Physics ISC Class XII, Schemes and Mind Maps of Physics

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Note: to Electric charge (Q) SI unit: Coulomb (C) Methods of charging + By friction By conduction Basic properties: Charge is * Quantised Q = +ne > © Conserved + Additive/scalar + Invariant (speed independent) LL Charge distribution ~~ —J Discrete or point Continuous charge ee Linear charge Linear charge density (a) _ Charge ea Length Surface/Areal charge Surface charge density (c) Ly Charge o= Area St unit: Cm? Volume charge Volume charge density (p) “s Charge Volume SI unit: C/m> Ls [Excess or deficiency of electron — Electric field intensity = Electric Charges and Fields Ample number of Multiple Choice Questions (MCQs) will help you prepare in CUET Examinations, WAGE ELECTRIC CHARGES AND FIELDS —— Force between two point Electrostatic re per charges (Coulomb's taw) k unit charge F = & Fo ste es : SI unit: N/C or Vm Electric flux @ = f Es Total electric field lines passing through an area, Arey dS = Area enclosing charge Due to multiple charges J ae + \E i =q; Due to point ie drawn asthe, Surface, [> Ane? z=! Gauss’s theorem (using Superposition principle droge Netelectric flux throughaclosed pura ‘ties charge q. ge2 ey Eas Applications of Gauss's theorem + Electric field due to infinitely tong straight conductor z= _4 Qnegr * Electric field due to infinite plane sheet of charge E= Baht .E) Electric dipole Equal and opposite charge separated by some distance. Dipole moment p a 2aq i, 2 — Linear charge density Electric field at a point on the axial line of dipole ~ EF = fo i a okpr E= en o — Surface charge density [> (P-a)? ° Electric field due to uniformly charged spherical elfr>>a shell = _ 2p E, =0, &, = Sa then E = <2 ee ee p = q_. — out = “anage Electric field at a point on the TE equatorial line of dipole ip 7. P-aye Electric field lines Electric field lines are straight or curved lines tangent to which at a point gives the direction - of electric field. * Electric field lines diverge from positive charge, direction of electric field lines is towards direction of electric field. * If charge particle enters electric field with > —kp © ifr >> a, Then F = Torque experienced by electric dipole in uniform electric field velocity v LE then its path will be a Lee, m L, == pxé Force experienced by dipole parabola, with displacement y = ; 5 eacoe: ad >ACITANCE tl u V — eens Potential Electric potential energy capacitor Work done in moving a Work done in moving a charge +> Potential difference (V) + Davico to store charge unit charge from infinity to W = U,-U, Work done in moving a ooo = a a point in an electric field. unit charge from one point : Gapactian” vad Vv . Is fal y= Wok Ww RE. of system of two to another st untt Be Charge = 9 2: kg <{ PO. = Va- as point charges = —- rare Spherical capacitor «| = fed 6 = Argh, © aR RE. of a system of three Due to a point charge Q point charges - A a ae ae plate capacitor ie IE On equipotential surface verre % c Are + Due to dipole < __ kpcos® cf 2 ESP U =U, + U, + Us p — Dipole moment f = | Melts fs | | Due to charged conducting fo fs As sphere ~ PE. of a system of four Vy OF Vig = a point char 4 R — Radius of sphere a4 % vee + out PIRI rescence qk U = Uj, + U3 + Usq t + Uy + Uys + Us OPE. of charge placed in ‘uniform electric field = <4 Cy = PD. = 0 Car enenienaencrenan nn With dielectric of With conducting slab, dielectric constant K, t a5 1 A. Us Poy = 3 Up = Dy aW= Deh * In series combination, charge remains same and if parallel combination, potential remains same. Force experienced by @ charge -~ (q) in a magnetic fletd (B) Force between two straight long current cartying conductors of length L. F _ Mo Ahk fe LL to 4n Ff * I direction of Z, and Jp is parallel then force is attractive. * tH direction of 2, and J, is anti-parallel then force is repulsive. Lorentz force: When charge q is moving Lin combined E and & F = q+ xB) Blot-Savart law Magnetic fleld due to small y y Current carrying coll In Ampere's circuital law magnetic fleld experiences Line integral of Velocity selector _» Ei Band F, = Fp v= F/B ‘Net force on a current carrying coll of Ni > tums and area A In uniform magnetic fleld F=Q fea ge x8) current element torque magnetic field y= Velocity of charge = 8 Wi xt c= MxB around a closed path + Direction of force is given by 4n op t= MBsina enclosing current J. aming’s lef tule Th antB Bdl = Fleming's left hand Ty Bcc (Inverse square law) > Angle b/w M andB. § Hol é Thumd r wininmaniecneeeert scmasernannton — To be continued To be continued Furst finger at vod page" 2 next page** Middle finger ——— Y Application « Magnetic field along on the axis of circular coil carrying current. p= 2M = BO tmat fr 4n M = magnetic dipole moment M = NAY, N-No. of turns in coil At the centre of coil of N-turns Nu piol er 4 ecmuaremaercme es If angle b/w v and B is 6 then path is helical y t When v 18 then force Flv 1B athe : : _> bg When ¥ || 8 then Path is circular of radius r, Le. F=ooQ ¥ m Path is a straight tine "= a ri om Ee a Ween Pitch r= qB Horizontal distance covered in one time period Pitch = T.v cos @ = 2man-c0s® gB *Continued from previous page T_T Oo Moving coil galvanometer uses radial magnetic field so that the sre of col 1S always parallel to B Current per unit angular deflection Current se } nsitivity Voltage sonsitivity pefecting torque = Restoring torque of coil eal per unit angular deflectior WB! = Ke 6 _ NBA of coll jx 60, /= Gd I k 7 = NBA 9 > Deflection k = Torsion constant i sascnencnsg een (ettememmansianninsenlenn ag ist a ee ' 7 Voltmeter Ammeter Device to measure RD. + High resistance (R) connected in series of the galvanometer. *R=G+R ett is connected in parallel with circuit. em RE CSMRI LAR OURS Device to measure electric current * Low resistance shunt (S) is connected in parallel with the galvanometer, qa 1,xG I-t, * Net resistance of galvanometer decreases = 85 Age @4S + Ammeter is connected In series. ecrerinrsiannaseinirtinnectam nn Ampere circuital law Line integral of the magnetic field B around a **Continued from previous page * Magnetic field due to long straight Current carrying conductor Hol 2nr Z~ Current in the conductor T~ Perpendicular distance from conductor * Direction of B is given by Right Hand Thumb rule. Wai closed loop is equal to up times the total current 7 passing through loop § Bal = nol Solenoid (air core) Magnetic flux (4) Total number of the magnetic field > lines of force Passing through a surface normally. ¢ = BA cos 6 ® = Angle between B and A SI unit is weber (Wb) CGS unit ~ maxwell + Itis a scalar quantity. Laws of EMI Given by Faraday First law: Whenever there is a change in magnetic flux linked with a circuit an induced emf is produced in it. The induced emf lasts as long as the > change in the magnetic flux continues. Second law: Induced emf « Rate of change of magnetic flux ay eo dt Lenz’s law: Direction of induced emf is such that it always opposes the change L,. in magnetic flux linked with the circuit. Nobg dt Conservation of energy Induced emf produced is equal to mechanical work done in changing the magnetic flux against the opposition of induced emf. & Induced emf is produced by * Relative motion of magnet and coil. + Relative motion of one coil and Current carrying coil. ~<—_—— + Changing current in the coil. — 7 vy Motional electromotive force Induced emf produced in a conductor coil, moving with velocity v, normal to magnetic field B, s=-Bly / — Length of the arm of coil Fleming’s Right Hand Rule * Gives direction of the induced emf produced in a moving coil in magnetic field. * Stretching the thumb, the forefinger and the central finger of right hand +» af mutually perpendicular. FA Thumb (motion) Central finger T Forefinger (field) * Induced current 7 = & — Blv R J R ‘> * Magnetic force F = Br * Power P = fy = BV R . Selt and mutual induction To be continued at next page Applications Electromagnetic damping in moving coil galvanometer. Induction furnace. Magnetic braking in electric powered trains. In speedometer to record the instantaneous speed of the vehicle. ~—* Self and Mutual Induction Self-induction Phenomenon of production of induced emt ina * Oppost Mutual induction coll when changing current Passes through it, beh whe ee hee ; id er + Magnetic flux (b,) linked with a coil ig fly ieee proportional to the current, / “ alas pe ae 2 «Tt! or =L 2 iy OF by = ME, bg % 4g a a When unit current flows in the second * Induced emf « « qe a coll then M = 4, : “ : * On changing the current In the primary ci L — Coefficient of self-induction emf induced in the secondary colt SI unit henry (H) = WbA of Tm2/q eeipeticcenmanremietinincenin _ Mat, ~ At Self-inductance of long solenoid When Fate of change of current in one cc Solenoid: Coil having length very large ise Mien M =e. compared to its diameter —— i —— N if O000600) Mutual inductance of fwo long <—_— |—>» coaxial solenoids > For air core hy s, NN, Ai, : | Self-inductance, L = ee ihe aw ; For magnetic core p = HoH, <—/—>' 1 UMA + at = batted at Bical scheme * SI unit of M is henry. Energy stored in the inductor | U= 1 LP Factors on which mutual inductance (M) Ly a) depends Energy stored per unit volume * Number of turns, i.e. B? M cc NM, me py * Cross-sectional area, i.e. ‘Geremmneieceicnemne M«A 1 a i ation. —- Relative separ: “i Relative orientation of the two coils. : Z fr : corte saat AC through L-c-R to Alternating Current 193 a circuit Rt om us page nn eta wes AL devices average Power Associated in ac ———— circuit Transformer r— Devi i . A.C. generator Enns/rms COS ce which increases decr : or Produces electrical ener : sases:the, alternating Voltage from mechanical work. 7 eee Lp Pay = T power factor cos = user = Principle Principle Based on the princi : c ple of mutual Based on the phi |, induction that change in the et nue, Wattless current The current which consumes no power for its maintenance in the ly circuit ie, P,, = Oas cos =0 In a.c. circuit containing either inductor or capacitor current is wattless. dewcmemnsammemetrie tae rie Magnetic flux in Primary coil Produces an induced emf in the secondary coil. Construction L. Primary coil and secondary coil wounded over the soft laminated iron core. Transformer ratio é tp Me _ Ng Is Vp Np > © For step up transformer Ng > Np, Ig < Ip * For step down transformer Ns < Np, Is > Ip Energy Losses is due to * Flux leakage * Resistance of the windings lL» » Eddy currents: Produce heating in the metal core. + Hysteresis: Energy loss in magnetisation and demagnetisation Uses electromagnetic induction, i.e. changing magnetic flux linked “| with a coil produces induced emf. Main Parts Armature: Soft iron core with large number of turns of the copper wire wound on it ° Field = magnet: Two <4 Pole pieces of strong electromagnet * Slip rings Alternating induced emf is produced when armature of coil is rotated in the uniform magnetic field. e = NBA sin ot Peak value c, = NBAw ! « In induction furnaces: For extraction of metal (metallurgy) “> . in voltage regulator: Adjust requirement of voltage. « In welding (step down) enorme Displacement Current (I,) The current which originates in the region where the electric field and the electric flux are changing with time 1 = fate at Ampere-Maxwell’s Circuital law The line integral of the magnetic field B Over a closed path is equal to Hy times the sum of {, and i, through closed path §BaT = will, +t) /, - Conduction current Properties of EM waves Propagate. properties of the medium vice i vue 8 * Energy is equally divided between F and 8, U, = Uy U;,= peal 1B Uy = 2 Bo * It exerts Momentum p = - —— It does not require any medium to Speed (v) of EM wave in a medium depends on electric and Magnetic Waves radiated by an accelerated charge which ' Propagates through space as coupled electric and - Magnetic fields oscillating mutually perpendicular. ELECTROMAGNETIC WAVES with the direction of propagation. < pressure and has. t Source of EM wave An accelerated charge is the source of EM wave or fast moving electrons suddenly stopped by Metal target of high atomic number (for X-ray). —__| Transverse nature of EM wave Electric and magnetic fields in an EM wave are Mutually perpendicular to the direction of Propagation. E, = Ey sin (kz - of) L B, = By sin (ke - al) XTE B z ‘ett tnneuteeranneteet einen ane X-rays * Produced by collision of high Speed electron with high atomic mass metal target. * 3X 10 Hz to 3 x 102 Hy <4] * Use: In surgery to detect the fracture, flaws, cracks and holes in the metal products, Wiese imate Gamma rays * Itis originated by decay of radioactive Substance, L 13x 10 He to 5 x 102 He . Use: In radio therapy, food industry to kill Pathogen. ‘Sttevtencnrninnnnste on —--eaw a 5 Flectromagne ‘ Cg The orderty attanges Wave in increasing or “tty 9 OF deorere Order of wavelength * ia) Mey, Radio Waves : They ate produced by Oscillating Charge, % * v— 500 kHz to 1000 ty * Use: In TV ang radio ; Communication, Microwaves They are produced by the vacuums * 1 GHz to 300 Ghz Infrared rays * It is known as heat waves, Produced by heat radii bodies, * 3x 10" Hzto4 x 10H + Use: In satellite, heat sensos, physiotherapy. aeead Visible rays : © Ttis visible to human eye rat by excited atoms. > = 4 x 10" He to 7 x 10! Lah * Use: By optical organ of 2 to see. mes Ultraviolet rays oe * It is produced by special and very hot bodies. = 10" Hzto 10 Ha ilise § « Use: » To Steri ae instrument. oth In Lasik eye SU + In Burglar ast aut Gontinued trom, Disperston Phenomenon ot s light Into Its Component colours Spectrum: Pattern o of white light [vigayor) = Dlitting of the white f colour component previous page ov Cause of dispersion ' itferel nt colours. of white light have (ore wavelengths and the angle jviation Is inversely proportional 1 tor valenath of light 8 e 5 Continued from previous page Optical instruments ——-———> Help to view things Clearly and distinctly we Y Ralnbow q * Disperston of the sunlight through water drops In the atmosphere * It Is due to combined effect of refraction dispersion, and total. internal reflection of sunlight. t Y Telescope amo: image of close Used for observing distinct Image of ; minute object heavenly bodies consist of two coaxial convex lens. y * Objective of larger aperture and large (Fem viru al eas and magnified £ i | 5 : i east distance of dintinct Compound Microscope Consists of two coaxial convex lenses ¢ Objective of small aperture and very short focal length + Eyepiece of larger aperture and larger focal length. ¢ Magnification (m) For image at near point m=m, xm, D = (1+ mm a4) For image at infinity, m = a ‘Oo focal length * Eyepiece of smaller aperture and small focal length * Magnification (1m) For image at infinity b mmo For image at near point Berea) D a Y M Refracting Telescope “They can he used both for terrestrial and astronomical observations. nn Reflecting Telescope Used concave mirror of large apertur * Magnification (m) For image at near point f f = 144% iB *( +3) For image at infinity m=) f ‘OAR nsaonncrnne ‘ ‘Study of various Phenomenon of light related to wave nature. WAVE optics Wavefront Light propagates in the form of wavefront, [wavefront is the locus of points having the same phase of vibration and ray of light is pempendicular to it. pttanaa vera eie saree Spherical wavefront lL» When the source of fight is a point “source. ~ Gylindrical wavefront When the source of light i is linear. Nacllsts tonto ~ Plane wavefront When the source of light is at large distance from wavefront then {Portion of the. wavefront is plane. "Wtesitetentienemasnasscocesie Huygen’s principle '* Each point on the given wavefront is Oe the source of a secondary wavelets. "A surface tangential to secondary © Wavelets j in forward direction at any insta nt is the secondary wavefront. ‘s | } Interference Superposition of two light waves of the same frequency having constant ~— phase difference and propagating in the same direction. In the redistribution of energy, alternate dark and bright bands are formed. Constructive interference Region of maximum intensity where > Phase difference » = 2nn,n = 1, 2,3 Path difference = nr Intensity « (@ + b)* a, b — Amplitude of interfering waves Destructive interference Region of minimum intensity where Phase difference, 6 = (2n — 1)x i = (ont) L, Path difference = (2n-1) 3 Intensity ec (a - b)? a, b — Amplitude of interfering waves cecsaccerncrrectureaaoemsronstestecaerein anne eceppraunermscubonrncaciwenssgrmeutemtrtinatenneomne U Diffraction To be continued on next page Coherent sources Sources of light which emit light [> waves of the same frequency and have constant phase difference at a point. ‘eta wbenaie nee vaemetemepinneemtemrentn Young’s double slit experiment Intensity at a point P=l, +h + 2/hb cos $ — Phase difference Bright fringes Ll, Position y, = AON D — Distance of screen from slit d — Separation between slit Dark fringes Position Vy = (en 1) 5% Fringe width B = ee ba (Satensreinsdnmaanammae meena based on _» It is basic constituent : ATOMS: . of matter | Atomic model 4 “Bohr’s model of | To be continued at next page* BD Adal oe hydrogen atom —_ | o-particle scattering experiment by H. Geiger and E.Marsden. "Observations * Most of the «-particle passed through gold foil. + Only 0.14% scattered by more than 1° and Rutherford nuclear mode! Based on a-particle scattering experiment * Atom consists of small, positive central core known as nucleus i which whole mass and positive charge of an atom is concentrated * Flectrons revolve around the nucleus in various circular orbits du to electrostatic attraction between the nucleus and the electron. 1 in 8000 deflected by more than 90°. Conclusions « Atom has most of the space empty. * All the positive charge and most of the mass is concentrated in small region at the centre of atom, known as nucleus. 1 1 * Radius of e Limitations , electron orbit © Arey + It could not explain the stabil © Total ener 9 sas of an atom. of pee == ¢ It could not explain the tine Bnegr spectrum of hydrogen atom. SEES paren omasaaieeumneeN Raeumnnematee eceassiseccspeoncenutnncaeaniema merece eens Distance of closest approach (rp) Closest distance of a-particle moving towards the nucleus at which its whole :K.E. converts to PE. ee 270 9 Amey (KE) ltis 1 dist a-particle Impact parameter (b) ! Angle of scattering The angle by which an a-particle gels deviated from its original path, while moving towards the nucleus. ance of initial velocity vector of from nucleus axis, seaastosemnanaunverscenirs * continued from previous 7 Page Bohr’ S model of __hydrogen atom Postulates * Electrons revoly ® around nucleus in stati i iona whose angular momentum is quantised naa L =m = 2 n=1,2,,2% * Electron on transition from Ww ctr TO. i a upper energy level to lower, emit AE = Iv =£,-£, De Broglie explanation Integral multiple of stationary waves is associated with electron in the stationary orbit of radius r,. anf, = mr creepers nnemasinmnennt © Bobr radius (r) n=1,2=4 Due to transition of electron from higher energy level (77,) to lower energy level (n,) AE = £,-E, = hv fit Di af te racer] 1.097 x 10’ mt Y Radius tne nth orbit Velocity of electron in the ath orbit Total energy of electron in the ne wh vy, = 2akze? iad stationary orbit 4n’mkze? etenenhag 2. A 5 = wontmi’et a Na = fol ane 1 For H-atom, £,= 713.6 gy peta abs fi 4reg 1 Evel. 3 n (temascomemescmmemmecteremes Line spectra of hydrogen atom Sencetinecneennmavare sows NAS Balmer series ny = 2:9) = By 4p. Paschen series ny = 3,0, = 4, 5, ..- Infrared radiations Brackett series Ny, = 4, My = 5, 6, ... Infrared radiations Y Pfund series 1, = 5, = 6,7, .., For infrared radiations Visible radiations) citer = _ andar (Senate Continued from previous page NUCLEI ¥ Nuclear fusion : yis 00 fighter ea nucleus of higher average binding nergy st f huge energy equivalent to mass ject between the reactant and product. equire extreme high temperature and Assure, s source of energy in the sun. iH Sth te tiv 0.42 meV aaa shares tsevecnerasiiniiee! nuclei combine to form a Nuclear fission e|n this heavy nucleus breaks up into two lighter nuclei of comparable masses with higher average B.E. 25 + in — pa + Sgr + 3gn + 200 MeV * Principle of nuclear reactor. pee oe Nuclear reaction stable nuclei of E. with release Process to form higher average B. of energy. Thermal neutron j Slow moving neutron of energy ~~ 9.9995 eV that causes nuclear fission when collide with heavy nucleus. © semiconDUCTOR AND ELECTRO! ! q Energy band in solid * Collection of the closely spaced energy levels formed due to the continuous energy variation in different energy levels. * Valence band: Energy band of the energy levels filled with valence electrons. * Conduction band: Energy band above the valence band. * Forbidden gap (E,): Energy gap between the conduction band and the valence band. + Fermi level (E,): Energy of free electrons at the absolute zero (0°K). (A, | _ Classification of Materials ‘WR Ra tourna nt ner Conductors * Have very low resistivity p = 107 to. 10% om. * Conduction band and the valence band overlap, i.e, there is no energy gap. + Electrons easily acquire “energy to get free. 1 p-a junction diode Ly n Extrinsic semiconductor with one half as p-type and the other half as n-type, * Depletion layer: Region at junction devoid of free charge carriers. * Potential barrier: Potential difference ar across the depletion region. Biasing The method of connecting external emf source to a p-n junction diode. To be continued ‘on next page* q Forward Bias * +ve terminal of the external battery is connected to p-side and —ve terminal with n-side of junction diode. [ca * Has low resistance and conduction is by majority charge carriers, « Knee voltage-Forward beyond which current bias voltage tj i Setanta aSeS api, Insulators * Have high resistivity p = {Qt + Energy gap between the Col the valence band E> to 1078 om, nduction band an 3 eV. : Y Reverse Bias * +ve terminal of the external battery is connected to n-side and —ve terminal to p-side of the junction diode. imi VT 44 a I * Has high resistance and conduction is by minority charge carriers. + Zener voltage: Minimum reverse vottagé up to which current is independent of voltage Semiconductors 5 * Have intermediate resistivity p = 10 7 10° om. * Energy gap between the valence bard and the conduction band E, < 9 & - To be continued on next page**