gujarat technological university electrical & …

GUJARAT TECHNOLOGICAL UNIVERSITY

ELECTRICAL & ELECTRONICS ENGINEERING (08) & ELECTRICAL

ENGINEERING (09) FIELD THEORY

SUBJECT CODE: 2140909

B.E. 4th SEMESTER

Type of Course: Engineering Science (Electrical)

Prerequisite: Basics of Electrical Engineering

Rationale: This course will provide strong fundamental of Electromagnetic field theory of

Electrical/Electronics & Communication/Electronic Instrumentation Engineering. The students will

understand the nature of electrostatic and electromagnetic fields. The students will also understand the

behavior of transmission lines under steady state and transient condition essential concepts for the design and

analysis of all communication and radar systems. Moreover, they will also be able to interpret

electromagnetic interference in the systems for compatibility studies.

Teaching and Examination Scheme:

Teaching Scheme Credits Examination Marks Total

Marks L T P C Theory Marks Practical Marks

ESE

(E)

PA (M) ESE (V) PA

(I) PA ALA ESE OEP

3 2 0 5 70 20 10 30 0 20 150

Content:

Sr.

No. Topics

Teaching

Hrs.

Module

Weightage

1

Vector Analysis

Scalars and Vectors, Vector Algebra, The rectangular co-ordinate

system, Vector components and unit vectors, The vector field, The dot

product, The cross product, Circular cylindrical co-ordinates, Spherical

co-ordinate system.

3 9

2

Coulomb’s law and Electric Field Intensity

The experimental law of Coulomb, Electric field intensity, Field due to

a continuous volume charge distribution, Field of a line charge, Field of

a sheet charge.

4 9

3

Electric Flux Density, Gauss’ law and Divergence

Electric flux density, Gauss’ law, Application of Gauss’ law: some

symmetrical charge distributions, Application of Gauss’ law to

differential volume element, Divergence, Maxwell’s first equation, The

divergence theorem.

4 9

4

Energy and Potential

Energy expended in moving a point charge in electric field, The line

integral, Definition of potential and potential difference, The potential

field of a point charge, The potential field of a system of charges,

Potential gradient, The dipole, Energy density in the electrostatic field

4 9

5 Current and Conductors

Current and current density, Continuity of current, Metallic conductors,

3 7

Conductor properties and boundary conditions, Semiconductors.

6

Dielectrics and capacitance

The nature of dielectric materials, Boundary conditions for perfect

dielectric materials, Capacitance, Several capacitance examples,

Capacitance of a two wire line

3 7

7

Poisson’s and Laplace’s Equation

Derivation of Poisson’s and Lapalce’s equations, Uniqueness theorem,

Example of the solution of Laplace’s equation Example of solution of

Poisson’s equation

3 8

8

The Steady Magnetic Field

Biot Savart law, Ampere’s circuital law, Curl, Stoke’s theorem,

Magnetic flux and magnetic flux density, The scalar and vector

magnetic potentials, Derivation of steady magnetic field laws.

4 10

9

Magnetic Forces, Materials and Inductance

Force on a moving charge, Force on a differential current element,

Force between differential current elements, Force and torque on a

closed circuit, The nature of magnetic materials, Magnetization and

permeability, Magnetic boundary conditions, The magnetic circuit,

Potential energy and forces on magnetic materials, Inductance and

mutual inductance

4 9

10

Time Varying Fields and Maxwell’s equation

Faraday’s Law, Displacement current, Maxwell’s equation in point

form, Maxwell’s equation in integral form,

3 7

11

Transmission Lines

Physical description of transmission line propagation, The transmission

line equation, Lossless propagation, Lossless propagation of sinusoidal

voltages, Complex analysis of sinusoidal voltages, Transmission line

equations and their solutions in phasor form

4 8

12

Effects of Electromagnetic Fields

Electromagnetic Interference and Compatibility (EMI/EMC), EMI

Sources, Effects of EMI, Methods to eliminate EMI, EMC Standards,

Advantages of EMC standards, Biological effects of EMI/EMR

(Electromagnetic Interference, Electromagnetic radiation)

3 8

Suggested Specification table with Marks (Theory):

Distribution of Theory Marks

R Level U Level A Level N Level E Level

20 15 15 10 10

Legends: R: Remembrance; U: Understanding; A: Application, N: Analyze and E: Evaluate and above Levels

(Revised Bloom’s Taxonomy)

Note: This specification table shall be treated as a general guideline for students and teachers. The actual

distribution of marks in the question paper may vary slightly from above table.

Reference Books:

1. Engineering Electromagnetics by W.H. Hayt and J A Buck, Tata McGraw Hill Publications

2. Electromagnetic Field Theory and Transmission Lines by G.S.N. Raju, Pearson Education

3. Fundamentals of Electromagnetics by A.V. Mahatme, University Science Press

4. Elements of Electromagnetics by Matthew N.O. Sadiku, Oxford University Press

5. Electromagnetics with Applications by Kraus and Fleisch, Tata McGraw Hill Publications

6. Fundamentals of Engineering Electromagnetics by Sunil Bhooshan, Oxford University Press

Suggested Resource Material for tutorials based on above topics

Numericals based on solving Engg. Electromagnetics problems using MATLAB for tutorials are

available in CD accompanied with the book of “Fundamentals of Engineering Electromagnetics by

Sunil Bhooshan”

Matlab Experiments manual for Electromagnetics by Dr. M.H. Bakr

Course outcome: After the completion of this course the student will have understanding of electrostatic and

magnetostatic fields which in future will help to understand its applications in Electrostatic generators,

Electric power transmission, Lighting protection, Electro deposition, Magnetic separators, Development of

motors, Transformers, Electromagnetic pump and so on

Active Learning Assignments (ALA) : Preparation of power-point slides: which may include videos,

animations, pictures, graphics for better understanding of theory and practical work. The faculty will allocate

chapters/ parts of chapters to groups of students so that the entire syllabus can be covered. The power-point

slides should be put up on the web-site of the College/ Institute, along with the names of the students of the

group, the name of faculty and the department.

Laxmi Institute of Technology , Sarigam Department of Electrical Engineering

Academic Year 2018-19

Assignments Cum Question Bank

Name of Subject : Field Theory Subject Code : 2140909

Chapter/Unit: 1&2

Sr.

No. Questions Remarks

1

Explain (i) Spherical coordinate system.

(ii) Dot Product and Cross Product

(iii) Cylindrical coordinate syste

(iv) Position vector and unit vector

Short Answer

type Questions

2 Explain Electric Field Intensity. Short Answer

type Questions

3 Define Coulomb’s Law Short Answer

type Questions

4

Convert the A(-1,2,3 ) to cylindrical and spherical coordinates,

B(3,600,6) to Cartesian and spherical, C(4, 1100, 1200) in Cartesian

and cylindrical system.

3 mark question

5 Given vector M = 5ax-3ay- 8az and N = 2ax-7ay+5az, find (a) unit

vector along -M+2N (b) magnitude of 5ax + N - 3M 3 mark question

6 Calculate E at P (-1,4,-2) in free space caused by charge Q1= 2µC at

A(0,4,1) and Q2= -3µC at B(1,-2,-1)

4 mark question

7 A 5 mC charge is located in vaccum at M (3,-2,- 4) and -5µC charge

at N(1,-4,2). Find the force on Q1

4 mark question

8 Transform B = y ax – x ay + z az to Cylindrical System. 7 mark question

9 Derive the expression for E at any point P due to infinite uniform

Line charge distributed in free space. 7 mark question

Chapter/Unit: 3 and 4

Sr.

No. Question Remarks

1 State and explain Gauss’s Law. Derive the point form of Gauss’s Law

which relates the flux leaving any closed surface to the charge enclosed. 7 mark question

2 Explain Electric flux and flux density. Also state the relationship between

flux density and electric field intensity. 3 mark question

3 Give the physical significance of Divergence. 3 mark question



4 Derive Maxwell’s first equation applied to electrostatic using Gauss’s Law. 7 mark question

5 Using Gauss’s Law for differential volume element prove divergence of D=

ρv 7 mark question

6 Define Potential gradient. Derive relationship between potential and electric

field intensity. 7 mark question

7 Derive equation of potential difference VAB within the electric field

produced by a point charge Q. 7 mark question

8 Find the work required to move the charge from point A to point B in static

electric field. 7 mark question

9 What is meant by equipotential surface. 3 mark question

Chapter/Unit: 5,6,7

Sr.


1 Define displacement current and current density 3 mark question

2 State and Explain Ampere circuit law 3 mark question

3 State and explain Stoke’s Theorem. 3 mark question

4 Let 𝑉1(𝑟,𝜃,∅) = 6 r and 𝑉2(𝑟,𝜃,∅) = 3. State weather 𝑉1,𝑉2

satisfied Laplace’s equation 7 mark question

5 Explain phenomenon of polarization 3 mark question

6 Give examples of different capacitor configuration. 4 mark question

7 If a potential 𝑉 = 𝑥2𝑦𝑧 + 𝐴𝑦3𝑧 Find ‘A’ So that Laplace’s equation

is satisfied 7 mark question

8 Obtain the Expression for field intensity H at the centre of a circular

carrying current I, using Biot-Savart law 7 mark question

9 Derive boundary condition between two perfect Dielectrics 7 mark question

10 Explain magnetic dipole moment. 4 mark question

11 Derive magnetic boundary condition 7 mark question

12 Derive equation of continuity for current 4 mark question



Chapter/Unit: 8,9,10

Sr.


1 Write Maxwell’s equations for Static Electromagnetic field in point

form and integral form 7 mark question

2 Define curl and write significance to decide types of field on bases

of curl 3 mark question

3 Classify magnetic materials 3 mark question

4 List out any four effects of EMI 4 mark question

5 Discuss inductance. Explain self-inductance and mutual

inductance. 4 mark question

6 Derive transmission line Equation in terms of voltage and current. 7 mark question

7 Explain primary constant and secondary constant of transmission

line 4 mark question

8 Discuss methods for controlling of EMI 7 mark question

9 State and Explain Lorentz force equation on charged particles. 7 mark question

10 Derive transmission line equation with help of equivalent circuit 7 mark question

11 Write sources of Electromagnetic Interference. 3 mark question

12 Give physical description of transmission line propagation 4 mark question

Laxmi Institute of Technology , Sarigam Approved by AICTE, New Delhi; Affiliated to Gujarat Technological University, Ahmedabad


Centre Code: 086 Examination : Mid Semester I Examination

Branch: Electrical Semester: IV Date: 28/1/2019 Sub Code: 2140909

Sub: Field Theory Time:- 9.00 to 10.00 am Marks: 20

Note: Q.1 is compulsory.

Attempt ANY THREE from the remaining.

Letters in Bold are vectors.

Q.1 Derive the expression for Electric field intensity due to line charge

OR

Derive the expression for Electric field intensity due to Surface

charge

5

Q.2(a) Explain (i)Position vector (ii) Dot Product (iii) Cross Product 3

(b) Find the unit vector along - M + 2N, where M = -10ax + 4ay - 8az

and N = 8ax + 7ay - 2az 2

Q.3(a) Transform B = yax - xay + zaz to Cylindrical System. 3

(b) Convert the A(4 ,25o, 120o) to cylindrical and cartesian

coordinates. 2

Q.4(a) Define Coulomb’s Law 1

(b) Calculate E at P (2,5,-1)in free space caused by charge Q1= 2µC at

A(1,0,1) and Q2= -3µC at B(-1,2,3). 4

Q.5(a) Explain the Cylindrical Coordinate system in detail. 4

(b) Find unit vector of A = 5ax + 3ay - 2az 1

1

Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV (NEW) - EXAMINATION – SUMMER 2017

Subject Code: 2140909 Date: 08/06/2017 Subject Name: Field Theory Time: 10:30 AM to 01:00 PM Total Marks: 70 Instructions:

1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks.

MARKS

Q.1 Short Questions 14

1 The direction of vector normal to the plane containing two vectors is

given by ________of those two vectors.

a) dot product b) cross product c) addition d) vector triple product

2 A sharp beam in a cathode ray tube is an example of ______

a) Volume charge b) point charge c) line charge d) surface charge

charge.

3 Choose equation which represents divergence theorem.

= b) =

c) × = d) none of these.

4 The differential volume in spherical co-ordinate system is

a) b) c) d) .

5 At any point on spherical surface, is always directed in the direction

a) b) c) d) .

6 Work done along a path forming a closed contour is_________

a) Infinite b) maximum c) zero d) negative.

7 The flow of charges under the influence of electric field intensity results

in to ________ current

a) drift b) diffusion c) displacement d) radiation

8 Identify poisson’s equation

a) b) c) d)

9 The relation between and is

a) b) c) d)

10 Divergence of vector field never be

a) zero b) positive scalar c) negative scalar d) vector

11 is

a) Point form of Ampere’s circuit law

b) Integral form of Ampere’s circuit law

c) Maxwell’s first equations

d) Faraday’s law

12 The electric field can exert force on

a)stationary charge only b) moving charge only

c) stationary charge and moving charge d) none of above

13 For time varying field

a) =0 b) = 0 c) = d) =0

2

14 The unit of attenuation constant α is

a) neper/km b) rad/km c) degree/km d) decibel/km

Q.2 (a) Define and Explain unit vectors in Cartesian and cylindrical co-ordinate

systems. 03

(b) Explain dot product and cross product of two vectors with their one

application. 04

(c) Derive the expression for at point P on the axis of charged circular

ring, carrying a charge uniformly along its circumference with density

07

OR

(c) An infinite uniform linear charge = 2.0 nC/m lies along the x axis in

free space, while point charge of 8.0 nC is located at (0, 0, 1)

Find E at (2, 3, 4).

07

Q.3 (a) State Gauss’s law. Also write limitations of Gauss’s law 03

(b) Find Divergence of at point P (2,-1,3) 04

(c) Obtain Expression for continuity in integral and differential form. 07

OR

Q.3 (a) Write Maxwell’s equations for Static Electromagnetic field in point form

and integral form. 03

(b) Discuss properties of dielectric materials and define Dielectric strength. 04

(c) Derive expression for electric field intensity and potential due to an

electrical pole. 07

Q.4 (a) Define curl and write significance to decide types of field on bases of

curl. 03

(b) Derive the relation between I and J 04

(c) Using Biot-savart law, find due to infinitely long straight conductor

carrying current of I amp.

07

OR

Q.4 (a) Classify magnetic materials. 03

(b) Given the potential V= 10 (X2 + XY) and a point P (2, -1, 3) on a

conductor to free space boundary. Find V and E̅ at a point P.

04

(c) Explain Stoke’s theorem with its mathematics expression. 07

Q.5 (a) List out any four effects of EMI 03

(b) Explain the terms conduction current density and displacement current

density. 04

(c) Discuss inductance. Explain self-inductance and mutual inductance. 07

OR

Q.5 (a) State the importance property of infinite transmission line. 03

(b) Explain Magnetic dipole moment and magnetization. 04

(c) A line with zero dissipation has R= 0.006ohms/m, L = 2.5 µH/m and

C=4.45pF/m If line is operated at 10 Mhz.

Find i) Characteristics impedance ii) attenuation constant

iii) phase constant iv) velocity of propagation.

v) wave length

07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV (NEW) - EXAMINATION – SUMMER 2018

Subject Code:2140909 Date:28/05/2018 Subject Name:Field Theory Time:10:30 AM to 01:00 PM Total Marks: 70 Instructions:


MARKS

Q.1 (a) State and explain Coulomb’s law. 03

(b) Explain physical Significance of Curl related to types of field. 04

(c) Obtain the Spherical co-ordinates of 10�̅�𝑥 at the point P(x = 2, y = 3, z = 4). 07

Q.2 (a) State and Explain various types of charge distribution with mathematical

equation. 03

(b) Derive relation between current density and Volume charge Density. 04

(c) Define potential difference and potential gradient. Also Establish relation

between Electrical field and potential gradient. 07

OR

(c) An Electrical potential is given by 𝑉 =60 sin 𝜃

𝑟2 v. Find V and E at spherical co-

ordinate P (3, 60°, 25° ) .

07

Q.3 (a) Give examples of different capacitor configuration. 03

(b) If a potential 𝑉 = 𝑥2𝑦𝑧 + 𝐴𝑦3𝑧 Find ‘A’ So that Laplace’s equation is

satisfied.

04

(c) Obtain the Expression for field intensity H at the centre of a circular carrying

current I, using Biot-Savart law 07

OR

Q.3 (a) Write Poisson’s and Laplace equation. also state use of this equation and

uniqueness theorem 03

(b) State and Explain Ampere’s circuit Law. 04

(c) Derive boundary condition between two perfect Dielectrics. 07

Q.4 (a) State and Explain Stoke’s theorem 03

(b) A copper conductor having a 0.8 mm diameter and length 2 cm carries a current

of 20 A. Find Current density, Electrical Field Intensity, voltage drop and

resistance for 2 cm length. Take conductivity of copper is 5.8× 107 S/m.

04

(c) Explain force between two differential current elements. 07 OR

Q.4 (a) Explain magnetic dipole moment. 03

(b) Given point C (5,-2, 3) and D (4,-1, 2) and current element IdL =10-4 (4,-3, 1)

Am at point C, which produce a field dH at point D .Find |𝐝𝐇| . 04

(c) Derive Point form of Maxwell’s equation for static field and time varying field

using Faraday’s law 07

Q.5 (a) Define term Electromagnetic Interference and Electromagnetic compatibility. 03

(b) Write Name of EMC standards bodies. 04

(c) Derive transmission line Equation in terms of voltage and current. 07

2

OR

Q.5 (a) Explain primary constant and secondary constant of transmission line. 03

(b) Give physical description of transmission line propagation. 04

(c) Discuss methods for controlling of EMI 07

*************

1


GUJARAT TECHNOLOGICAL UNIVERSITY BE - SEMESTER–IV (NEW) EXAMINATION – WINTER 2018

Subject Code:2140909 Date:10/12/2018 Subject Name:Field Theory Time: 02:30 PM TO 05:00 PM Total Marks: 70 Instructions:


MARKS

Q.1 (a) State and Explain Coulomb’s law 03

(b) Define unit vector and explain it in each co-ordinate system. 04

(c) Explain spherical co-ordinate system and give relationship between Cartesian and

spherical co-ordinate system. 07

Q.2 (a) State parameters of transmission line and give difference between lumped

parameters and distributed parameters. 03

(b) State and explain Gauss’s law. 04

(c) Explain Physical meaning of divergence and state it’s properties. 07

OR

(c) Obtain equation for flux density due to infinite line charge using Gauss’s law 07

Q.3 (a) Explain Electrical dipole. 03

(b) Explain phenomenon of polarization. 04

(c) Two uniform line charges of density 𝜌𝑙 = 4nc/m lie on the x=0 plane and 𝑌 = ±4 are parallel to Z-axis. Find E at (4,0,10) m.

07

OR

Q.3 (a) Define conservative field. 03

(b) State Maxwell’s equation in point form and integral form for static electromagnetic

field. 04

(c) A dielectric-free space interface has the equation 3𝑥 + 2𝑦 + 𝑧 = 12 𝑚.The origin

side of the interface has ∈𝑛 = 3.0 𝑎𝑛𝑑 𝐸1 = 2𝑎𝑥̅̅ ̅ + 5𝑎𝑧̅̅ ̅ v/m. Find 𝐸2 .

07

Q.4 (a) Define displacement current and current density. 03

(b) State and Explain Ampere circuit law. 04

(c) Derive the expression for potential difference duce to infinite line charge. 07 OR

Q.4 (a) Write Effect of Electromagnetic Interference. 03

(b) State and explain Stoke’s Theorem. 04

(c) Define relaxation time and derive equation for Relaxation time. 07

Q.5 (a) Explain difference between steady magnetic field and time varying magnetic field. 03

(b) Let 𝑉1(𝑟, 𝜃, ∅) = 6

r and 𝑉2(𝑟, 𝜃, ∅) = 3. State weather 𝑉1, 𝑉2 satisfied Laplace’s

equation.

04

(c) Derive transmission line equation with help of equivalent circuit. 07

OR

Q.5 (a) Write sources of Electromagnetic Interference. 03

(b) A circular loop located on 𝑥2 + 𝑦2 = 25, Z=0 carries a direct current of 10 A along

𝑎∅̅̅ ̅ .Determine �̅� at (0,0,4) and (0,0,-4)

04

(c) State and Explain Lorentz force equation on charged particles. 07

*************

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