Syllabus Physics Course : B.Tech Branch : Mechanical Engineering

Bihar Engineering  University, Patna, Bihar, India

Physics Syllabus        Course : B.Tech

Branch : Mechanical Engineering

MODULE 1: ELECTROSTATICS IN VACUUM 

Calculation of electric field and electrostatic potential for a charge distribution; Divergence and Curl of electrostatic field; Laplace’s and Poisson’s equations for electrostatic potential and uniqueness of their solution and connection with steady state diffusion and thermal conduction; practical examples like Farady’s cage and coffee-ring effect; Boundary conditions of electric field and electrostatic potential; Method of images; Energy of a charge distribution and its expression in terms of electric field.

MODULE 2: ELECTROSTATICS IN A LINEAR DIELECTRIC MEDIUM 

Electrostatic field and potential of a dipole. Bound charges due to electric polarization; Electric displacement; boundary conditions on displacement; solving simple electrostatics problems in presence of dielectrics – point charge at the centre of a dielectric sphere, charge in front of a dielectric slab, dielectric slab and dielectric sphere in uniform electric field.

MODULE 3: MAGNETOSTATICS

bio-savart law, divergence and curl of static magnetic field; vector potential and calculating it for a given magnetic field using stokes’ theorem; the equation for the vector potential and its solution for given current densities.

MODULE 4: MAGNETOSTATICS IN A LINEAR MAGNETIC MEDIUM

Magnetization and associated bound currents; auxiliary magnetic field; boundary conditions on and. solving for magnetic field due to simple magnets like a bar magnet; magnetic susceptibility and ferromagnetic, paramagnetic and diamagnetic materials; qualitative discussion of magnetic field in presence of magnetic materials.

MODULE 5: FARADAY’S LAW

Faraday’s law in terms of emf produced by changing magnetic flux; Equivalence of Faraday’s law and motional emf; Lenz’s law; electromagnetic breaking and its applications; Differential form of Faraday’s law expressing curl of electric field in terms of time-derivative of magnetic field and calculating electric field due to changing magnetic fields in quasi-static approximation; Energy stored in a magnetic field.

MODULE 6: DISPLACEMENT CURRENT, MAGNETIC FIELD DUE TO TIME-DEPENDENT ELECTRIC FIELD AND MAXWELL’S EQUATIONS

Continuity equation for current densities; Modifying equation for the curl of magnetic field to satisfy continuity equation; displace current and magnetic field arising from time- dependent electric field; calculating magnetic field due to changing electric fields in quasi- static approximation. maxwell’s equation in vacuum and non-conducting medium; energy in an electromagnetic field; flow of energy and poynting vector with examples. qualitative discussion of momentum in electromagnetic fields.

MODULE 7: ELECTROMAGNETIC WAVES

The wave equation; plane electromagnetic waves in vacuum, their transverse nature and polarization; relation between electric and magnetic fields of an electromagnetic wave; energy carried by electromagnetic waves and examples. momentum carried by electromagnetic waves and resultant pressure. reflection and transmission of electromagnetic waves from a non-conducting medium-vacuum interface for normal incidence.

Syllabus Physics Course : B.Tech Branch : Civil Engineering

Bihar Engineering  University, Patna, Bihar, India

Physics Syllabus        Course : B.Tech

Branch : Civil Engineering

MODULE 1 

TRANSFORMATION OF SCALARS AND VECTORS UNDER ROTATION TRANSFORMATION; FORCES IN NATURE; NEWTON’S LAWS AND ITS COMPLETENESS IN DESCRIBING PARTICLE MOTION; FORM INVARIANCE OF NEWTON’S SECOND LAW; SOLVING NEWTON’S EQUATIONS OF MOTION IN POLAR COORDINATES; PROBLEMS INCLUDING CONSTRAINTS AND FRICTION; EXTENSION TO CYLINDRICAL AND SPHERICAL COORDINATES.

MODULE 2  

POTENTIAL ENERGY FUNCTION; F = - GRAD V, EQUIPOTENTIAL SURFACES AND MEANING OFGRADIENT; CONSERVATIVE AND NON-CONSERVATIVE FORCES, CURL OF A FORCE FIELD;; ENERGY EQUATION AND ENERGY DIAGRAMS; ELLIPTICAL, PARABOLOIC AND CENTRAL FORCES; CONSERVATION OF ANGULAR MOMENTUM HYPERBOLIOC ORBITS; KEPLER PROBLEM; APPLICATION: STELLITE MANOEUVRES.

MODULE 3

NON-INERTIAL FRAMES OF REFERENCE. ROTATING COORDINATE SYSTEM: FIVE-TERMACCELERATION FORMULA. CENTRIPETAL AND CORIOLIS ACCELERATIONS; APPLICATIONS: WEATHER SYSTEMS, FOUCAULT PENDULUM.

MODULE 4 :

HARMONIC OSCILLATOR; DAMPED HARMONIC MOTION – OVER–DAMPED, CRITICALLY DAMPED AND LIGHTLY-DAMPED OSCILLATORS; FORCED OSCILLATIONS AND RESONANCE.

MODULE 5

DEFINITION AND MOTION OF A RIGID BODY IN THE PLANE. ROTATION IN THE PLANE; KINEMATICS IN A COORDINATE SYSTEM ROTATING AND TRANSLATING IN THE PLANE; ANGULAR MOMENTUM ABOUT A POINT OF A RIGID BODY IN PLANAR MOTION. EULER LAW’S OF MOTION THEIR INDEPENDENCE FROM NEWTON’S LAWS, AND THEIR NECESSITY IN DESCRIBING RIGID BODY MOTION; EXAMPLES.

MODULE 6  

INTRODUCTION TO THREE-DIMENSIONAL RIGID BODY MOTION -- (A) ANGULAR VELOCITY VECTOR, AND ITS RATE OF CHANGE AND (B) MOMENT OF INERTIA TENSOR; THREE-DIMENSIONAL MOTION OF A RIGID BODY WHEREIN ALL POINT MOVE IN A COPLANAR MANNER: e.g. ROD EXECUTING CONICAL MOTION WITH CENTER OF MASS FIXED --ONLY NEED TO SHOW THAT THIS MOTION LOOKS TWO-DIMENSIONAL BUT IS THREE-DIMENSIONAL AND TWO –DIMENSIONSAL FORMULATION FAILS.

Assignment Module 01 No. CE 01 Vector Mechanics of Particles

Transformation of Scalars and Vectors under Rotation Transformation

Q.1. Explain “Transformation of Scalars under Rotation Transformation” .

Q.2. Explain “Transformation of Vectors under Rotation Transformation” .

Q.3. Explain “Transformation of Scalars and Vectors under Rotation Transformation” .

Q.4. If a vector of magnitude A is rotated through certain degree, then what is the change in that    
        vector? 

 forces in nature

 
Q.5. Explain forces in nature.
Q.6. Explain about the basic forces in nature with its range and magnitude.

Form Invariance of Newton’s Second Law

Q.7. What do you mean by form Invariance of Newton’s second law, Explain. 

Q.8. Define Galelian Transformations. Derive the Transformation Equations.

Friction

Q.9.Define the term friction ? Explain types of friction.

Q.10. write the differences between static friction and dynamic friction.

Q.11. State the laws of friction.

Q.12. Explain the term angle of friction.

Q.13. Define coefficient of friction and limiting friction.

Newton’s equations of motion in Cartesian Coordinates

 Q.14. The position of a particle of mass m under the influence of a free particle is given by  

             Find the expression for its momentum.                                                   (AKU 2020)

 Q.14.The transformation matrix to move from a set of coordinates axes to a new set x¢, y¢, z¢ through   
         an angle q is 

       

Q.15. If a position vector is represented in a set of x,y,z co-ordinate

         system and x,y co-ordinate is rotated through angle 45° about z-axis. Find the
         transformed value of the components of the position vector A in new co-ordinate
         system of x¢, y¢,z¢.