following statement

A) It may be a scalar or a vector

B) It is a time dependent quantity

C) A Phasor Vs may be represented as V0 ej

D) It is a complex quantity

4. Maxwell’s third equation is Curl H


Magnetic Field Intensity due to infinite straight long current carrying conductor is

πρ) C) I a∅ / (4πρ) D) I a∅ / (2πρ)

Current densities are related as

B) IdL=KdS=JdV C) IdL=KdV=JdS D) None of these

Which of the following statement is not true of a phasor

A) It may be a scalar or a vector

B) It is a time dependent quantity

C) A Phasor Vs may be represented as V0 ejθ where V0=|Vs|

Curl H = J�� (OR) ∇∇∇∇�� H = Jc

g current carrying conductor is [ D ]

[ B ]

D) None of these

[ B ]

5. Ampere’s circuital Law is ∫H.dl = I

6. If H is 15×10-3 A/m, then the value of B in free space is 60π x10-10

(OR) 188.4 x10-10

.

7. According to Maxwell’s fourth equation B= zero

Questions 1. State Bito-Savart’s law.

2. Derive an expression for MFI due to a straight current carrying filament .Use ampere circuital law.

3. a).Obtain MFI due to a infinite sheet of surface current density K��

b).Discuss point form of Ampere’s circuital law

4. a).Prove div(B)=0.

b).Derive an expression for MFI due to square current carrying wire at its center.

5. Define Ampere’s circuital law and its applications.

6. Obtain Maxwell’s second equations.

7. a) The Magnetic Field Intensity � due to a infinite current carrying sheet , Assume a current k in

xz-plane ,Prove that ,H= !"

# �ny

b). Find the magnetic Field Intensity � at a point P(0.01,0, 0)m, if current through a co axial cable

is 6A, which is along z-axis and a=3mm, b=9mm, c=11mm?

8. By using Ampere circuital law, derive the Expression for magnetic Field Intensity � due to a

infinite long current carrying conductor .Find the magnetic Field Intensity at a radius of 0.5m from

a along straight line conductor carries a current of 2A/m.

9. Define Magnetic field intensity.

10. Write the applications of Ampere’s circuital law?

11. a).State and explain Biot-Savart’s law and derive the expression for the magnetic field at a point

due to an infinitely long conductor carrying current.

b).What are the limitations of Ampere current law? How thus law can be modified to time varying

field?.

12. a).Derive Maxwell’s second equation div (B)=0.

b).Derive magnetic field intensity due to a square current carrying element.

13. Write the formula of Ampere’s circuital law.

14. What is Maxwell’s second equation?

15. a) Deduce the relationship between magnetic flux , magnetic flux density and magnetic flux

intensity .

b) A square conducting loop 4cm on each side carries a current of 10A. Calculate the magnetic

field intensity at the center of the loop.

16. a) State and explain Biot–Savart’s law.

b) A circuit carrying a direct current of 10A forms a regular hexagon inscribed in a circle of radius

of 1.5m. Calculate the magnetic flux density at the center of the hexagon. Assume the medium to

be free space.

33. Find the magnetic field intensity of a solenoid.

34. By applying Ampere’s circuital law, determine the field due to a circular loop.

b) A current sheet $� = 9%�x A/m lie in z=10m plane and current filament is located at y=0 , z=5m.

Determine I in current filament if &�=0 at P(5,0,3)m.

17. Justify div (B) = 0

18. Define Magnetic Field Intensity, magnetic flux density and express the relation between them.

19. a) State Biot-Savart’s law. Also derive the expression for magnetic field intensity due to circular

loop placed on xy plane with radius ‘r’.

b) Define Magnetic Flux, Magnetic flux lines and Magnetic flux density and state the relation

between Magnetic flux and Magnetic flux density and also mention their units.

20. State Ampere’s Circuital law and also state differences between Biot-Savart’s law and Ampere’s

circuital law. Apply Ampere’s Circuital law to an infinite sheet and derive its magnetic field

intensity H.

21. a) Express the possible limitations of Amperes current law and write about how this law can be

modified to time varying field.

22. b) Determine H for a solid cylinder conductor of radius ρ, where the current I is uniformly

distributed over the cross section.

23. State Biot – Savart’s law.

24. Write the point form of amperes circuit law.

25. Derive the expression for H due to finite length wire carrying a steady current I.

26. Obtain the expression for H at any point on the axis of circular loop carrying current I and deduce

H in the center of the circular loop.

27. Derive an expression for magnetic field intensity on the axis of a circular loop carrying a current of

I amperes.

28. a) State and explain Ampere’s circuital law.

b) Derive Maxwell’s equation.

29. a) State and explain Biot – savart’s law.

b) A steady current of 1000A is established in a long straight, hallow aluminum conductor of

inner radius 1cm and outer radius 2cm. Assuming uniform resistivity, calculate '� as a function

of radius ‘r’ from the axis of the conductor.

30. a) Explain the Ampere’s circuital law and list the few applications.

b) State and prove Maxwell’s third equation.

31. Evaluate the closed line integral of H about the rectangular path P

(4.3.1) to P4 (2.3.1) to P1. Given H = 3z

32. State Biotsavart’s law and obtain the expression for magnetic field intensity due to an infinitely

long straight filament carrying current by applying Biotsavart’s law.

33. A cylindrical conductor of radius 10

(3x10-2

)] Φ.A/m. Determine the total current of the conductor using

(i) The integral form and

(ii) Point form of ampere circuital law.

UNIT – IV: Force in Magnetic fields and Magnetic Potential


) Explain the Ampere’s circuital law and list the few applications.

b) State and prove Maxwell’s third equation.

Evaluate the closed line integral of H about the rectangular path P1 (2.3.4) to P

Given H = 3z ax – 2x3

az A/m.

State Biotsavart’s law and obtain the expression for magnetic field intensity due to an infinitely

long straight filament carrying current by applying Biotsavart’s law.

A cylindrical conductor of radius 10-2

m has an Internal magnetic field =4.77x10

.A/m. Determine the total current of the conductor using

The integral form and

Point form of ampere circuital law.

Force in Magnetic fields and Magnetic Potential

Definitions:

(2.3.4) to P2 (4.3.4) to P3

State Biotsavart’s law and obtain the expression for magnetic field intensity due to an infinitely

=4.77x104 [

(

# - r

2 /

Force in Magnetic fields and Magnetic Potential


1. Unit of Permeability is ______

A) F/m B) A/m C) H/m

2. Which of the following statement is not true about electric force Fe and magnetic force Fm on a

charged particle

A) E and Fe are parallel to each other, where as B and Fm are perpendicular to each other

B) Both Fe and Fm are produced when a charged particle moves at a constant velocity

C) Fm is generally small in magnitude in comparison to Fe

D) Both Fe and Fm depend on the velocity of the charged particle

3. Vector Poisson’s equation is _______

A) ∇2A =)0J B)−∇2

A =)

4. Energy density in a magnetic field is ______

A) (1/4) B.H B) 2 H.B

5. Neumann’s formula is ______

A) )0∫∫ (�*1. �*2) / (4+,)

6. Lorentz force equation is F =

7. A differential current loop has dimensions of 1m by 2m and lies in uniform field

az T. The loop current is 4mA. Magnitude of Torque on the loop is

8. A solenoid with length ‘L’ m and radius ‘a’ m has ‘N’ turns, then its inductance is

9. Magnetic energy (in Joules) stored in an inductor


Unit of Permeability is ______

C) H/m D) None of these

Which of the following statement is not true about electric force Fe and magnetic force Fm on a



C) Fm is generally small in magnitude in comparison to Fe

D) Both Fe and Fm depend on the velocity of the charged particle

Vector Poisson’s equation is _______

)0J C) ∇2V=)0J D) None of these

a magnetic field is ______

B) 2 H.B C) ) (1/2) B.H D) H.B

Neumann’s formula is ______

B) )02+ ∫∫�*1 .�*2 , C) µ0π∫∫ �*1 .�*2 / ,

= Q [E+ v x B] (OR) F = m��v / ��t

A differential current loop has dimensions of 1m by 2m and lies in uniform field

. The loop current is 4mA. Magnitude of Torque on the loop is 4.8 mN-m

L’ m and radius ‘a’ m has ‘N’ turns, then its inductance is

Magnetic energy (in Joules) stored in an inductor Wm= (1/2) LI2

[ C ]

Which of the following statement is not true about electric force Fe and magnetic force Fm on a

[ D ]



[ B ]

[ C ]

[ A ]

, D) None of these

A differential current loop has dimensions of 1m by 2m and lies in uniform field, '0= -0.6 ay+0.8

m

L’ m and radius ‘a’ m has ‘N’ turns, then its inductance is N2 ) S / L .

Questions 1. What are the applications of permanent magnets?

2. Define self – inductance and mutual inductance?

3. a).Obtain the expression for the inductance of a toroidal ring

b).A coil of 500 turns is wounded in a closed iron ring mean radius of 10cm and cross section area

of 3cm2.Find the self-inductance of the winding if the relative permeability of iron is 800?

4. a).Derive an expression for scalar and vector magnetic potentials.

b).Derive an expression for mutual inductance between a long straight wire and rectangular loop

lying in the same plane.

5. Derive expression for Vector Magnetic Potential.

6. Write the applications of Parameters Magnets.

7. . Derive the expression for the coefficient of coupling and equivalent inductance for various

connections of magnetic circuits? If a coil of 800µH is magnetically coupled to another coil of

200µH. The coefficient of coupling between two coils is 0.05. Calculate the inductance, if two

coils are connected in a) series aiding b) series opposition c) parallel aiding and d) parallel

opposing.

8. Derive the expression for Scalar and Vector magnetic potentials. Derive the expression for the

Laplace’s and poisson’s equation for magnetic field.

9. What is the vector Poisson’s equation?

10. What are the applications of permanent magnets?

11. a).Derive the Neumman’s formulae for the calculation of self and mutual inductances.

b).Explain the concept of vector magnetic potentials.

12. a).Determine the inductance of a toroid.

b).A rectangular coil of area 10cm2 carrying a current of 50 A lies on plane 2x+6y-3z=7 such that

the magnetic moment of the coil is directed away from the origin. Calculate its magnetic moment

13. What is scalar magnetic potential?

14. What is magnetic dipole moment?

15. a) Derive the Neumann’s formulae for the calculation of self inductance of a solenoid and toroid.

b) Explain about the Vector Poisson’s equation for steady magnetic field.

16. a) A two conductor transmission line is made up of conductors, which are separated by a distance

of 2meters. The radius of each conductor is 1cm. The medium is air. Compute the exact value of

inductance of each conductor per km length. Derive the formula used.

17. a) Derive the expression for force between two straight long and parallel current carrying

conductors.

b) Obtain Torque on a current loop placed in a magnetic field.

18. a) Determine self inductance of i) Solenoid ii) Toroid

b) A solenoid with length 20cm and radius 3cm has 400 turns. Calculate its inductance.

19. Define scalar magnetic potential and vector magnetic potential.

20. Mention the characteristics of permanent magnets.

21. a) Obtain the expression for force between two current elements.

b) Compare the electric dipole and magnetic dipoles.

22. a) Define vector magnetic potential and derive its corresponding expression. Also mention its

properties.

23. b) If magnetic vector potential is A=10r 1.5

az Wb/m in free space , find magnetic flux density H

24. Explain the following in detail:

25. a) Lorentz force equation.

b) Force on a straight and a long current carrying conductor in a magnetic field.

26. a) Discuss the nature and behavior of magnetic materials and explain the term magnetization.

b) Explain the Laplace’s and Poisson’s equations for steady magnetic fields.

27. What is the differences between scalar and vector magnetic potential?

28. What is the expression for torque experienced by a current carrying loop, placed in a magnetic

field?

29. a) Explain the characteristics and applications of permanent magnets.

b) Obtain an expression for self inductance of a solenoid.

30. a) Derive an expression for force between two straight parallel current carrying conductors.

b) Obtain an expression for Lorentz force equation.

31. a) Derive Lorentz force equation.

b) Show that the force between two parallel conductors carrying current in the same direction is

attractive.

32. a) Differentiate between scalar and vector magnetic potential.

b) Derive Neumanns’s formula for mutual inductance.

33. a) Derive Lorentz force equation.

b) Find the torque expression of a current loop placed in a magnetic field.

34. a) Explain the differences between scalar and vector magnetic potentials.

b) Derive expression for inductance of a toroid.

35. If A = 10ρ 1.5 az Wb/m in free space. find (a) Magnetic field intensity H (b) current density J and

current I (c) show that ∮ . �� = l for circular path with ρ =1.

36. Obtain the Expression for magnetic torque in terms of magnetic dipole moment.

UNIT


UNIT – V: Time Varying Fields



1. The flux through each turn of a 100 turn coil is ( t3-2t) mwb, where t is in sec induced emf at t= 2 s

is [ B ]

A)1V B)-1V C) 4mV D) 0.4V

2. The concept of displacement current was a major contribution attributed to [ D ]

A) Maxwell B) Lorentz C) Lenz D) Faraday

3. Displacement current is Current through Capacitor (////0000)))) 2222d = C dv dt (////0000) Id = Jd s . d S.

4. Maxwell’s equation in differential form of ampere’s law for time varying field ∇∇∇∇��H = J + ∂D / ∂t (OR) ��E + 3333 ��E ��

5. Electric flux density is 16×106є0� Sin 106t. Displacement current density is 20. 16X8.85 ρ Cos

106t A/m2

Questions 1. State Faraday’s law of electromagnetic induction.

2. Deduce an expression for Maxwell’s fourth equation.

3. a).State and explain Faraday’s law of electromagnetic induction in integral and point forms.

b).A square coil with a loop area 0.01m2 and 50turns is isolated about its axis at right angle to a

uniform magnetic field B = IT. Calculate the instantaneous value of emf induced in the coil when

its plane is:

i)at right angle to the field.

ii).in the plane of the field.

iii).when the plan of coil is 45° to the field.

4. a). In a material for which � = 4.5V/m and Ɛr=1, the electric field intensity is E=300 sin 109 t ax

V/m .Determine the conduction and displacement current densities and the frequency at which

they equal magnitude ?.

b).Derive an expression for Displacement current.

5. State Faradays law of Electromagnetic induction.

6. What is displacements current Explain.

7. Derive the Maxwell’s Equations for Time Varying Field?

8. a).A conductor of length 100cm moves at right angles to uniform field of strength 10000 lines per

cm2 , with a velocity of 50 m/s. Calculate e.m.f induced it when the conductor moves at a angle

30° to the direction of field?

b).An a.c voltage source Ɵ(t)=V0 sin wt is connected across a parallel plate capacitor of

capacitance ‘C’ .Show that the displacement current in the capacitor is the same as the conduction

current in the wires.

9. Define time varying fields.

10. How dynamically induced EMF is produced?

11. a). Explain concept of displacement current and obtain an expression for the displacement current

density.

b).Explain in details about modifications Maxwell’s equations for time varying fields.

12. a).Explain Faraday’s laws of electromagnetic induction and derive the expression for induced

EMF.

b).Derive Maxwell’s equation in integral form for time varying fields.

13. Define displacement current

14. What is statistically and dynamically induced emfs?

15. a) State and derive the Maxwell’s fourth equation.

b) The parallel plate capacitor with plane area of 5cm2 and plate separation of 3mm has a voltage

of 50sin 103 t V applied to its plates. Calculate the displacement current assuming Ɛ = 2Ɛ0.

16. a) Obtain an expression for the displacement current density.

b) Let the current I= 80t A be present in the az direction on the Z axis in free space within the

interval -0.1 <z<0 .1m. Find Az at P(0,2,0)

17. a) Explain what inconsistency of Ampere’s circuital law is and also how this inconsistency can be

overcome.

b) If σ = 0 , Ɛ = 2.5 , Ɛ0 and µ=10µ0, Determine whether or not the following pairs of fields satisfy

Maxwell’s equations.

i) 4�� = 2y�� ; &��=5x��

ii) 4�� =100sin (6x107t) sin �� ; &�� = -0.1328cos(6x10

7t) cos ��

18. State Faraday’s laws of electromagnetic induction.

19. Express four Maxwell’s equations in point form.

20. a) State poynting’s theorem and explain its significance, also derive its corresponding expression.

b) The magnetic field H of a plane wave has a magnitude of 5 mA/m in a medium defined by Ɛr =4

, µr=1, determine the average power flow.

21. Write the Maxwell’s equations in free space and derive the Maxwell’s equations in good

conductors for time varying fields and static fields both in differential and integral form.

22. Define dynamically induced e.m.f.

23. Give the Maxwell’s equation – IV in both integral form and point form.

24. State and explain Faraday’s Laws of electromagnetic induction.

25. Derive the expression for displacement current density.

26. a) State and explain Faraday’s laws of electromagnetic induction.

b) Derive Maxwell’s fourth equation.

27. a) Write Maxwell’s fourth equation for time varying fields.

b) State pointing theorem and explain its significance.

28. In free space E = 20 cos (ωt – 50x) ay V/m. Calculate (a) displacement current density and (b)

Magnetic field intensity H.

29. a) Find the conduction and displacement current densities in a material having conductivity of

10-3

S/m and Ɛr = 2.5. If the electric field in the material E = 5.0x10-6

sin (9.0x109 t) V/m

b) Explain the significance of displacement current.

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