IMPORANT AUN Chapter-1: Electric Charges and Fields 1, Coulomb's force F between two point charges kept in a medium of dielectric constant (K), 1 ae “Grek For air between the charges, dielectric constant K = 1. pois at Txty gt =, ul fe. In vector form, Pu-gGa em Where Fy, is the force on charge gz due to 4, and fy, is the unit vector in the direction from 4110 qo. 2. Electric field strength E at any point in the field where F is the force experienced by a test F charge qy kept at that point, E = dim ( Electric field strength due to a point charge at a distance r where is unit vector along 7; 7 = (i) Due to sphere charge (@) Inside point ( < R) E=— pnker i (@Ousside point r= Ry B=z Z Fey Ee 7 q ‘On the ‘fac =f) p= (c) On the surface (r = R) te, RP (ii) Due to hollow sphere of charge iz (@ Inside point (7 $ R), E = 0 BI cert a | (b) Outside, p= 4 WOuwide, B= Fea Oran ? (© On the surface, E= Fy() Electric field strength due to infinite line charge having linear charge density (A) coulomb/metre. 1K ame, E (v) Electric field strength near an infinite thin sheet of charge. poo (vi) Blectric field strength near a conductor E = =, where fi isa unit vector normal to the surface in the outer direction. Electric field strength inside a conductor E = 0. 3. Electric Dipole: (@ Dipole moment ‘| (i) Torque on a dipole in uniform electric field ¢ = px E 21 (21 being the separation from - to +4) (ii) Potential energy of dipole, U = where 0 is the angle between pand E (») Work done in rotating the dipole in uniform electric field from orientation 0, to 0, is W = U,-U, = pE(cos 0, - cos 05) Work done in rotating the dipole from equilibrium p W = pE (1 -cos 0) (v) Electric field due to a short dipole: ition © = 0 to orientation @ is (a) ataxial point g,, = 12 Chapter-2: Electrostatic Potential and Capacitance 1. Electric Potential ai Due to a charged conducting sphere or charged spherical shell of radius R. [New 4 é 14 —te< poe ——— (Imside, Vise Fee, RO SR) i) Outside, Vou = Fer F (> R) dl ; 2, Relation between electric field and potential, av _V pe aor taking a charge q from one point to another in elect W = q(V,—V,) joule otential at initial point, Vy = potential at final point. (numerically) 3. Work don field where V;4, Work done in carrying a charge on equipotential surface is always zero. 5. Electric potential due to dipole, Tp (i) at axii Vow a (0 ataxia point Vax = Fe (i at an equatorial point Y= 0 6. Capacitance for isolated conductor, C Cnet Coir 8. Capacitance of parallel plate capacitor A c= af (in air) KegA d € 7. Dielectric constant K = 3 = @) C= when medium of dielectric constant K fills the space between plates. (iii) When the space between the plates is partly filed with a dielectric of thickness ¢, then &)A d- (! _ 1) K) 9. Combination of Capacitors: ( Capacitors in seri (@) Net capacitance Gis given by Lo. 1 1 capacitance ¢ = oe CG GG (0) In series charge is the same on all capacitors 1 = 2 = 45 (©) Net potential difference V = V, + Vz + Vs (ii) Capacitors in Parallel: (@) Net capacitance, C = C, + Cz + Cs () Potential difference is same across all capacitors Vy = Vo = V5 = V (same for all) (©) Charge, q= 9 + 42 + 93 10. Energy stored in a capacitor, u=ley?=2 ly De eo ag: 11. Electrostatic energy density, U.=4eo8*(in air) and Fe6? (in medium)Effect of Introducing a dielectric between plates of a charged parallel plate capacitor s. Physical When battery ‘When battery is removed No. Quantity remains connected before introduction of dielectric L._| Capacitance (©) increases Ketimes increases K-times| Charge (O) increases Ketimes remains constant decreases “> times K 4, Electric Potential (V) decreases 2 times: x remains constant i 5, | Electrostatic Energy Stored increases K-times decreases + times | | | Chapter-3: Current Electricity cE 1. Drift velocity, v, = m where E is electric field strength, t is relation time, e is the charge on electron and m is the mass of electron. 2, Relation between Current and Drift Velocit 1 = -neAvg where n = number of free electrons per m°, A = cross-sectional area 3. Ohm’s law Or J =GcE (alternative forms of Ohm's law) 4, Resistance 5. Specific resistance &. 6. Current density 7. Electrical conductivity 8, Temperature dependence of resistance R, = Ry (1+ at) where ais the temperature coefficient of resistance or Ry = Ry [1+ a-4)] 9. Internal resistance of a cell: r -(F- ie where E is emf of cell, V = terminal p.d. across external resistance R. 10. Combination of Cells ( When n-identical cells are connected in series Gurrent,i(= "ot = 82 _ current |= ROR, | Rtn For useful series combination, the conditi nis Rox >> Rin, vn(i) When m-identical cells are connected in parallel Ena E Rig * Rigg RE Tin i Condition of useful parallel combination is R < rim. (ii) When N = mn, cells are connected in mixed grouping (m-rows in parallel, each row containing n cells in series) Current, i ee nee mR + nr Condition for useful mixed grouping is Rex, = Rin. ny ie, =a (v) When two cells of different emfs £ and B, and different internal resistances 7, and ry are connected in parallel as shown in fig. then net emf of combination is E, Se 11, Joule’s Law of heating effect of current W=PR o =Vit joule. 12, Electric Power Value of External Current Terminal Power Consumed in Resistance from the Cell Potential Difference | External Resistance R veer p=PR ee VE P=0 (Shor circuit) . eee ar (xm Open circuit, 7=0 V=E-0 P=0 R V=EChapter-4: Mor 1g Charges and Magnetism 1. Biot-Savart Law: Magnetic field due to a current element ‘by Ldixr an 3. Magnetic field due to a current carrying circular coil ( Atcentre B, = Hot 2R u,NIa® (@ Ata point on the axis Buy = SEP (where a = radius of coil) and x is the distance of the point) 4, Ampere’s circuital law: { B.d! =u, 5. Magnetic field strength wi B=pgnl wheren jin solenoid number of turns per metre length. 7. Magnetic force on a moving charge in a magnetic field E=qoxB 8. Magnetic force on a current carrying conductor 1x 9. Force per unit length between parallel currents: F obits 1 nr 10. Torque experienced by a current carrying loop in a uniform magnetic field T= MAxB= MxB 11. Magnetic moment of a current loop M=NA 12. Deflection in moving coil galvanometer 6 NAB I c E, Current sensitivity of a galvanometer S13. For conversion of galvanometer into ammeter, Shunt resistance required S Chapter-5: Magnetism and Matter 1, Magnetic dipole moment, m = q,, x 2 2. Magnetic dipole moment of a current loop, m = NIA 3. Magnetic field due to a short magnetic dipole (@ Ataxis = eM at an _ Yo M. (i Avequavorial, By, = Faas 5. Magnetic moment of an orbital electron core 7. Magnetic susceptibil £ » where C is Curie constant. 8. CurieLaw: xa = x= istinction between Dia-, Para—and Ferromagnetics Property Diamagnetic | Paramagnetic | Ferromagnetic | _ Remark @ | Magnetic induction B | B By BSB, Bi, is magnetic induction in free space (i | Intensity of magnetisation | small and small and very high and | mis magnetic i negative positive positive moment Maz (Gi) | Magnetic suscepaiility | small and small and very high and Mt negative positive positive x= (i) [Relative permeability | a, <1 up>1 Hu, >> Lot —— the order the 0 thousands)Chapter-6: Electromagnetic Induction 1. Magnetic flux $,=3.4 = BA cos0 where @ is the angle between A and 5 2. Induced emfin a coil o=- <2 3. EMF induced in a moving conductor, € = Bul where B, x, [are mutually perpendicular 4. Magnetic flux = 6=LI where L is the coefficient of self-induction. 5. IfL is self inductance, emf induced & 6. Self inductance of a solenoid ae w NPA 7 L=pptyn® Al= N,N, A 1 where N, = number of turns/metre in solenoid, Ny = number of turns in coil. LP = or 8. Mutual inductance of solenoid coil system M = 9. Energy stored in inductance U, 2 Direction of Current Induced in Some Cases System Primary Current Induced Current, 1. | Straight wire-coil system (@ Current increasing Clockwise current > (ii) Current decreasing “Anticlockwise current 7 2. | Self inductive circuit @ Key is pressed ‘Opposite to direction of PECOTTOT- ‘main currents (ii) Key is released In the direction of main current 1 iecoil 3. | Magnetic-coil system (i North pole approaching | Anticlockwise current Man observing direction of current Oney 8 7 (ii) North pole receding coil | Clockwise current Oe Chapter-7: Alternating Current 1, For an alternating current circuit V=Vysin of; [= Jy sin (ot +6) 2. RMS value of an alternating current Ze 4, Phase angle between J and V, tan! 6. Q-Factor: 7. Average power dissipated in LCR-circuit, P,, = Vong lona080= FVilqcos 0 8, Peak emf in a rotating coil of generator 9. For LC oscillations For a step down transformer, y=: <1 iIndividual Components (R or Lor C) ‘TERM R L c I R HOH LI Circuit L c © © & Supply Voltage | V=Vsin ot V=Vosin ot V=Vpsin ot corn Tehsines Tahsin [ut Peak Current p= R Impedance (0) ie ee pala hr Te To In R= Resistance X= Inductive reactance Xe= Capacitive reactance Phase difference | zero (in same phase) +5 (V leads 1) =F leads 1) Phasor Diagram 7 v ——-v 1 Variation of | R Zwith v x Kev eet Xe! R does not depend on v Combination of Components (RL or RC or LC) TERM RL RC Le Cireuit Tis same in R & L Tis same in R & C Tis same in L & C j 500 | R L | I R c Cac (\) “) &Y Phasor diagram Ww Vv nev v, eV 1 d 7, v, Vv " Vevien? 1 Ko(M> Fo) Vm Vo~Vi(Vo> Yi)Supply Voltage V=Vosin ot V=Vosin ot V=Vsin ot Current T=hsin (ot-) I= hsin (ot +4) isin (+3) Pedifownein Tg gk a Viegs I between Vand | Vieads/ ($= 0% 2) Viags 1 ($= 00 A 2 (6--Barxe> mi) Vieads 1 (6+ $y x. > xe) Impedance z= 22 (RKP Z=|X,-Xol Variation of Z As v increases, As v increases, As v increases, Z first with v increases Z. decreases decreases then increases z z z R R S R Chapter-8: Electromagnetic Waves 1. Maxwell’s equations (@ Gauss’s law for electrostatics, fEdA (ii) Gauss’s law for magnetism, { B.dA = 0 oe dt (iii) Faraday's law, {dl = db, (iv) Ampere-Maxwell law, fB.dT= tpi.+ Ho) 2. For a wave frequency v, wavelength 2, propagating along z-direction, the equations for electric field and magnetic fields are: E, = E,sin(ke- wt) B, = Bo sin (kz - ot) where k= 2% 3. Wave velocity, v = vi. 4, The speed of electromagnetic wave in vacuum, ¢ =5. The speed of electromagnetic wave in a material medium, 6. The amplitude ratio of electric and magnetic fields is 3 0 7. The magnitude of the total momentum delivered by an electromagnetic wave, p= where, U = total energy transferred to a surface in time /. 8. Average energy of an electromagnetic wave: u=U,+Y, 2 2 egkg + 2 Chapter-9: Ray Optics and Optical Instruments 1. Reflection (iii) Magnification, m= Ay ‘© Magnification m is —ve for real images and +ve for virtual images. f @ fand R are -ve for a concave mirror and +ve for a convex mirror. © Fora real object u is -ve, v is -ve for real image and +ve for virtual image 2. Refraction () Snell’s law, <* sinr 1 (i) yn, = @ m= speedoflightin vacuum __2, amedium (ii) Refractive index, n = (iv) If object is in medium of refractive index n. Real depth t ‘Apparent depth ~ fayp ‘Apparent shift, -t=(1-4) 2. Critical angle for total internal reflection sini, ‘Total internal reflection occurs when i > i,. 8. A fish or diver in water at depth h sees the outside world in a horizontal circle of radius r given by A4, (i) Thin Lens formulas + =+-+, f _f-v (i Linear magnification: m=] = p= 77 = (iii) For refraction from rarer to denser medium Ny ‘My avi ween (iv) For refraction from denser to rarer medium AB vu (@) Power of a surface ny P=2 = R (vi) Lens maker's formula (For air) Foca) ; diopter (fis in metres) (viti) Lens immersed in a liquid of refractive index, m, (vii) Power of a lens: p = ise fiseetal atl Fale ar- Fy) and fie Ge Liquid mH Gass Liquid where f, is focal length of lens in air. (ix) Lenses in contact 5. Refraction through a Prism: a+ i +i =A+8 A | A = angle of prism angle of deviation sini, _ sin pone oe sing, sin, For minimum deviation i, = ig =i andr, :. Angle of minimum deviation 8, = 2i-A At in na sini 2 sinr A sinf 4 2 For a thin prism: 5 = (n—1)A ""simple Microscope: (For final image at D) (For final image at infinity) 7. Compound Microscope: ( Magnification: M = my x m, (ii) Magnification: M = -"2! (For final image at D) (iii) Magnification: (for final image at =) 8, Astronomical Telescope: (®) Magnification: M ft (for final image at infinity), L=fothe (i) Magnification: yy fi ae (For final image at distinct vision) L=fot te Chapter-10: Wave Optics 1. (@ Condition of Maxima for Young’s Double Slit Experiment on Interference of light: Phase difference, Path difference, (ii) Condition of Minima: Phase difference, Pathdifference, A=(2n a 2 (ii) Relation between Path difference (A), Phase difference ($) and Time difference (¢) : 2 =, where wavelength (2) and time period (7) 2. If sources of amplitude a, and a, are coherent, intensity J at a point in the region of superposition where phase difference between waves is 6 1 =a! + 4,2 +240, coso= I, + I, + 24h) cos (@ Maximum Intensity, Ip, % (a; + @3)"(i) Minimum Intensity, Ii 0 (a; — 42)" Danae _ (Gy #4)" Toy (= 44)" In interference energy is conserved. It is simply transferred from minima to maxima (ii) Intensity of light 2 Width of slits w, (iv) Ratio of slit widths, Ena 3. Young’s double slit experiment: (iii) Fringe width, B=, 4) - yn =PR where D = distance between sources and screen, d = distance between slits (iv) Angular fringe width, 6, 4, Diffraction at a single slit of width ‘a’: @ Directions of ima are, a sin @ = (ii) Directions of maxima are, asin © (ii) Angular half-width of central maximum, 0 = sn'(*) (jv) Total angular width, 90 = 9 sin! (3) a For small , linear half-width ata screen at distance D from slit, Ay = @ (2) Total linear width = 242 a Chapter-11: Dual Nature of Radiation and Matter 1. Photon: ( Energy of a photon, £ = in If? is in A, then energy of photon in eV is hy _h (i) Momentum of a photon, p= == con (ii) Rest mass of a photon = zero (iv) Kinetie mass of a photon, m=" a 2. Einstein's photoelectric equation: (E,),_ = hv-W = h(v—vy) = h (F - x) °3. Work function: where vp = threshold frequency and Ay = threshold wavelength 4. Photoelectrons emitted have kinetic energy ranging from zero to a certain maximum limit, The maximum kinetic energy is 1 Ean = 5a 5. For photoelectric emission to take place, energy of photon E > W or v2 vp ork Shy 6. Intensity of radiation, = Energy __ Power Areax Time Area eV, where Vs = stopping potential. 7. de Broglie hypothesis () de Broglie wavelength associated with moving particle ae 7 mv 2mE, —2mqV 12.27 (i) For electrons, 2 = ——"A «i F 7. Some important characteristics curves: Effect of intensity of the Effect of anode potential Effect of frequency of the incident radiation incident radiation P 2. 7 g ii | Eaton BE ie h satu a é a Cure ona Seer pasar | Tota Gf Povena Effect of frequency on _| Variation of particle momentum | Variation of de-Broglie wavelength| stopping potential with de-Broglie wavelength _| with accelerating potential Metal Stopping Penta aie] t 4 » Frequency of Radiation 1— wo Chapter-12: Atoms 1. KE of w-particle, KE2. Distance of closest approach, feline aden alae 0” ane, KE ane,” mo? 3. Radius of orbit egh?n? : = " nmZe* + For, n= Luaay 5. Energy of Orbiting Electron i) Kineti Lae alec (® Kinetic energy, Ke gm" = Fre. Or 1 @oce_ ae (é) Potential energy, ame, (ii) Total energy Note: -2KE=26, 6. Hydrogen Spectrum (® Energy of absorbed photon a AE = E,-E, nie -52) (i) Iv is the frequency of emitted radiation, we have from Bohr’s fourth postulate Re _{_Re 14 pies ee ef a aaa (ii) The wave number (i.¢., reciprocal of wavelength) of the emitted radiation is given by 7, Ionisation potential =8. Time period of orbiting Electron, 7, = Chapter-13: Nuclei 1. Nucleus consists of protons and neutrons. Number of protons in a nucleus, ,X “is Z and number of neutrons, n = A -Z 2. Radius of Nucleus: R = Ry A’ where Ro =1.2 x 10"''m 3. Density of Nuclear Matter: D, = 10!7 kg/m* 4. Einstein’s Mass Energy Equivalence Relation: E = mc’ Tamu = lu =931 MeV 5. Mass Defect nass of nucleons in given nucleus ~— mass of nucleus Am = Zmy, + (A ~ 2) my — Myceus zm, +(A-Z)m, ~ M, 2 \n = Niese* Binding Energy (B.E.) = Chapter-14: Electronic Devices 1. Energy band gap: E,= 2. In intrinsic semiconducotr: », = nj, = n; n, = number wher lensity of electron in conduction band 1m = number density of holes in valence band 1; = intrinsic carrier concentration 3. Total current through the pure semiconductor: I = I, + I, 4, In n-type semiconductor: n,~ N,>> where, Ny = density of donor atoms. 5. In p-type semiconductor: n, = N, >> n, where, N, = density of acceptor atoms. 6. Mass-action law: At equilibrium in any semiconductor, nm = nF 7. Diode as Rectifi In half wave rectifier ( The output ripple frequency = f h (@ Average value of de obtained, 1,,= = In full wave rectifier ( The output ripple frequency af 2l, (ii) Average value of de obtained I,, = where, / = Input fundamental frequency Jy = Peak value of current