Physics BSc Syllabus Sargodha University

Physics (Elective)


Note:    The Paper A, B, & C are Subjective and Paper D & E are of Practical. The each Subjective paper is of 50 marks and Paper D & E are of 25 marks each. The Papers are further subdivided into sections


PAPER: A                                                                                                        50 Marks



Vector in 3 dimensions Introduction; Direction Cosines; Spherical polar coordinates;


Vector derivatives and operations Divergence and curl of a vector, and gradient of a scalar.
Gradient, Divergence and Curl of a Vector Physical application of each type; Divergence and Flux of a

vector field, curl and line integral (mutual relation)

Divergence Theorem, Stokes’ Theorem Derivation, physical importance and applications to specific

cases. Converting from differential to integral forms

Reference Book: FIELD AND WAVE ELECTROMAGNETICS (Second Edition) by David K. Cheng, Addison-Wesley Series in Electrical Engineering (ISBN 0-201-52820)

Particle Dynamics

Topics Scopes
(Advanced applications of Newton’s laws) Dynamics of Uniform motion Frictional forces: microscopic basis of this force    Conical pendulum; the rotor, circular the banked curve.
Equations of motion. Deriving kinematics equations X(V), v(t) using integrations. Constant and Non constant Forces and special examples.
Time dependent forces Obtaining x(t), v(t) for this case using integration method
Effect of drag forces on motion Applying Newton’s Laws to obtain v(t) for the case of motion with time dependent drag(viscous) forces; terminal velocity. Projectile motion/ air resistance.
Non inertial frames and Pseudo forces Qualitative discussion to develop understanding. Calculation of pseudo forces for simple cases ( linearly accelerated references frame). Centrifugal force as an example of pseudo force; Carioles force.
Limitations of Newton’s Laws. Discussion.
Suggested level Ch: 6: Resnick , Halliday and Krane(R.H.K)
Work done by a constant force, work done by a variable force(1-dimension). (Essentially a review of grade-XII Concepts use of integration technique to calculate work done (e.g. in vibration of a spring obeying Hooks Law)
Work done by a variable(2-dimensional case) Obtaining general expression force  and applying to simple cases e.g. pulling a mass at the end of a fixed string against gravity.
Work energy theorem. General proof Of work energy theorem. Qualitative Review of work energy
Power Theorem. Derivation using integral calculus. Basic formula and applications.
Reference Frames Energy changes with respect to observers in different inertial frames.
Suggested Level: Ch. 7 of R.H.K.
Conservative, and non Conservative forces Definition of either type of force & examples; work done in a closed path.

1-D conservative system; force as the gradient of potential energy; applications to the case a spring and force of gravity.

One dimensional conservative system Obtaining velocity in terms of U and E ; stable, unstable and neutral equilibrium. Analytic solution for x(t).
2, 3 dimensional conservative systems Change in P.E. for motion in 3-d force. Force as the gradient of the potentials. Work done in 2, 3 dimensional motion.
Conservation of energy in a system of particles Law of conservation of total energy of an isolated system
Suggested Level: Ch.8 of H.R.K.
Two particle system and Generalization to many particle systems. Centre of mass: Its position velocity and equation of motion
Centre of mass of solid objects Calculation of center of mass of solid objects using integral calculus.

Calculating C.M. of,

I.                                                                                                                                                                                                     Uniform Rod.



Momentum Changes in a system of        variable mass. Derivation of basic equation; application to motion of a rocket (determination of its mass as a function of time).
Suggested level…. Ch.9 of H.R.K.
Elastic Collisions (a) one dimensions.
Conservation of momentum during Collision. (b) Two dimensions (Oblique Collisions)
Inelastic collision One and two dimensions
Collisions in centre of Mass reference frame Simple applications: obtaining Velocities in c.m. frame.
Suggested Level Ch.: 10 of H.R.K.
Overview of rotational Dynamics Relationships between linear & angular variables; scalar and vector form.

Kinetic energy of rotation; Moment of Inertia.

Parallel axis theorem Prove and Illustrate; apply to simple cases
Determination of moment of inertice of various shapes. Rotational dynamics of rigid bodies. Equations of rotational motion and effects of application of torques.
Combined rotational and transnational motion Rolling without slipping
Suggested Levels Ch. 12 of H.R.K
Angular Velocity Definition, Conservation of angular momentum, effects of Torque
Stability of spinning objects Discussion with examples.
The spinning Top Effects of torque on the angular momentum, precessional motion.
Suggested Level Ch 13 H.R.K
Review of basic concepts of gravitation. Gravitational effect of a spherical mass distribution Mathematical treatment
Gravitational Potential Energy Develop using integration techniques; calculation of escape velocity
Gravitational field & potential Develop the idea of field of force
Universal Gravitational Law Motion of Planets and Keplers laws. (Derivation & explanation) Motion of satellites. Energy considerations in planetary and satellite motion. Qualitative discussion on application of gravitational law to the Galaxy.
Suggested Levels Ch 16 of H.R.K
Elastic Properties of Matter Physical basic of elasticity Tension, compression & Shearing

Elastic Modulus; Elastic limit

Suggested Level Ch 14 H.R.K
Fluid Statics Variation of Pressure in fluid at rest and with height in the atmosphere.
Surface Tension Physical basis; role in formation of drops and bubbles
Suggested Level Ch 17 H.R.K
Fluid Dynamics General concepts of fluid flow, streamline and the equation of continuity
Bernoulli’s Equation Derivation and some applications such as dynamic lift thrust on a rocket
Viscosity Physical basis; obtaining the coefficient of viscosity, practical example of viscosity; fluid flow (Poisenille’s law)
Suggested Level Ch 18 R.H.K
Trouble with classical Mechanics Qualitative discussion of inadequacy or paradoxes in classical ideas of time, length and velocity.
Postulates of Relativity Statements and Discussion
The Lorentz Transformation inverse transformation Derivation, Assumptions on which derived application of the same Transformation of velocities.
Consequences of Lorentz transformation Relativity of time, relativity of length
Relativistic momentum Derivation
Relativistic energy Derive E=mc2
Suggested level Partially covered by Ch: 21 of H.R.K




Harmonic oscillations
Simple harmonic oscillation (SHM) Obtaining and solving the basic equation of motion x(t), v(t), a(t). Energy considerations in SHM
Application of SHM Torsional Oscillators; Physical pendulum,

Simple pendulum

SHM and uniform circular motion

Lissaajous patterns.

Combinations of Harmonic motion.
Damped Harmonic Motion Equation of damped harmonic motion,

Discussion of its solution.

Forced Oscillations and resonances Equation of forced oscillation, discussion of its solution. Examples of resonances.
Suggested level Ch.:15 of H.R.K


Mechanical waves Travelling waves Phase velocity of traveling waves; Sinusoidal waves; group speed and dispersion.
Waves speed Mechanical analysis
Wave equation. Discussion of solution.
Power and intensity in wave motion. Derivation and discussion
Principle of superposition (basic ideas). Interference of waves, standing waves. Phase changes on reflection; Natural frequency, resonance.
Suggested level Ch.: 19 of H. R. K.


Beats Phenomenon Analytical treatment
Doppler Effect Moving source, moving observer, both object and source moving.
Suggested level Ch.: 20 of H. R. K.


Nature of light Visible light (Physical characteristics)
Light as an Electro-magnetic wave Speed of light in matter: physical aspect path difference, phase difference etc.
Suggested level Ch : 42 H. R. K.
Adding of Electromagnetic waves using phasors. Coherence of sources; Double slit interference, analytical treatment.
Interference from thin films Michelson Interferometer Newton’s rings (analytical treatment).

(Discussion to include use of a compensating plate; Michelson interferometer use in determining velocity of light.)

Fresenel’s Biprism and its use.
Suggested level Ch : 45 H. R. K.
Diffraction Difference at single slit; Intensity in single slit diffraction using phasor treatment and analytical treatment using addition of waves. Slit interference & diffraction combined. Diffraction at a circular aperture
Diffraction from multiple slits Discussion to include with of the maxima.
Diffraction grating. Discussion, use in spectrographs. Dispersion and resolving power of gratings.
Holography Qualitative discussion.
Suggested level Ch : 46, 47 H. R. K.
Polarization Basic definition, production of polarization by polarizing sheets, by reflection, by double refraction and double scattering.
Description of polarization states Linear, Circular, elliptic polarization
Rotation of plane of polarization Use of Polarimeter.
Suggested level Ch : 48 H. R. K.

PAPER: B                                                                                                    50 Marks



Kinetic theory of the ideal gas,

Work done on an ideal gas

Review of previous concepts.
Internal energy of an ideal gas To include the Equi-partition of energy.
Intermolecular forces.

Quantitative discussion.

Van der Waals equation of state.
Suggested level Ch : 23 H. R. K.
Statistical, distribution and mean values Mean free path and microscopic calculations of mean free path.
Distribution of molecular speeds

Distribution of energies

Maxwell distribution; Maxwell-Boltzmann energy distribution; Internal energy of an ideal gas.
Brownian motion Qualitative description. Diffusion, conduction and Viscosity
Suggested level: Ch: 24 H.R.K.
Review of previous concepts. first law of Thermodynamics& its applications
First law of thermodynamics,

Transfer of heat.

cyclic and free expansion.
Suggested level: Ch 25 H.R.K.


Reversible and irreversible Definition , discussion.   Definition,
Process, second law. Heat engine. Refrigerator and second law.
Cycle; Carnot engines. Calculation of efficiency of heat engines.
Thermodynamics temperature scale Absolute zero: negative temperature, (discussion)
Entropy   .. Entropy in reversible process

Entropy in irreversible process

Entropy and second law

Entropy and probability.

Suggested level Ch :26H.R.K.
Low temperature physics liquification of gases : Joules – Thomason effect.



Electric charge

Conductors and Insulators Vector form of Coulomb’s Law.

(Review of Previous concepts) Coulomb’s law, law for point charges.

Quantization and conservation of charge. (Discussion)

Suggested level Ch : 27 H.R.K.
Electric Field  
Field due to a point charge; due to several point charges, Electric dipole.
Electric field of continuous charge distribution. e.g. Ring of charge; disc of charge; infinite line of charge.
Point Charge in an electric field

Dipole in an electric field

Torque on and energy of a dipole in uniform field.
Gauss’s Law Electric flux; Gauss’s law; (Integral and differential forms)
Applications of Gauss’s Law (Integral form) Charged isolated conductors; conductor with a cavity, field near a charged conducting sheet. Field of an infinite line of charge; Field of an infinite sheet of charge. Field of spherical shell. Field of spherical charge distribution.
Suggested level: Ch :  29 H.R.K.
ELECTRICAL POTENTIAL Potential due to point charge. Potential due to collection of point charges. Potential due to dipole. Electric potential of continuous charge distribution. Equipotential surfaces.
Calculating the field from the potential Field as the gradient or derivative of potential. Potential and field inside and outside an isolated conductor
Suggested level Ch  : 30 H. R. K.
Capacitors and dielectrics Capacitance; calculating the electric field in a capacitor. Capacitors of various shapes, cylindrical, spherical etc. Energy stored in an electric field. Energy per unit volume.
Capacitor with dielectric Electric field of dielectric

(1)                     An atomic view

(2)                     Application of Gauss’s Law to capacitor with dielectric.

Suggested level Ch: 31 H.R.K.
Electric current Current density, Resistance, resistivity, conductivity (Microscopic & macroscopic view of resistivity)
Ohm’s Law Basic definition. Analogy between current and heat flow. Microscopic view of Ohms Law.
Energy transfers in an electric circuit
Semiconductors, Super- conductors Descriptive giving basic idea
Suggested level Ch : 32 H.R.K.
Calculating the current in a single loop, multiple loops; voltages at various elements of a loop. Use of Kirchoff’s 1st and 2nd Law.
RC circuits. Growth and decay of charge/ current in an RC circuit. Analytical treatment.
Suggested Level Ch 33 H.R.K


Magnetic Field, B. Basic idea.
Magnetic force on a charged particle magnetic force on a current. Recall the previous results. Do not derive.
Torque on a current loop Magnetic dipole Define Energy of magnetic dipole in field. Discuss quantitatively
Ampere’s LAW
Biot-Savarts Law Analytical treatment and applications to a current loop, force on two parallel current changing conductors.
Ampere’s Law Integral and differential forms, applications to solenoids and Toroids. (Integral form)
Suggested Level Ch : 35 H.R.K


Faraday’s Law Magnetic Flux. Consequences of Faraday’s Law.
Lenz’s Law Discussion, Eddy currents etc.
Motional E.M.F. Quantitative analysis
Induced Electric fields Calculation and applications
Suggested level Ch 36 H.R.K
Magnetic Properties of Matter
Gauss’s Law for magnetism Discussing and developing concepts of conservation of magnetic flux
Differential form of Gauss Law
Origin of Atomic and Nuclear magnetism Basic ideas’ Bohr Magnetron
Magnetization Defining M. B. u.
Magnetic Materials Para magnetism, Diamagnetism, Ferromagnetism Discussion. Hysteresis in Ferromagnetic materials.
Suggested level Ch 37 H.R.K
Inductance Basic definition. Inductance of a Solenoid; Toroid.
LR Circuits Growth and decay of current, analytical treatment.
Energy stored in magnetic field Derive Energy density and the magnetic field
Electromagnetic Oscillation Qualitative discussion

Quantitative analysis using differential equations (without considering damped and forced oscillations) Forced electromagnetic oscillations and resonance

Suggested Level: Ch 38 H.R.K
Alternating current CIRCUITS AC current in resistive, inductive and capacitive elements.
Single loop RLC circuit Analytical expression for time dependent solution Graphical analysis phase angles
Power in AC circuits Power Phase angles RMS values power factor
Transformer basic transformer equation
Suggested level: Ch,39 R.H.K.
Maxwell’s equations
Summarizing the electromagnetic equations Gauss’s law for electromagnetism; Faraday Law; Ampere’s law
Induced magnetic fields and .Displacement current Development of concepts, applications.
Maxwell’s equations.. (integral & differential forms) discussion and implications.
Suggested level: Ch:40: H.R.K

Electromagnetic waves

Generating an electromagnetic wave.
Traveling waves and Maxwell’s equations Analytical treatment; obtaining differential form  Maxwell’s equation obtaining the velocity of

Light from Maxwell’s equations.

Energy transport and the Poynting vector.. Analytical treatment and discussion of physical concepts.
Suggested level: Ch.41 H.R.K.

Paper: C                                                                                            50 Marks



Semiconductor materials Idea of energy bands and energy gaps (qualitative P-type, N-type material.
Junction diode Structure, Characteristics and Application as rectifiers
Transistor basic structure and operation
Transistor biasing.. Biasing for amplifiers; Characteristics of common base, Common emitter, Common collector, Load line, Operating  point, Hybrid parameters.
Transistor as an amplifier Common emitter mode.
Amplification with feedback oscillators. Positive & negative feedback Oscillators. Multivibrators.
Logic Gates OR, AND, NOT , NAND, NOR and their basic applications.
Suggested level A-Level Physics by ROGER MUNCASTER, 2nd Edition.

Understanding Physics for Advance Level by JIM BREITHAUPT, Published

by Hutchinson,

ISBN 0 09 1645816.


Modern physics

Quantum physics

Thermal radiations..

(Black body radiation)

Stefan Boltzmann, Wien and Planck’s law….. Consequences.
The quantization of energy. Quantum numbers; Correspondence principle.
Photoelectric effect.
. Einstein’s photon theory. Explanation of photoelectric effect.
The Compton Effect Analytical treatment.
Line Spectra Quantitative discussion; Explanation using quantum theory.
Suggested level Ch: 49 H.R.K.


Wave behavior of particles De Broglie hypothesis
Testing De Broglie’s hypothesis Davisson-Germer Expt and explanation.
Waves, Waves Packets and Particles Localizing a wave in space and time
Heisenberg’s uncertainty principle (HUP) HUP for momentum-position and Energy Time; HUP applied to single slit diffraction
Wave Function Definition, relation to probability of particle.
Schrödinger Equation. To be presented without derivation, and applied to specific cases e.g. step potentials and free part particle, Barrier. Tunneling (basic idea).

State and Energy Levels

Trapped  Particles and probability Densiti Barrier tunneling. Particles in a well, Probability density using wave function of states.    Discussion of Particle in a     well.
The correspondence principles Discussion.
Dual nature of matter

(waves and particles)

Suggested level  Ch.50 H.R.K


Bohr’s theory Derivation and quantitative discussion; Frank Hertz experiment.

Energy levels of electrons; Atomic Spectrum.

Angular Momentum of Electrons (Vector atom model) orbital angular momentum; Space quantization, Orbital angular momentum & magnetism, Bohr’s magnetor
Electron Spin Dipole in non-uniform field; Stern-Gerlach experiment, Experimental results.
Suggested Level: Ch.51H.R.K


X-ray Spectrum Continuous and Discrete Spectrum- Explanation
X-ray & Atomic number Moseley’s Law.
Development of periodic table Pauli exclusion principle and its use in developing the periodic table.
Laser Basic Concepts & Working of He-Ne Laser.
Suggested Level: Ch.52 H.R.K


Discovering the nucleus Review. Rutherford’s Experiment and interpretation.
Some Nuclear Properties (a) Nuclear systematic (Mass No., Atomic No. Isotopes.

(b) Nuclear Force (Basic Ideas).

(c) Nuclear Radii.

(d) Nuclear Masses Binding Energies Mass defect.

(e) Nuclear Spin & Magnetism.

Radioactive decay Law of decay; half life, mean life.
Alpha decay Basic ideas.
Beta decay Basic ideas
Measuring ionizing radiation (Units) Curie, Rad: etc.
Natural Radioactivity Discussion, radioactive dating.
Nuclear Reactions Basic ideas e.g. reaction energy, Q. Value, exothermic-endothermic.

(Some discussion of reaction energies in the contact of nuclear stationery states).

Suggested Level Ch. 54 H.R.K.


Nuclear Fission Basic process: Liquid drop model, description, Theory of N. Fission
Nuclear Reactors Basic Principles.
Thermonuclear Fusion (T.N.F.) Basic process; T.N.F. in stars.
Controlled Thermonuclear Fusion Basic Ideas and requirements for a T.N. reactor.
Suggested Level; Ch.54 H.R.K.

PAPER:D                25 Marks

Note:  The candidate must perform at least 50% of the practical of each sub section.


  • Surface tension by capillary rise
  • ‘g’ by compound pendulum
  • Elastic constants of a wire by a spiral spring
  • Modulus of rigidity of a wire by dynamic method
  • Modulus of rigidity of a wire using Barton’s apparatus
  • Modulus of rigidity of a wire using Maxwell’s needle


  • Calibration of a thermo couple by a potentiometer
  • Mechanical equivalent of heat by Calendar and Barne’s apparatus


  • Frequency of A.C. using sonometer.
  • Velocity of sound by Kundr’s tube.


  • Vertical distance by a sextant
  • Wavelength of sodium light by Newton’s rings
  • Wavelength of sodium light by diffraction grating
  • Wavelength of sodium light by Fresenel’s biprism
  • Resolving power of a diffraction grating 


  • Measurement of high resistance and capacitance of a capacitor by neon bulb.
  • I-H Curve by Magnetometer
  • Conversion of a moving coil galvanometer into an ammeter.
  • Conversion of a moving coil galvanometer into a voltmeter.
  • Calibration of an ammeter by a potentiometer.
  • Calibration of a voltmeter by a potentiometer.
  • Low resistance by Carey Foster Bridge.
  • Charge sensitivity of a ballistic galvanometer
  • Comparison of capacities by ballistic galvanometer
  • Measurement of magnetic flux by a search coil

PAPER:E                                                                                                 25 Marks

Note:  The candidate must perform at least 50% of the practical of each sub section.


  1. Work function of metal using sodium light.
  2. Determine Plank’s constant ‘h’ by cut-off method using a photo Cell.
  3. Measurement of Planck’s constant using a spectrometer.
  4. Determination of e/m of electron by deflection method.
  5. Determination of ionization potential of Mercury.
  6. To study the characteristics of an acceptor circuit.
  7. To study the characteristics of a rejecter circuit.
  8. Characteristic curves of a Geiger-Muller tube.
  9. To determine the Dead time of a Geiger-Muller tube.
  10. Absorption co-efficient of beta-particles using a Geiger counter.
  11. Stopping power for alpha particles.
  12. Range of alpha particles.


  1. Characteristics of a semi-conductor diode
  2. Setting up half and full-wave-rectifier.
  3. To study the input and output static characteristics of a PNP transistor.
  4. To study the input and output static characteristics of a NPN transistor.
  5. Transistor as a single stage amplifier and its voltage gain.
  6. Transistor as an oscillator.