## Topics with syllabus and resources

- Electric Charges
- Basic Properties of Electric Charge
- Conservation of Charge
- Additivity of charges
- Charge is conserved
- Quantisation of charge

- Quantisation of Charge
- Coulomb’s Law
- Coulomb’s force law between two point charges

- Force Between Two Point Charges
- Forces Between Multiple Charges
- Forces Between Multiple Electric Charges
- principle of superposition

- Superposition Principle of Forces
- Electric Field
- Electric Field Due to a Point Charge
- Electric Field Lines
- Electric Dipole
- Electric Dipole and Dipole Moment
- Electric Field Due to a Dipole
- The field of an electric dipole
- Physical significance of dipoles

- Dipole in a Uniform External Field
- Torque on a Dipole in Uniform Electric Fleld

- Electric Flux
- Uniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside)
- Applications of Gauss’s Law
- Statement of Gauss'S Theorem and Its Applications to Find Field Due to Infinitely Long Straight Wire
- Field due to an infinitely long straight uniformly charged wire
- Field due to a uniformly charged infinite plane sheet
- Field due to a uniformly charged thin spherical shell - Field outside the shell, Field inside the shell

**Electric charges; conservation and quantisation of charge, Coulomb's law; superposition principle and continuous charge distribution.**

**Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field.**

**Electric flux, Gauss’s theorem in Electrostatics and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell**

- Coulomb's law, S.I. unit of charge; permittivity of free space and of dielectric medium. Frictional electricity, electric charges (two types); repulsion and attraction; simple atomic structure - electrons and ions; conductors and insulators; quantization and conservation of electric charge; Coulomb's law in vector form; (position coordinates r
_{1,}r_{2}not necessary). Comparison with Newton’s law of gravitation; Superposition principle (vecF_1=vecF_12+vecF_13+vecF_14+ ....) - Concept of electric field and its intensity; examples of different fields;gravitational, electric and magnetic; Electric field due to a point charge vecE =
- Electric charges; conservation and quantisation of charge, Coulomb's law; superposition principle and continuous charge distribution.
- Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric field.
- Electric flux, Gauss’s theorem in Electrostatics and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell
- Coulomb's law, S.I. unit of charge; permittivity of free space and of dielectric medium. Frictional electricity, electric charges

(two types); repulsion and attraction; simple atomic structure - electrons and ions; conductors and insulators; quantization and conservation of electric charge; Coulomb's law in vector form; (position coordinates r_{1,}r_{2}not necessary). Comparison with Newton’s law of gravitation; Superposition principle (vecF_1=vecF_12+vecF_13+vecF_14+ ....) - Concept of electric field and its intensity; examples of different fields;gravitational, electric and magnetic; Electric field due to a point charge vecE = vecF/qo (q0 is a test charge) vecE for

a group of charges (superposition principle); a point charge q in an electric field E experiences an electric force vecF_E = qvecE. Intensity due to a

continuous distribution of charge i.e. linear, surface and volume. - Electric lines of force: A convenient way to visualize the electric field; properties of lines of force; examples of the lines of force due to (i) an

isolated point charge (+ve and - ve); (ii) dipole, (iii) two similar charges at a small distance;(iv) uniform field between two oppositely charged parallel plates - Electric dipole and dipole moment; derivation of the vecE at a point, (1) on the axis (end on position) (2) on the perpendicular bisector (equatorial i.e. broad side on position) of a dipole,

also for r>> 2l (short dipole); dipole in a uniform electric field; net force zero, torque on an electric dipole: vect = vecpxxvecE and its derivation. - Gauss’ theorem: the flux of a vector field; Q=vA for velocity vector vecv||vecA, vecA is area vector. Similarly for electric field vecE , electric flux Φ
_{E}= EA for vecE||vecA and phi_EvecE.vecA for uniform vecE. For non-uniform field phi_E = intdphi = intvecE.dvecA. Special cases for = 0º, 90º and 180º. Gauss’ theorem, statement: ΦE =q/∈_{0 }or phi_E = intvecE.dvecA = q/epsilon_0 where Φ_{E }is for a closed surface; q is the net charge enclosed, ∈_{o}is the permittivity of free space. Essential properties of a Gaussian surface. - Applications: Obtain expression for vecE due to 1. an infinite line of charge, 2. a uniformly charged infinite plane thin sheet, 3. a thin hollow spherical shell (inside, on the surface and outside). Graphical variation of E vs r for a thin spherical shell

- Electric Potential
- Electric Potential Difference
- Potential Due to a Point Charge
- Electric Potential Due to Point Charge

- Potential Due to a System of Charges
- system of charges

- Equipotential Surfaces
- Equipotential surfaces for a uniform electric field, Some equipotential surfaces for a dipole and two identical positive charges.
- Relation between field and potential

- Electrical Potential Energy of a System of Two Point Charges and of Electric Dipole in an Electrostatic Field
- Conductors and Insulators Related to Electric Field
- Free Charges and Bound Charges Inside a Conductor
- Capacitors and Capacitance
- Combination of Capacitors
- Combination of Capacitors in Series and in Parallel
- Capacitors in series
- Capacitors in parallel

- Capacitance of a Parallel Plate Capacitor with and Without Dielectric Medium Between the Plates
- Energy Stored in a Capacitor

**Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field.**

**Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel. Capacitance of a parallel plate capacitor, energy stored in a capacitor**

Concept of potential, potential difference and potential energy. Equipotential surface and its properties. Obtain an expression for

electric potential at a point due to a point charge; graphical variation of E and V vs r, VP=W/q0; hence V_{A} -V_{B} =

W_{BA}/ q_{0} (taking q_{0} from B to A) = (q/40)(1/rA - 1/rB); derive this equation; also VA = q/40 .1/rA ; for

q>0, VA>0 and for q<0, VA < 0. For a collection of charges V = algebraic sum of the potentials due to each charge; potential due to a dipole on its axial line and equatorial line; also at any point for r>>2l (short dipole). Potential energy of a point charge (q)

in an electric field E , placed at a point P where potential is V, is given by U =qV and U =q (VA-VB). The

electrostatic potential energy of a system of two charges = work done W21=W12 in assembling the system; U12

or U21 = (1/4piepsilon_0 ) q1q2/r12. For a system of 3 charges U_{123} = U_{12} + U_{13} + U_{23 = }1/4pielipson_0((q_1q_2)/r_12+(q_1q_3)/r_13+(q_2q_3)/r_23).

For a dipole in a uniform electric field, derive an expression of the electric potential energy U_{E} = -vecp .vecE , special cases for Φ=0º, 90º and 180º.

Capacitance of a conductor C = Q/V; obtain the capacitance of a parallelplate capacitor (C = ∈_{0}A/d) and equivalent capacitance for capacitors in series and parallel combinations. Obtain an expression for energy stored (U = 1/2CV^2=1/2QV=1/2Q^2/C^2) and enery density.

Dielectric constant K = C'/C; this is also called relative permittivity K = ∈_{r} = ∈/∈_{o}; elementary ideas of polarization of matter in a uniform electric field qualitative discussion; induced surface charges weaken the original field; results in reduction in E and hence, in pd, (V);

for charge remaining the same Q = CV = C' V' = K. CV'; V' = V/K; and E' = E/K; if the Capacitor is kept connected with the source of emf, V is kept constant V = Q/C = Q'/C' ; Q'=C'V = K. CV= K. Q increases; For a parallel plate capacitor with a dielectric in between, C' = KC = K.∈_{o} . A/d = ∈_{r} .∈_{o} .A/d. Then C' = (∈_0A)/(d/∈_r). for a capacitor partially filled dielectric, capacitance C'= ∈_0A/(d-t+t/∈_{r)}

- Electric Current
Electric Current and Electrical Resistance

- Flow of Electric Charges in a Metallic Conductor
- Drift of Electrons and the Origin of Resistivity
- Ohm’s Law
- V-I Characteristics (Linear and Non-linear)
- Electrical Energy and Power
- Electrical Resistivity and Conductivity
- Resistivity of Various Materials
- Combination of Resistors – Series and Parallel
- Resistors and Series and Parallel Combination of Resistors

- Temperature Dependence of Resistance
- Cells, Emf, Internal Resistance
- E.M.F. and Internal Resistance of Cell

- Potential Difference and Emf of a Cell
- Cells in Series and in Parallel
- Kirchhoff’s Rules
- Kirchhoff's Laws and Simple Applications

- Wheatstone Bridge
- Metre Bridge
- Potentiometer
- Conductivity and Conductance;

**Mechanism of flow of current in conductors. Mobility, drift velocity and its relation with ****electric current; Ohm's law and its proof, resistance and resistivity and their relation to ****drift velocity of electrons; V-I characteristics (linear and non-linear), electrical energy and ****power, electrical resistivity and conductivity. Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance and resistivity**

**Internal resistance of a cell, potential difference and emf of a cell, combination of cells in series and in parallel, Kirchhoff's laws and simple applications, Wheatstone bridge,metre bridge. Potentiometer - principle and its applications to measure potential difference, ****to compare emf of two cells; to measure internal resistance of a cell.**

Free electron theory of conduction; acceleration of free electrons, relaxation timeτ ; electric current I = Q/t; concept of drift velocity and electron mobility. Ohm's law, current density J = I/A; experimental verification, graphs and slope, ohmic and non-ohmic conductors; obtain the relation I=v_{d}enA. Derive σ = ne^{2}t/m and ρ = m/ne^{2} τ ; effect of temperature on resistivity and resistance of conductors and semiconductors and graphs. Resistance R= V/I; resistivity ρ, given by R = ρ.l/A; conductivity and conductance; Ohm’s law as J = σvecE ; colour coding of resistance.

Electrical energy consumed in time t is E=Pt= VIt; using Ohm’s law E = (V^{2}/R)t = I^{2}Rt. Potential difference V = P/ I; P = V I; Electric power consumed P = VI = V2 /R = I2 R; commercial units; electricity consumption and billing. Derivation of equivalent resistance for

combination of resistors in series and parallel; special case of n identical resistors; R_{s} = nR and R_{p} = R/n. Calculation of equivalent resistance of mixed grouping of resistors (circuits).

The source of energy of a seat of emf (such as a cell) may be electrical, mechanical, thermal or radiant energy. The emf of a source is defined as the work done per unit charge to force them to go to the higher point of potential (from -ve terminal to +ve terminal inside the cell) so, ∈ = dW /dq; but dq = Idt; dW = ∈dq = ∈Idt . Equating total work done to the work done across the external resistor R plus the work done across the internal resistance r; Idt=I^{2}R dt + I^{2}rdt; =I (R + r); I=/( R + r ); also IR +Ir = ∈ or V=- Ir where Ir is called the back emf as it acts against the emf ; V is the terminal pd. Derivation of formulae for combination for identical cells in series, parallel and mixed grouping. Parallel combination of two cells of unequal emf. Series combination of n cells of unequal emf.

Statement and explanation of Kirchhoff's laws with simple examples. The first is a

conservation law for charge and the 2nd is law of conservation of energy. Note change

in potential across a resistor ΔV=IR<0 when we go ‘down’ with the current (compare with flow of water down a river), and ΔV=IR>0 if we go up against thecurrent across the resistor. When we go through a cell, the -ve terminal is at a lower level and the +ve terminal at a higher level, so going from -ve to +ve through the cell, we are going up and

ΔV=+∈ and going from +ve to -ve terminal through the cell, we are going down, so ΔV

= -∈ . Application to simple circuits. Wheatstone bridge; right in the beginning

take Ig=0 as we consider a balanced bridge, derivation of R_{1}/R_{2} = R_{3}/R_{4}

[Kirchhoff’s law not necessary]. Metre bridge is a modified form of Wheatstone

bridge, its use to measure unknown resistance. Here R_{3} = l1 and R4=l2; R3/R4=l1/l2. Principle of Potentiometer: fall in potential ΔV α Δl; auxiliary emf ∈1 is balanced against the fall in potential V_{1} across length l1. ∈1 = V1 =Kl1 ; ∈1/∈2 = l1/l2; potentiometer as a voltmeter. Potential gradient and sensitivity of potentiometer.Use of potentiometer: to compare emfs of two cells, to determine internal resistance of a cell.

- Magnetic Force
- Concept of Magnetic Field
- Sources and fields
- Magnetic Field, Lorentz Force
- Magnetic force on a current-carrying conductor

- Oersted’s Experiment
- Magnetic Field Due to a Current Element, Biot-Savart Law
- Biot Savart’s Law
- its application to current carrying circular loop

- Ampere’s Circuital Law
- Ampere's Law and Its Applications to Infinitely Long Straight Wire

- Straight and Toroidal Solenoids (Only Qualitative Treatment)
- Force on a Moving Charge in Uniform Magnetic and Electric Fields
- Motion in Combined Electric and Magnetic Fields
- Force on a Current - Carrying Conductor in a Uniform Magnetic Field
- Force Between Two Parallel Currents, the Ampere
- Definition of Ampere
- Force Between Two Parallel Current-carrying Conductors
- Roget's Spiral For Attraction Between parallel currents

- Torque on a Current Loop in Magnetic Field
- Moving Coil Galvanometer
- Moving Coil Galvanometer
- Moving Coil Galvanometer Conversion to Voltmeter and Ammeter
- Moving Coil Galvanometer Current Sensitivity

Concept of magnetic field, Oersted's experiment. Biot - Savart law and its application. Ampere's Circuital law and its applications to infinitely long straight wire, straight and toroidal solenoids (only qualitative treatment). Force on a moving charge in uniform magnetic and electric fields, cyclotron. Force on a currentcarrying conductor in a uniform magnetic field, force between two parallel current-carrying conductors-definition of ampere, torque experienced by a current loop in uniform magnetic field; moving coil galvanometer - its sensitivity. Conversion of galvanometer into an ammeter and a voltmeter.

- Current Loop as a Magnetic Dipole and Its Magnetic Dipole Moment
- Magnetic Dipole Moment of a Revolving Electron
- Magnetic Field Intensity Due to a Magnetic Dipole (Bar Magnet) Along Its Axis
- Magnetic Field Intensity Due to a Magnetic Dipole (Bar Magnet) Perpendicular to Its Axis
- Torque on a Magnetic Dipole (Bar Magnet) in a Uniform Magnetic Field
- The Bar Magnet
- Magnetic Field Lines
- Bar magnet as an equivalent solenoid
- The dipole in a uniform magnetic field
- The electrostatic analog

- The Earth’S Magnetism
- Earth’s Magnetic Field and Magnetic Elements
- Magnetic declination and dip

- Magnetic Properties of Materials
- Diamagnetic, Paramagnetic, and Ferromagnetic Substances, with Examples
- Diamagnetism
- Paramagnetism
- Ferromagnetism

- Permanent Magnets and Electromagnets
- Permanent Magnets
- Electromagnets and Factors Affecting Their Strength

- Magnetic Force
- Concept of Magnetic Field
- Sources and fields
- Magnetic Field, Lorentz Force
- Magnetic force on a current-carrying conductor

- Magnetisation and Magnetic Intensity
- Magnetization

**A current loop as a magnetic dipole, its magnetic dipole moment, magnetic dipole moment of a revolving electron, magnetic field intensity due to a magnetic dipole (bar magnet) on the axial line and equatorial line, torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; earth's magnetic field and magnetic elements. Diamagnetic, paramagnetic, and ferromagnetic substances, with examples. Electromagnets and factors affecting their strengths, permanent magnets.**

Only historical introduction through Oersted’s experiment. [Ampere’s swimming rule not included]. Biot-Savart law and its vector form; application; derive the expression for B (i) at the centre of a circular loop carrying current; (ii) at any point on its axis. Current carrying loop as a magnetic dipole. Ampere’s Circuital law: statement and brief explanation. Apply it to obtain vecB near a long wire carrying current and for a solenoid (straight as well as torroidal). Only formula of vecB due to a finitely long conductor.

Force on a moving charged particle in magnetic field vecF_B = q(vecv xx vecB); special cases, modify this equation substituting dl / dt for v and I for q/dt to yield vecF = I dvecl xx vecB for the force acting on a current carrying conductor placed in a magnetic field. Derive the expression for force between two long and parallel wires carrying current, hence, define ampere (the base SI unit of current)

and hence, coulomb; from Q = It. Lorentz force, Simple ideas about principle, working, and limitations of a cyclotron.

Derive the expression for torque on a current carrying loop placed in a uniform vecB, using vecF = Ivecl XX vecB and vect = vec r xx vecF

;t = NIAB sinΦ for N turns =vecm × vecB where the dipole moment vec m = NI vecA , unit: A.m^{2}. A current carrying loop is a magnetic dipole;directions of current and vecB and vecm using right hand rule only; no other rule necessary. Mention orbital magnetic moment of an electron in Bohr model of H atom. Concept of radial magnetic field. Moving coil galvanometer; construction, principle, working, theory I= kΦ , current and voltage sensitivity. Shunt. Conversion of galvanometer into ammeter and voltmeter of given range.

Magnetic field represented by the symbol vecB is now defined by the equation vecF =qo(vecv xx vecB); vecB is not to be

defined in terms of force acting on a unit pole, etc.; note the distinction of vecB from vecE is that vecB forms closed loops as there are no magnetic monopoles, whereas vecE lines start from +ve charge and end on -ve charge. Magnetic field lines due to a magnetic

dipole (bar magnet). Magnetic field in end-on and broadside-on positions (No derivations). Magnetic flux Φ =vecB.vecA = BA for B uniform and vecB||vecA ; i.e. area held perpendicular to For Φ = BA(VecB||vecA), B=Φ/A is the flux density [SI unit of flux is weber (Wb)]; but note that this is not correct as a defining equation as B is vector and and /A are scalars, unit of B is tesla (T) equal

to 10^{-4} gauss. For non-uniform vecB field, Φ= ∫dΦ=∫B. dA . Earth's magnetic field vecB_{E} is uniform over a limited area like that of a lab; the component of this field in the horizontal direction BH is the one effectively acting on a magnet suspended or pivoted horizontally.

Elements of earth’s magnetic field, i.e. BH, δ and Θ - their definitions and relations.

Properties of diamagnetic, paramagnetic and ferromagnetic substances; their susceptibility and relative permeability. It is better to explain the main distinction, the cause of magnetization (M) is due to magnetic dipole moment (m) of atoms, ions or molecules being 0 for dia, >0 but very small for para and > 0 and large for ferromagnetic materials; few examples; placed in external B , very small (induced) magnetization in a direction opposite to B in dia, small magnetization parallel to B for para, and large magnetization parallel to B for ferromagnetic materials; this leads to lines of B becoming less dense, more dense and much more dense in dia, para and ferro, respectively; hence, a weak repulsion for dia, weak attraction for para and strong attraction for ferro magnetic material. Also, a small bar suspended in the horizontal plane becomes perpendicular to the B field for dia and parallel to B for para and ferro. Defining equation H = (B/0)-M; the magnetic properties, susceptibility m = (M/H) < 0 for dia (as M is opposite H) and >0 for para, both very

small, but very large for ferro; hence relative permeability μ_{r} =(1+ χ_{m}) < 1 for dia, > 1 for para and >>1 (very large) for ferro; further, χ_{m}1/T (Curie’s law) for para, independent of temperature (T) for dia and depends on T in a complicated manner for

ferro; on heating ferro becomes para at Curie temperature. Electromagnet: its definition, properties and factors affecting the strength of electromagnet; selection of magnetic material for temporary and permanent magnets and core of the transformer on the basis of

retentivity and coercive force (B-H loop and its significance, retentivity and coercive force not to be evaluated

- Electromagnetic Induction
- Fleming's right hand rule
- Direct current (DC)
- Alternating current (AC)

- Faraday’s Law of Induction
- Laws of Electromagnetic Induction Or Faraday'S Laws of Induction

- Induced Emf and Current
- Lenz’S Law and Conservation of Energy
- Lenz's Law

- Eddy Currents
- Electromagnetic damping

- Inductance
- Magnetic Flux

**Fraday's laws, induced emf and current; Lenz's Law, eddy currents. Self-induction and mutual induction. Transformer**

- Electromagnetic induction, Magnetic flux, change in flux, rate of change of flux and induced emf; Faraday’s laws. Lenz's law, conservation of energy; motional emf ε = Blv, and power P = (Blv)
^{2}/R; eddy currents (qualitative); - Self-Induction, coefficient of selfinductance, Φ= LI and L = ε/(dI/dt); henry = volt. Second/ampere, expression for coefficient ofselfinductance of a solenoid L = (mu_0N^2A)/l = mu_0n^2Axxl
- Mutual induction and mutual inductance (M), flux linked Φ
_{2}= MI_{1}; induced emf ε_{2 = }(dphi_2)/dt = (MdI_1)/dt_{. }Definition of M as M = epsilon_2/(dI_1)/dt or M = (phi_2)/I_1. SI unit henry. Expression for coefficient of mutual inductance of two coaxial solenoids M = (mu_0N_1N_2A)/l=mu_0n_1N_2A Induced emf opposes changes, back emf is set up, eddy currents. - Transformer (ideal coupling): principle, working and uses; step up and step down; efficiency and applications including transmission of power, energy losses and their minimisation.

- Alternating Currents
- Peak and Rms Value of Alternating Current Or Voltage
- Reactance and Impedance
- Lc Oscillations
- LC Oscillations (Qualitative Treatment Only)

- Ac Voltage Applied to a Series Lcr Circuit
- LCR Series Circuit
- Phasor-diagram solution
- Analytical solution
- Resonance - Sharpness of resonance

- Forced Oscillations and Resonance
- Free, Forced and Damped Oscillations
- resonance
- Small Damping, Driving Frequency far from Natural Frequency
- Driving Frequency Close to Natural Frequency

- Power in Ac Circuit: the Power Factor
- Power in Ac Circuit
- Power Factor
- Wattless Current

- Transformers
- AC Generator and Transformer

**Peak value, mean value and RMS value of alternating current/voltage; their relation in sinusoidal case; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current. AC generator.**

Sinusoidal variation of V and I with time, for the output from an ac generator; time period, frequency and phase changes; obtain mean values of current and voltage, obtain relation between RMS value of V and I with peak values in sinusoidal cases only.

Variation of voltage and current in a.c. circuits consisting of only a resistor, only an inductor and only a capacitor (phasor representation), phase lag and phase lead. May apply Kirchhoff’s law and obtain simple differential equation (SHM type), V = Vo sin t, solution I = I0 sinωt, I0sin (ωt + π/2) and I0 sin (ωt - π/2) for pure R, C and L circuits respectively. Draw phase (or phasor)

diagrams showing voltage and current and phase lag or lead, also showingresistance R, inductive reactance XL;(XL=L) and capacitive reactance X_{C}, (X_{C} = 1/ωC). Graph of X_{L} and X_{C} vs f.

The LCR series circuit: Use phasor diagram method to obtain expression for I and V, the pd across R, L and C; and the net phase lag/lead; use the results of 4(e), V lags I by π/2 in a capacitor, V leads I by π/2 in an inductor, V and I are in phase in a resistor, I is the same in all three; hence draw phase diagram, combine VL and Vc (in opposite phase; phasors add like vectors) to give V=VR+VL+VC (phasor addition) and the max. values are related by V2 m=V2 Rm+(VLm-VCm)2 when VL>VC Substituting pd=current x

resistance or reactance, we get Z2 = R2+(XL-Xc) 2 and tan = (VL m -V_{Cm})/VRm = (X_{L}-X_{c})/R giving I = I m sin (wt-Φ) where I m =Vm/Z etc. Special cases for RL and RC circuits. [May use Kirchoff’s law and obtain the differential equation]Graph of Z vs f and I vs f.

Power P associated with LCR circuit = 1/2V_{o}I_{o} cos =V_{rms}I_{rms} cosΦ = Irms 2 R; power absorbed and power dissipated; electrical resonance; bandwidth of signals and Q factor (no derivation); oscillations in an LC circuit (0 = 1 sqrt(LC) ). Average power consumed

averaged over a full cycle P = (1/2) V_{o}I_{o} cosΦ, Power factor cos = R/Z. Special case for pure R, L and C; choke coil (analytical only), XL controls current but cos = 0, hence P =0, wattless current; LC circuit; at resonance with XL=Xc , Z=Z_{min}= R, power delivered to circuit by the source is maximum, resonant frequency f_0= 1/(2pisqrt(LC))

Simple a.c. generators: Principle, description, theory, working and use. Variation in current and voltage with time for a.c. and d.c. Basic differences between a.c. and d.c.

- Displacement Current
- Basic Idea of Displacement Current and Maxwell Experiment
- Maxwell’s equations

- Electromagnetic Waves
- Electromagnetic Waves and Their Characteristics
- Sources of electromagnetic waves
- Nature of electromagnetic waves

- Transverse Nature of Electromagnetic Waves
- Electromagnetic Spectrum
- Radio waves, Microwaves, Infrared waves, Visible rays, Ultraviolet rays , X-rays, Gamma rays,

- Elementary Facts About Electromagnetic Wave Uses

**Basic idea of displacement current. Electromagnetic waves, their characteristics, their transverse nature (qualitative ideas only). Complete electromagnetic spectrum starting ****from radio waves to gamma rays: elementary facts of electromagnetic waves and their uses.**

Concept of displacement current, qualitative descriptions only of electromagnetic spectrum;

common features of all regions of em spectrum including transverse nature (vecE and vecB perpendicular to vec c); special features of the common classification (gamma rays, X rays, UV rays, visible light, IR, microwaves, radio and TV waves) in their production (source), detection and other properties; uses; approximate range of or f or at least proper order of increasing f or λ..

- Reflection of Light by Spherical Mirrors
- Sign convention
- Focal length of spherical mirrors
- The mirror equation

- Ray Optics - Mirror Formula
- Refraction
- Refraction of Light

- Total Internal Reflection
- Total Internal Reflection and Its Applications
- Total internal reflection in nature and its technological applications - Mirage, Diamond, Prism, Optical fibres

- Refraction at Spherical Surfaces and by Lenses
- Lenses
- Thin Lens Formula
- Lensmaker's Formula
- Magnification
- Dispersion by a Prism
Dispersion of white light by a glass prism

- Some Natural Phenomena Due to Sunlight
- The rainbow
- Scattering of Light
- Tyndall Effect
- blue colour of sky
- reddish apprearance of the sun at sunrise and sunset

- Optical Instruments
- The Microscope
Microscopes (Reflecting and Refracting) and Their Magnifying Powers

- Telescope
- Astronomical Telescopes (Reflecting and Refracting) and Their Magnifying Powers

- The Microscope
- Snell’s Law

**Ray Optics: Reflection of light by spherical mirrors, mirror formula, refraction of light at plane surfaces, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens maker's formula, magnification, power****of a lens, combination of thin lenses in contact, combination of a lens and a mirror, refraction and dispersion of light through a prism. Scattering of light.**

**Optical instruments: Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers and their resolving powers.**

- Reflection of light by spherical mirrors. Mirror formula: its derivation; R=2f for spherical mirrors. Magnification.
- Refraction of light at a plane interface,Snell's law; total internal reflectionand critical angle; total reflecting prisms and optical fibers. Total reflecting prisms: application to triangular prisms with angle of the prism 300, 450, 600 and 900 respectively; ray diagrams for Refraction through a combination of media,
_{1}n_{2}X_{2}n_{3}X_{3}n_{1}= 1 , real depth and apparent depth. Simple applications. - Refraction through a prism, minimum deviation and derivation of relation between n, A and δ
_{min}. Include explanation of i-δ graph, i_{1}= i_{2}= i (say) for δ_{m}; from symmetry r_{1}= r_{2}; refracted ray inside the prism is parallel to the base of the equilateral prism. Thin prism. Dispersion; Angular dispersion; dispersive power, rainbow - ray diagram (no derivation). Simple explanation. Rayleigh’s theory of scattering of light: blue colour of sky and reddish appearance of the sun at sunrise and sunset clouds appear white. - Refraction at a single spherical surface; detailed discussion of one case only - convex towards rarer medium, for spherical surface and real image. Derive the relation between n1, n2, u, v and R. Refraction through thin lenses: derive lens maker's formula and lens formula; derivation of combined focal length of two thin lenses in contact. Combination of lenses and mirrors (silvering of lens excluded) and

magnification for lens, derivation for biconvex lens only; extend the results to biconcave lens, plano convex lens and lens immersed in a liquid; power of a lens P=1/f with SI unit dioptre. For lenses in contact 1/F= 1/f_{1}+1/f_{2}and P=P_{1}+P_{2}. Lens formula, formation of image with combination of thin lenses and mirrors. - [Any one sign convention may be used in solving numericals].
- Ray diagram and derivation of magnifying power of a simple microscope with image at D (least distance of distinct vision) and infinity;

Ray diagram and derivation of magnifying power of a compound microscope with image at D. Only expression for magnifying power of

compound microscope for final image at infinity. - Ray diagrams of refracting telescope with image at infinity as well as at D; simple explanation; derivation of magnifying power; Ray diagram of reflecting telescope with image at infinity. Advantages, disadvantages and uses. Resolving power of compound microscope and telescope.

- Huygens Principle
- Wave Front and Huygen's Principle

- Proof of Laws of Reflection and Refraction Using Huygen'S Principle
- Interference
- Interference of Light Waves and Young’S Experiment
- Young's Double Slit Experiment and Expression for Fringe Width or Young’s Experiment

- Coherent and Incoherent Sources and Sustained Interference of Light
- Fraunhofer Diffraction Due to a Single Slit
- Width of Central Maximum
- Polarisation
- Uses of Plane Polarised Light and Polaroids
- Polarisation by scattering
- Polarisation by reflection

- Plane Polarised Light
- Brewster's Law
- Law of Malus
- Refraction of Monochromatic Light

**Wave front and Huygen's principle. Proof of laws of reflection and refraction using Huygen's principle. Interference, Young's double slit experiment and expression for fringe width(β), coherent sources and sustained interference of light, Fraunhofer diffraction due to a single slit, width of central maximum; polarisation, plane polarised light, Brewster's law, uses of plane polarised light and Polaroids.**

- Huygen’s principle: wavefronts - different types/shapes of wavefronts;proof of laws of reflection and refraction using Huygen’s theory.

[Refraction through a prism and lens on the basis of Huygen’s theory not required]. - Interference of light, interference of monochromatic light by double slit. Phase of wave motion; superposition of identical waves at a point, path difference and phase difference; coherent and incoherent sources; interference: constructive and destructive, conditions for sustained interference of light waves [mathematical deduction of interference from the equations of two progressive waves with a phase

difference is not required]. Young's double slit experiment: set up, diagram, geometrical deduction of path difference Δx = dsinΘ, between waves from the two slits; using Δx=nλ for bright fringe and Δx= (n+½) for dark fringe and sin Θ = tan Θ =y_{n}/D as y and Θ are small, obtain yn=(D/d)n and fringe width β=(D/d). Graph of distribution of intensity with angular distance. - Single slit Fraunhofer diffraction (elementary explanation only). Diffraction at a single slit: experimental setup, diagram, diffraction pattern, obtain expression for position of minima, a sinn= n, where n = 1,2,3… and conditions for secondary maxima, asinn =(n+½)λ.; distribution of intensity with angular distance; angular width of central bright fringe.
- Polarisation of light, plane polarised electromagnetic wave (elementary idea only), methods of polarisation of light. Brewster's law; polaroids. Description of an electromagnetic wave as
- transmission of energy by periodic changes in vecE and vecB along the path; transverse nature as vecE and vecB are perpendicular to vecc. These three vectors form a right handed system, so that vecE x vecB is along vecc , they are mutually perpendicular to each other.For ordinary light, vecE and vecB are in all directions in a plane perpendicular to the vecc vector - unpolarised waves. If

vec E and (hence vecB also) is confined to a single plane only (vecc , we have linearly polarized light. The plane containing vecE (or B) and vecc remains fixed. Hence, a linearly polarised light is also called plane polarised light. Plane of polarisation (contains vecE and vecc); polarisation by reflection; Brewster’s law: tan ip=n; refracted ray is perpendicular to reflected ray for i= i_{p}; i_{p}+r_{p}= 90° ; polaroids; use in the production and detection/analysis of polarised light, other uses. Law of Malus.

- Dual Nature of Radiation
- Photoelectric Effect - Hertz’S Observations
- Photoelectric Effect - Hallwachs’ and Lenard’S Observations
- Hertz and Lenard's Observations
- Hallwach and Lenard's Experiment

- Einstein’s Equation - Particle Nature of Light
- Wave Nature of Matter
- Matter Waves - Wave Nature of Particles

- de-Broglie Relation
- Davisson-Germer Experiment
- Continuous and Characteristics X-rays
- Electron Emission

**Wave particle duality; photoelectric effect, Hertz and Lenard's observations; Einstein's photoelectric equation - particle nature of light. Matter waves - wave nature of particles, de-Broglie relation; conclusion from Davisson-Germer experiment. X-rays.**

Photo electric effect, quantization of radiation; Einstein's equation E_{max} = hv - W_{0}; threshold frequency; work function; experimental facts of Hertz and Lenard and their conclusions; Einstein used Planck’s ideas and extended it to apply for radiation (light); photoelectric effect can be explained only assuming quantum (particle) nature of radiation. Determination of Planck’s constant (from the graph of stopping potential Vs versus frequency f of the incident light). Momentum of photon p=E/c=hv/c=h/λ.

De Broglie hypothesis, phenomenon of electron diffraction (qualitative only). Wave nature of radiation is exhibited in interference, diffraction and polarisation; particle nature is exhibited in photoelectric effect. Dual nature of matter: particle nature common in that it possesses

momentum p and kinetic energy KE. The wave nature of matter was proposed by Louis de Broglie, λ=h/p= h/mv. Davisson and Germer experiment; qualitative description of the

experiment and conclusion.

A simple modern X-ray tube (Coolidge tube) – main parts: hot cathode, heavy element anode (target) kept cool, all enclosed in a vacuum tube; elementary theory of X-ray production; effect of increasing filament current- temperature increases rate of emission of electrons (from the cathode), rate of production of X rays and hence, intensity of X rays

increases (not its frequency); increase in anode potential increases energy of each

electron, each X-ray photon and hence, Xray frequency (E=hv); maximum frequency

hmax =eV; continuous spectrum of X rays has minimum wavelength λ_{min}=

c/v_{max}=hc/eV. Moseley’s law. Characteristic and continuous X rays, their origin.

- Alpha-particle Scattering and Rutherford’S Nuclear Model of Atom
- Alpha-particle Scattering Experiment and Rutherford's Model of Atom
- Alpha-particle trajectory
- Electron orbits

- Bohr'S Model for Hydrogen Atom
- The Spectral Lines for Atomic Hydrogen
- Explanation of Line Spectrum of Hydrogen
- Limitations of Bohr’s Model

- Energy Levels
- Hydrogen Spectrum

**Alpha-particle scattering experiment; Rutherford's atomic model; Bohr’s atomic model, energy levels, hydrogen spectrum**

- Rutherford’s nuclear model of atom (mathematical theory of scattering excluded), based on Geiger - Marsden experiment on α-scattering; nuclear radius r in terms of closest approach of α particle to the nucleus, obtained by equating ΔK=½ mv
^{2}of the α particle to the change in electrostatic potential energy ΔU of the system [U = (2exxZe)/4piepsilon_0r_0 r_0~10^(-15)m =1 fermi atomic structure; only general qualitative ideas including atomic number Z, Neutron number N and mass number A. A brief account of historical background leading to Bohr’s theory of hydrogen spectrum; formulae for wavelength in Lyman, Balmer, Paschen, Brackett and Pfund series. Rydberg constant. Bohr’s model of H atom, postulates (Z=1); expressions for orbital velocity, kinetic energy, potential energy, radius of orbit and total energy of electron. Energy level diagram, calculation of ΔE, frequency and wavelength of different lines of emission spectra;

agreement with experimentally observed values. [Use nm and not Å for unit of λ].

- Atomic Masses and Composition of Nucleus
- Composition and Size of Nucleus

- Radioactivity
- Alpha Decay
Alpha Particles Or Rays and Their Properties

- Law of Radioactive Decay
- Radioactive Decay Law

- Alpha Decay
- Mass-Energy Relation and Mass Defect
- Mass-energy and Nuclear Binding Energy
- Nuclear Binding Energy
- Binding Energy per Nucleon and Its Variation with Mass Number

- Nuclear Binding Energy
- Nuclear Energy

**Composition and size of nucleus, Radioactivity, alpha, beta and gamma particles/rays and their properties; radioactive decay law. Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; Nuclear reactions, nuclear fission and nuclear fusion.**

- Atomic masses and nuclear density; Isotopes, Isobars and Isotones – definitions with examples of each. Unified atomic mass unit, symbol u, 1u=1/12 of the mass of
^{12}C atom = 1.66x10^{-27}kg). Composition of nucleus; mass defect and binding energy, BE= (Δm) c^{2}. Graph of BE/nucleon versus mass number A, special features - less BE/nucleon for light as well as heavy elements. Middle order more stable [see fission and fusion] Einstein’s equation E=mc2. Calculations related to this equation; mass defect/binding

energy, mutual annihilation and pair production as examples - Radioactivity: discovery; spontaneous disintegration of an atomic nucleus with the emission of α or β particles and γ radiation, unaffected by physical and chemical changes. Radioactive decay law; derivation of N = N
_{o}e^{-λt}; half-life period T; graph of N versus t, with T marked on the X axis. Relation between half-life (T) and disintegration constant (λ); mean life ( τ) and its relation with λ. Value of T of some common radioactive elements. Examples of a few nuclear reactions with conservation of mass number and charge, concept of a neutrino. - Changes taking place within the nucleus included. [Mathematical theory of α and β decay not included].
- Nuclear Energy: Theoretical (qualitative) prediction of exothermic (with release of energy) nuclear reaction, in fusing together two

light nuclei to form a heavier nucleus and in splitting heavy nucleus to form middle order (lower mass number) nuclei, is evident from the shape of BE per nucleon versus mass number graph. Also calculate the disintegration energy Q for a heavy nucleus (A=240) with BE/A ~ 7.6 MeV per nucleon split into two equal halves with A=120 each and BE/A~ 8.5 MeV/nucleon; Q ~ 200 MeV. Nuclear fission: Any one equation of fission reaction. Chain reaction- controlled and uncontrolled; nuclear reactor and nuclear bomb. Main parts of a nuclear reactor including their functions - fuel elements, moderator, control rods, coolant, casing; criticality; utilization of energy output - all qualitative only. Fusion, simple example of 4^{1}H→^{4}He and its nuclear reaction equation; requires very high temperature ~ 10^{6}degrees; difficult to achieve; hydrogen bomb; thermonuclear energy production in the sun and stars. [Details of chain reaction not required].

- Materials, Devices and Simple Circuits
- Energy Bands in Conductors, Semiconductors and Insulators
- Semiconductor Diode
- Semiconductor Diode - I-V Characteristics in Forward and Reverse Bias
- p-n junction diode under forward bias
- p-n junction diode under forward bias

- Diode as a Rectifier
- Special Purpose P-n Junction Diodes
- Special Purpose p-n Junction Diodes: Led, Photodiode, Solar Cell and Zener Diode
- characteristics of Led, Photodiode, Solar Cell and Zener Diode
- Zener diode
- Optoelectronic junction devices - Photodiode, Light emitting diode, Solar cell

- Zener Diode as a Voltage Regulator
- Junction Transistor
- Transistor: Structure and Action
- n-p-n transistor, p-n-p transistor

- Transistor as an Amplifier (Ce-configuration)
Transistor as an Amplifier (Common Emitter Configuration)

- Transistor: Structure and Action
- NPN and PNP Transistor
- Transistor Action
- Transistor and Characteristics of a Transistor
- Digital Electronics and Logic Gates
- Logic Gates (OR, AND, NOT, NAND and NOR)
- Logic gates - NOT gate, OR Gate, AND Gate, NAND Gate, NOR Gate
- Basic Idea of Analog and Digital Signals

- Combination of Gates

**Semiconductor Electronics: Materials, Devices and SimpleCircuits. Energy bands in conductors, semiconductors and insulators (qualitative ideas only).Intrinsic and extrinsic semiconductors.**

**Semiconductor diode: I-V characteristics in forward and reverse bias, diode as a rectifier; Special types of junction diodes: LED, photodiode, solar cell and Zener diode and its characteristics, zener diode as a voltage regulator**

**Junction transistor, npn and pnp transistor, transistor action, characteristics of a transistor and transistor as an amplifier (common emitter configuration).**

**Elementary idea of analogue and digital signals, Logic gates (OR, AND, NOT, NAND and NOR). Combination of gates.**

- Energy bands in solids; energy band diagrams for distinction between conductors, insulators and semiconductors - intrinsic and extrinsic; electrons and holes in semiconductors.
- Elementary ideas about electrical conduction in metals [crystal structure not included]. Energy levels (as for hydrogen atom), 1s, 2s, 2p, 3s, etc. of an isolated atom such as that of copper; these split, eventually forming ‘bands’ of energy levels, as we consider solid copper made up of a large number of isolated atoms, brought together to form a lattice; definition of energy bands - groups of closely spaced energy levels separated by band gaps called forbidden bands. An idealized representation of the energy bands for a conductor, insulator and semiconductor; characteristics, differences; distinction between conductors, insulators and semiconductors on the basis of energy bands, with examples; qualitative discussion only; energy gaps (eV) in typical substances (carbon, Ge, Si); some electrical properties of semiconductors. Majority and minority charge carriers - electrons and holes; intrinsic and extrinsic, doping, p-type, n-type; donor and acceptor impurities.
- Junction diode and its symbol; depletion region and potential barrier; forward and reverse biasing, V-I characteristics and numericals; half wave and a full wave rectifier. Simple circuit diagrams and graphs, function of each component in the electric circuits, qualitative only. [Bridge rectifier of 4 diodes not included]; elementary ideas on solar cell,photodiode and light emitting diode (LED) as semi conducting diodes. Importance of LED’s as they save energy without causing atmosphericpollution and global warming. Zener diode, V-I characteristics, circuit diagram and working of zener diode as a voltage regulator
- Junction transistor; simple qualitative description of construction - emitter, base and collector; npn and pnp type; symbols showing direction of current in emitter-base region (one arrow only)- base is narrow; current gains in a transistor, relation between , and numericals related to current gain, voltage gain, power gain and transconductance; common emitter configuration only, characteristics; I
_{B}vs V_{BE}and I_{C}vs V_{CE}with circuit

diagram and numericals; common emitter transistor amplifier - circuit diagram; qualitative explanation including amplification, wave form and phase reversal. - Elementary idea of discreet and integrated circuits, analogue and digital signals. Logic gates as given; symbols, input and output, Boolean equations (Y=A+B etc.), truth table,

qualitative explanation. NOT, OR, AND, NOR, NAND. Combination of gates [Realization of gates not included]. Advantages of Integrated Circuits.

- Elements of a Communication System
- Elements of a Communication System (Block Diagram Only)
- Introduction and Modes of Communication

- Bandwidth of Signals
- Bandwidth of Signals (Speech, TV and Digital Data)

- Bandwidth of Transmission Medium
- Propagation of Electromagnetic Waves
- Propagation of Electromagnetic Waves in the Atmosphere, Sky and Space Wave Propagation
- Ground wave
- Sky waves
- Space wave

- Modulation and Its Necessity
- Modulation
- Types of Modulation - frequency and amplitude
- Size of the antenna or aerial
- Effective power radiated by an antenna
- Mixing up of signals from different transmitters

- Need for Modulation and Demodulation
- Advantages of Frequency Modulation Over Amplitude Modulation
- Elementary Ideas About Internet
- Elementary Ideas About Mobile Network
- Elementary ideas about global positioning system (GPS)
- Amplitude Modulation

Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Modes of propagation of electromagnetic waves in the atmosphere through sky and space waves, satellite communication. Modulation, types (frequency and amplitude), need for modulation and demodulation, advantages of frequency modulation over amplitude modulation. Elementary ideas about internet, mobile network and global positioning system (GPS).

Self-explanatory- qualitative only.