It gives us immense pleasure and profound satisfaction to present the book “Electrodynamics-I”, meticulously prepared in accordance with the National Education Policy (NEP) 2020 and the revised syllabus prescribed by the University of Mumbai for the Undergraduate Semester III Physics Programme under Major Vertical – I. This book has been designed to meet the academic requirements of students enrolled under Scheme–I, Scheme–II, and Scheme–III.
Electrodynamics forms one of the fundamental pillars of Physics and provides the conceptual framework for understanding electric and magnetic phenomena governing nature and modern technology. The subject not only develops analytical and mathematical skills but also lays the foundation for advanced studies in Electronics, Electromagnetic Theory, Optics, Communication Systems, Plasma Physics, and several interdisciplinary branches of science and engineering.
This book has been carefully designed to cater to the needs of undergraduate students by presenting the subject matter in a simple, systematic, and student-friendly manner. Every effort has been made to explain the concepts with clarity while maintaining the mathematical rigor expected at the university level. The treatment of topics follows the sequence prescribed in the syllabus and emphasizes conceptual understanding, derivations, problem-solving techniques, and physical interpretation.
The book covers important topics such as Coulomb’s Law, Electric Potential, Line, Surface and Volume Integrals, Gauss’s Law, Fundamental Theorems of Vector Calculus, Dirac Delta Function, Electric Field and its Divergence and Curl, Poisson’s and Laplace’s Equations, Uniqueness Theorems, Biot–Savart Law, and magnetic fields due to various current distributions including straight conductors, circular coils, and solenoids.
Contents –
Unit I
1. Electrodynamics and Vector Calculus
1.1 Introduction
1.2 Coulomb’s Law
1.2.1 Coulomb’s Law in Vector Form
1.3 Gradient, Divergence and Curl
1.3.1 The Gradient
1.3.2 The Divergence
1.3.3 The Curl
1.3.4 Formulae Involving
1.4 Vector Integration
1.4.1 Line Integral
1.4.2 Surface Integral
1.4.3 Volume Integral
1.5 Fundamental Theorems of Calculus
1.5.1 Fundamental Theorem for Gradient
1.6 Introduction to Dirac Delta Function (1-D Only)
1.6.1 Translated Dirac Delta Function
1.6.2 Properties of Dirac Delta Function
1.7 Electric Field
1.7.1 Electric Field Due to Point Charge
1.8 Divergence of Electric Field
1.9 Curl of Electric Field
Unit II
2. Electrostatic Potential
2.1 Introduction
2.2 Basics of Electrostatics
2.3 Comments on Potential
2.4 Poisson’s Equation and Laplace’s Equation
2.5 Solution and Properties of 1D Laplace Equation with Problem
2.6 Properties of 2D and 3D Laplace Equation
2.7 First and Second Uniqueness Theorem
3. Magnetostatics 55 – 74
3.1 Introduction
3.2 Magnetic Field
3.3 Biot-Savart Law
3.4 Magnetic Field Due to a Current Carrying Straight Wire (Conductor)
3.5 Magnetic Field Due to a Circular Loop
3.6 Magnetic Field Due to a Long Solenoid
Appendix