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ELECTROMAGNETIC THEORY & TRANSMISSION LINES(54011)

II - B.Tech.II Semester

ECE

INTRODUCTION

Prepared by

P.S.S.Pavan GaneshAssociate Professor, Dept of ECE

Sreyas Institute of Engineering & TechnologyNagole.

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CONTENTS

Sl. No Topic Page no

1. Introduction to vectors 0.3

2. Unit Vector 0.4

3. Vector Addition 0.5

4. Vector Subtraction 0.7

5. Position Vector, Distance Vector 0.10

6. Vector Multiplication-Dot Product 0.12

7. Cross Product 0.14

8. Scalar Triple Product 0.17

9. Vector Triple Product 0.18

10. Coordinate Systems-Rectangular 0.21

11. Circular Cylindrical Coordinate System 0.23

12. Spherical coordinates 0.26

13. Vector Calculus 0.30

14. Line, Surface, Volume Integrals 0.37

15. Gradient 0.42

16. Divergence 0.43

17. Divergence theorem 0.44

18. Curl 0.45

19. Stokes Theorem 0.46

20. Laplacian Operator 0.47

21. Class Test Questions 0.49

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CLASS TEST-1I nstructions to the students

1. Answer all questions, mark answer in OMR Sheet only.

2. Write Roll Number, Answers at the time of test only.PRE WRITTEN ANSWER SCRIPTS ARE NOT AL LOWED.

3. Time for Test is 25Min only.

1.1 Identify which of the following quantities is not a vector: [ ]

(a) Force (b) momentum (c) acceleration (d) work

1.2 Which of the following is not a scalar field? [ ]

(a) Displacement of a mosquito in space (b) Light intensity in a drawing room

(c) Temperature distribution in your classroom (d) Atmospheric pressure in a given region

1.3 The rectangular coordinate systems shown in below Figure are right-handed except: [ ]

1.4 Which of these is correct? [ ]

(a) A X A = |A|2 ( b ) A X B + B X A = 0 (c) axay= az (d) ak= ax- ay

where akis a unit vector.

1.5 Which of the following identities is not valid? [ ]

(a) a(b + c) = ab + bc (b) a X (b + c) = a X b + a X c (c) a b =b a (d) aA aB= cos AB

1.6 Let F = 2ax6ay+ 10azand G = ax+ Gyay+ 5az. If F and G have the same unit vector, Gyis [ ]

(a) 6 (b) 0 (c) - 3 (d) 6

1.7 At Cartesian point ( -3, 4, -1), which of these is incorrect? [ ]

1.8 At every point in space, a.a= 1. [ ](a) True (b) False (c) Cannot be determined (d) None of the above

1.9 The divergence theorem [ ]

a) relates a line integral to a surface integral. b) holds for specific vector fields only.

c) works for open surfaces. d) relates a surface integral to a volume integral.

1.10. Which of the following is a mathematically incorrect expression [ ]a) grad div b)grad curl c)div curl d)curl grad

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1.11. Which of the following is zero? [ ]

a)grad div b)curl grad c)div grad d)curl curl

1.12 The cross product of 8ax+6ay (first vector) and 9ax-4az(second vector) is [ ]

(a)72ax-24az (b)-24ax+32ay-54az (c) 72ax-24az+32ay (d) None of the above

1.13. When the origin (0,0,0) of the Cartesian coordinate system is transformed to a spherical representation

(,,), Then [ ](a) = 0 (b)

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OMR Answer Sheet

Student Roll Number:

Branch:_________________Subject:_________________________Unit:_______ Date:______________

Instructions:1. Use Blue or Black Ball point pen only.2. Marking more than one answer can be treated as wrong answer.

3. Each Wrong answer carries negative marks.

Q.No Answer Q.No Answer Q.No Answer

1 11 21

2 12 22

3 13 23

4 14 24

5 15 25

6 16 26

7 17 27

8 18 28

9 19 29

10 20 30

Marks

Obtained