Phys-3011-Electricity and Magnetism

MAJOR-PHYSICS COURSE

Semester III

MAJOR-III: PHYS3011: Electricity and Magnetism (Credits: Theory - 04, Practical - 01)

F.M. = 75 (Theory - 40, Practical – 20, Internal Assessment – 15)

Course Objective: The objective of this paper is to give the basic concept as well as an in-depth understanding of the principles of electricity and magnetism and apply them to solve the problems related.

60 Hours

Electrostatics

Unit I Quantization of electric charge, Coulomb’s law, Principle of superposition, Electric field (Physical concept, quantitative definition and its source), Electric field of a point charge, Electric field lines and their properties, Charge density, Volume charge density, Surface charge density, Line charge density, Electric fields due to continuous charge distributions, Electric field due to a uniformly charged non-conducting rod at an axial point and at a point on the perpendicular bisector of that rod, Electric field due to a circular disc on the axial point.

5 Hours

Unit 2 Electric flux, Gauss’ law, Differential form of Gauss’ law, Equivalence of Coulomb’s law and Gauss’ law, Gaussian surface, Application of Gauss’ law to evaluate the electric field at a point for charge distributions with spherical (A thin spherical shell of radius R with a charge +Q evenly distributed over its surface, thick shell, and a solid sphere of radius R with uniform volume charge density), planar (Infinitely large non-conducting plane with uniform surface charge density) and cylindrical symmetry (Infinitely long non-conducting rod of uniform line charge density).

6 Hours

Unit 3 Conservative nature of electrostatic field, Electric scalar potential, Relation between the electric field and the electric potential, Electric potential of a point charge and a group of point charges, Electric potential due to a continuous charge distribution, Electric potential and field due to an electric dipole, Force and torque acting on an electric dipole in a uniform electric field, Laplace’s and Poisson’s equations, The Uniqueness theorem (Proof required).

5 Hours

Unit 4 Electrostatic potential energy, Electrostatic potential energy of a collection of point charges, Electrostatic potential energy of a continuous charge distribution (general expression and a charged sphere as an example), Self energy, Classical electron radius, Electrostatic potential energy of an electric dipole in a non-uniform electric field.

4 Hours

Unit 5 Equipotential surfaces, Electrostatic equilibrium properties (regarding electric charge, electric field and electric potential) of a conductor in a uniform electric field, Surface charge and force on a conductor, Boundary conditions on the electric field at the interface between a vacuum and a conductor, Capacitor as a charge storing device, Capacitance and the energy stored in a capacitor, Capacitance of a system of charged conductors, Parallel-plate capacitor, Capacitance of an isolated conductor, Method of Images and its application to: (1) Plane infinite sheet and (2) Sphere.

6 Hours

Unit 6 Dielectric properties of matter: Electric field inside a matter, Polarization, Polarization charges, Electrical susceptibility and dielectric Constant, Capacitor (parallel-plate, spherical, cylindrical) filled with dielectric, Displacement vector D, Relations between E P and D, Gauss’ Law in dielectrics, Boundary conditions between two dielectric interfaces.

4 Hours

Steady Electric Current

Electric current, Current density, Continuity equation, Conductivity, Ohm’s law, Electromotive force, Kirchhoff’s first and second law- statement and applications, Thevenin′s, Norton′s and maximum power transfer theorems and their applications.

2 Hours

Magneto-statics

Unit 1 : Electric current as a source of magnetic field, Definition and units (SI) of: Magnetic flux density B, Magnetic field strength H and Magnetization vector M, Relation between B, H and M , Magnetic susceptibility and magnetic permeability, Boundary conditions between two magnetic media, Force (Lorentz force) on a moving charge in the simultaneous presence of both electric and magnetic fields, Trajectory of a charged particle in a crossed uniform electric and magnetic fields.

3 Hours

Unit 2 Biot Savart’s Law and its applications: B due to current in (i) a long straight conductor, a circular loop, a solenoid, Current loop as a magnetic dipole and its dipole moment.

3 Hours

Unit 3 -Ampere’s circuital law and its applications: ⃗ due to current in (i) a long straight conductor, a solenoid and a toroid.

2 Hours

Unit 4 Magnetic force on (i) a current element, (ii) a line current, Force between two current elements, Divergence and Curl of B (Gauss and Ampere’s laws), Physical significance of the nature of the divergence and curl of B, Magnetic vector potential.

3 Hours

Transient current

Growth and decay of currents in LR, CR and LCR circuits, Time constant.

2 Hours

Alternating Current

Source of alternating current, Mean value, Peak value and RMS value of alternating voltage and current, Inductive and capacitive reactance, Real power, Reactive power and apparent power, Power triangle, Power factor, Series LCR circuit analysis, Phasor diagrams (AC voltage from a source (V), Current through the resistor R (iR) and the voltage across R (VR), Current through the capacitor C (ic) and the voltage across C (Vc), Current through the inductor L(iL) and the voltage across L (VL), Calculation of total impedance of a series LCR circuit using the phasor diagram of V, VR, VL and Vc, Parallel LCR circuit analysis, Resonance in LCR circuits (series and parallel), LC oscillations.

7 Hours

Electromagnetic Induction

Faraday’s law, Lenz’s law and conservation of energy, Motional EMF, Eddy current, Principle of power generation, Self-inductance and mutual inductance, Induction oven, Induction brake, Reciprocity theorem, Energy stored in a magnetic Field, Introduction to Maxwell’s equations, Continuity equation.

4 Hours

Electrical equipment

Moving coil ballistic and dead beat galvanometers: Working principle, Derivation of the equation relating between the charge flowing through the coil and the ballistic throw of the galvanometer, Damping correction, Current, charge and voltage sensitivities of a moving coil galvanometer, Equation of motion of the coil, Non-oscillatory, aperiodic or dead beat motion, Critical damping, Light damping: Ballistic motion, Uses.

4 Hours

Course Outcome: At the end of this course, students will be able to comprehend the concept of electric field, electric flux, magnetic field and their origin. They will learn to apply the Gauss’s theorem to find the electric fields for different types of charge distribution. The students will develop a sound perception about Electrostatics, Magneto-statics, Electric current and electromagnetic induction.