ELECTRICITY AND MAGNETISM

1. Electric Charges and Fields

Conservation and quantization of charge, Coulomb’s Law, Energy of a system of charges. Electric field lines, Electric flux, Gauss’ Law with applications to charge distributions with spherical, cylindrical and planar symmetry. Conservative nature of Electrostatic Field. Electrostatic Potential. Potential as line integral of field, potential difference, Gradient of a scalar function, Derivation of the field from the potential, potential of a charge distribution, Uniformly charged disc. Force on a surface charge, energy associated with an electric field, Gauss’s theorem and differential form of Gauss’s law, Laplacian and Laplace’s equation, Poisson’s equation. Force and Torque on a dipole.

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2. Electric Fields Around Conductors

Conductors and insulators, General electrostatic problem. Boundary conditions, Uniqueness theorem, Electrostatic energy of system of charges. Electrostatic energy of a charged sphere. Conductors in an electrostatic Field. Surface charge and force on a conductor. Capacitance of a system of charged conductors. Parallel-plate capacitor. Capacitance of an isolated conductor. Method of Images and its application to: Plane Infinite Sheet and Sphere.

3. Dielectric Properties of Matter

Dielectrics, Moments of a charge distribution, Potential and field of a dipole, Atomic and molecular dipoles, Induced dipole moments, Permanent dipole moments, electric field caused by polarized matter, field of a polarized sphere, dielectric sphere in a uniform field, Gauss’s law in a dielectric medium, Electrical susceptibility and atomic polarizability, Energy changes in polarization, Polarization in changing fields. Displacement vector D. Relations between E, P and D.

4.The Fields of Moving Charges

Magnetic forces, Measurement of a charge in motion, invariance of charge, Electric field measured in different frames of reference, Field of a point charge moving with constant velocity, Field of a charge that starts or stops, Force on a moving charge, Interaction between a moving charge and other moving charges.

5. Magnetic Field

Magnetic force between current elements and definition of Magnetic Field B. Biot-Savart’s Law and its simple applications: straight wire and circular loop. Current Loop as a Magnetic Dipole and its Dipole Moment (Analogy with Electric Dipole). Ampere’s Circuital Law and its application to (1) Solenoid and (2) Toroid. Properties of B: curl and divergence. Vector Potential. Magnetic Force on (1) point charge (2) current carrying wire (3) between current elements. Torque on a current loop in a uniform Magnetic Field. Change in B at a current sheet; Transformations of electric and magnetic fields. Rowland’s experiment, Hall effect.

6. Magnetic Properties of Matter

Response of various substances to magnetic field, Force on a dipole in an external field, Electric currents in Atoms, Electron spin and Magnetic moment,types of magnetic materials, Magnetization vector (M). Magnetic Intensity (H). Magnetic Susceptibility and permeability. Relation between B, H, M. Ferromagnetism. B-H curve and hysteresis.

7. Electromagnetic Induction

Universal law of induction, Mutual inductance, Reciprocity theorem, Self inductance, Energy stored in a Magnetic field. A circuit containing self inductance, Displacement current and Maxwell’s equations.

8. Alternating Current Circuits

A resonance circuit, Kirchhoff’s laws for A.C. networks. Phasor, Complex Reactance and Impedance. Skin effect, Power and Energy in A.C. circuits, Anderson’s Bridge, Instantaneous Power, Average Power, Reactive Power, Power Factor.

9. Sinusoidal Circuit Analysis for RL, RC and RLC Circuits. Series LCR Circuit

1. Resonance,
2. Power Dissipation and
3. Quality Factor, and
4. Band Width. Parallel LCR Circuit.
5. Ballistic Galvanometer:Torque on a current Loop.
6. Ballistic Galvanometer:Current and Charge Sensitivity. Electromagnetic damping. Logarithmic damping.CDR.

Suggested Reading

1. Electricity and Magnetism (Berkley, Phys. Course 2), Edward M. Purcell, 1986 McGraw-Hill Education
2. Electricity and Magnetism: A.S. Mahajan & A.A. Rangwala (Tata- McGraw Hill), 1988.
3. Electricity, Magnetism & Electromagnetic Theory, S. Mahajan and Choudhury, 2012, Tata McGraw
4. Introduction to Electrodynamics, D.J. Griffiths, 3rd Edn., 1998, Benjamin Cummings.
5. Feynman Lectures Vol.2, R.P. Feynman, R.B. Leighton, M. Sands, 2008, Pearson Education
6. Elements of Electromagnetics, M.N.O. Sadiku, 2010, Oxford University Press.
7. Electricity and Magnetism, J.H.Fewkes & J.Yarwood. Vol. I, 1991, Oxford Univ. Press.