# ELECTROMAGNETIC WAVES(18EC55)

## ELECTROMAGNETIC WAVES

### Course Learning Objectives: This course will enable students to:

• Understand the applications of Coulomb‘s law and Gauss law to different charge distributions and the applications of Laplace‘s and Poisson‘s Equations to solve real time problems on capacitance of different charge distributions.
• Understand the physical significance of Biot-Savart‘s, Amperes‘s Law and Stokes‘theorem for different current distributions.
• Infer the effects of magnetic forces, materials and inductance.
• Know the physical interpretation of Maxwell‘ equations and applications for Plane waves for their behavior in different media.
• Acquire knowledge of Poynting theorem and its application of power flow.

### Module-1

Revision of Vector Calculus – (Text 1: Chapter 1)
Coulomb’s Law, Electric Field Intensity and Flux density: Experimental law of Coulomb,
Electric field intensity, Field due to continuous volume charge distribution, Field of a line charge,
Field due to Sheet of charge, Electric flux density, Numerical Problems. (Text: Chapter 2.1 to 2.5,
3.1) ### Module -2

Gauss’s law and Divergence: Gauss ‘law, Application of Gauss’ law to point charge, line charge,
Surface charge and volume charge, Point (differential) form of Gauss law, Divergence. Maxwell‘s
First equation (Electrostatics), Vector Operator ▼ and divergence theorem, Numerical Problems
(Text: Chapter 3.2 to 3.7).
Energy, Potential and Conductors: Energy expended or work done in moving a point charge in
an electric field, The line integral, Definition of potential difference and potential, The potential
field of point charge, Potential gradient, Numerical Problems (Text: Chapter 4.1 to 4.4 and
4.6).Current and Current density, Continuity of current. (Text: Chapter 5.1, 5.2)

### Module-3

Poisson’s and Laplace’s Equations: Derivation of Poisson‘s and Laplace‘s Equations, Uniqueness
theorem, Examples of the solution of Laplace‘s equation, Numerical problems on Laplace equation
(Text: Chapter 7.1 to 7.3)
Steady Magnetic Field: Biot-Savart Law, Ampere‘s circuital law, Curl, Stokes‘ theorem, Magnetic
flux and magnetic flux density, Basic concepts Scalar and Vector Magnetic Potentials, Numerical
problems. (Text: Chapter 8.1 to 8.6)

### Module -4

Magnetic Forces: Force on a moving charge, differential current elements, Force between
differential current elements, Numerical problems (Text: Chapter 9.1 to 9.3).
Magnetic Materials: Magnetization and permeability, Magnetic boundary conditions, The
magnetic circuit, Potential energy and forces on magnetic materials, Inductance and mutual
reactance, Numerical problems (Text: Chapter 9.6 to 9.7).
Faraday’ law of Electromagnetic Induction –Integral form and Point form, Numerical problems
(Text: Chapter 10.1)

### Module -5

Maxwell’s equations Continuity equation, Inconsistency of Ampere’s law with continuity
equation, displacement current, Conduction current, Derivation of Maxwell‘s equations in point
form, and integral form, Maxwell’s equations for different media, Numerical problems (Text:
Chapter 10.2 to 10.4)

Uniform Plane Wave: Plane wave, Uniform plane wave, Derivation of plane wave equations from
Maxwell’s equations, Solution of wave equation for perfect dielectric, Relation between E and H,
Wave propagation in free space, Solution of wave equation for sinusoidal excitation, wave
propagation in any conducting media (γ, α, β, η) and good conductors, Skin effect or Depth of
penetration, Poynting‘s theorem and wave power, Numerical problems. (Text: Chapter 12.1 to
12.4) #### Course Outcomes: After studying this course, students will be able to:

• Evaluate problems on electrostatic force, electric field due to point, linear, volume charges by applying conventional methods and charge in a volume.
• Apply Gauss law to evaluate Electric fields due to different charge distributions and Volume Charge distribution by using Divergence Theorem.
• Determine potential and energy with respect to point charge and capacitance using Laplace equation and Apply Biot-Savart’s and Ampere’s laws for evaluating Magnetic field for different current configurations
• Calculate magnetic force, potential energy and Magnetization with respect to magnetic materials and voltage induced in electric circuits.
• Apply Maxwell’s equations for time varying fields, EM waves in free space and conductors and Evaluate power associated with EM waves using Poynting theorem

#### Question paper pattern:

• Examination will be conducted for 100 marks with question paper containing 10 full questions, each of 20 marks.
• Each full question can have a maximum of 4 sub questions.
• There will be 2 full questions from each module covering all the topics of the module.
• Students will have to answer 5 full questions, selecting one full question from each module.
• The total marks will be proportionally reduced to 60 marks as SEE marks is 60.

#### Text Book:

W.H. Hayt and J.A. Buck, ―Engineering Electromagneticsǁ, 8th Edition, Tata McGraw-
Hill, 2014, ISBN-978-93-392-0327-6.

#### Reference Books:

1. Elements of Electromagnetics – Matthew N.O., Sadiku, Oxford university press, 4thEdn.
2. Electromagnetic Waves and Radiating systems – E. C. Jordan and K.G. Balman, PHI, 2ndEdn.
3. Electromagnetics- Joseph Edminister, Schaum Outline Series, McGraw Hill.
N. NarayanaRao, ―Fundamentals of Electromagnetics for Engineeringǁ, Pearson.
• Study the different coordinate systems, Physical significance of Divergence, Curl and Gradient.