ELECTROSTATICS Electric Field Intensity:- 2 0 1 Q E 4 r = vector unit:- N C dV E dr = − Electric Potential 0 1 Q V 4 r = scalar unit:- J C V E.dr = − Electric Dipole:- Equal and Opposite charge separated by small distance, Dipole moment P 2ql = vector(direction from negative to positive charge unit:- C m E & V on Axial Line:- E at pt. P on axial line is E E E = + − B A ( ) ( ) ( ) = − − + 2 2 0 0 1 q 1 q E 4 4 r l r l ( ) ( ) = − − + 2 2 0 q 1 1 E 4 r l r l ( ) ( ) = = − − 2 2 2 2 2 0 0 2 2qrl 2pr E 4 r l 4 r l = 3 0 2P E 4 r For short dipole r >> l (direction (-) to (+)) ( ) ( ) − = + = + + − A B 0 0 1 q 1 q V V V 4 4 r l r l ( ) = − 2 2 0 1 P 4 r l = 2 0 P V 4 r E & V on Equitorial line:- ( ) = + = = = = = = + A B A B A 2 0 3 3 0 2 2 0 E E cos E cos since E E E 2E cos 1 q l l E 2 cos 4 x x x 2ql P E 4 x 4 x l ( ) = + 3 2 2 2 0 P E 4 r l ( ) = 3 0 P E 4 r For short dipole r >> l Direction (+) to (-) (− ) = + = + = A B 0 0 1 q 1 q V V V 0 4 x 4 x Torque on Dipole:- Net force = +qE – qE = 0 Torque = Force × ⊥ distance = qE × BC [BC = 2l × sin θ = qE 2l sin θ = E (2ql) sin θ τ = PE sin θ = P E τmax = PE for θ = 90o work done in Rotating Dipole W d 1 cos PE = = − ( ) Energy of Dipole: U = –PE cos θ Stable equilibrium θ = 0, U= –PE Unstable equilibrium Θ = 180o ⇒ U = PE. Gauss Theorem:- Total electric flux (total no. of lines of forces) emerges from closed surface is 0 1 times the charge enclosed = in 0 q E.dS E due to long charged wire: Linear charge density = q l = in 0 q E.dS + + = in 1 2 3 0 q E.dS E.dS E.dS For dS2 and dS3 θ = 90o For curved surface dS1 θ = 0 = 0 q E dS ⇒ ( =) 0 q E 2 rl = = 0 0 2q q l E 2 rl 4 r ⇒ = 0 1 2 E 4 r E due to charged plane sheet: Surface charge density = q A For non conducting plate charge is on both side = 0 q 2 E.dS= 0 q 2EA= 0 q E 2 A = 0 E 2 For conducting sheet = 0 E * E is independent of distance from the sheet. E due to charged Hallow Sphere: Volume charge density = q V = in 0 q E.dS = 0 q E dS ( =) 2 0 q E 4 r = 2 0 1 q E 4 R On surface = 2 0 1 q E 4 r Outside & E 0= as q = 0 inside Capacitor:- Q = CV unit:- Farad, * C depends on dimensions Capacitance for parallel plate capacitor Consider || plate capacitor with area of plate A, capacitance C and dist. b/w plates d = = Q Q C V E d = 0 E for charged sheet = Q A for surface charge density = = 0 0 A A C d d If dielectric with dielectric constant k is filled b/w the plates. C ’ = kC Surface charge Density = = Q Q A A Electric field = + air dielectric E E E = + 0 0 k Potential V = E × d ( ) = + + 0 0 V a b t k = + + 0 t V a b k = − + 0 t V d t k Now = = − + 0 Q A C V t d t k Energy of Capacitor Energy = work done in bringing charge at potential V = = q dW V dq .dq C = = = = Q Q Q 2 2 0 0 0 1 1 q 1 Q U dW q dq C C 2 2 C = = = 2 1 Q 1 1 2 U CV QV 2 C 2 2 Energy Density (energy per unit volume) ( ) = = = 2 2 0 2 0 1 1 A CV E d 2 2 d 1 E volume A d 2 Unit of energy density:- J/m3
CURRENT ELECTRICITY Electric Current: q i t = , unit - Ampere * Scalar quantity nAle i q / t t = = Current I = neAVd eV I neA ml = 2 I ne A V ml = V = IR 2 V ml R I ne A = = Mobility Vd E = (m2 /sV) A – Area n – number of free electrons in unit volume resistivity ρ = RA l ρ 2 m ne = Also J E = I J A = = current density (vector) Drift velocity:- v u a = + if u = 0 –14 −relaxationtime (10 s) V a d = Also ma = eE = f eE a m = d eE V m = (10–5 m/s) as V = Exl d eV V ml = Temperature dependence of resistivity Electric Energy & power Colour Coding of Resistor with increase in temperature conductors : decrease. inc. semiconductors; n increase dec Power = Energy / Time = Work done / Time It is a scalar quantity 2 2 V E V.I.t I Rt t R = = = 2 2 V P V.I I R R = = = 1 unit = 1 KWh Series combination of resistance:- R = R1 + R2. Current same Parallel combination of resistance:- 1/R = 1/R1 + 1/R2 Voltage same E = V + ir charging E = V – ir discharging KIRCHOFF’S LAW i. i = 0 Junction law ii. iR = E = 0 Voltage law Cell in series I = nE /nr + R Cell in parallel nE i r nR = + Meter Bridge: Let Unknown Resistance = X R l X 100 l = − R(100 R) X l − = Resistivity RA L = Meter bridge in most sensitive when null pt. in middle. Wheatstone Bridge: Balance condition P / Q = R / S Potential at A & B same at null pt. Position of Galvanometer & battery can be interchanged at null pt. Potentiometer: Principle:- If constant current flows through wire of uniform cross section, then drop in directly proportional to length of that portion E K L = = Potential gradient When K1 inserted then E1 = K × L1 When K2 inserted then E2 = K × L2 1 1 2 2 E L E L = When only K1 is inserted then E = K × L1 When K1 and K2 both are inserted then V = K × L2 = E – r 1 2 1 l r R l = − Advantage of Potentiometer over voltmeter:- 1. Preferred over voltmeter as it give exact reading draw no current 2. Sensitivity increase with increase in length 3. A small P. D can be measured accurately with the help of potentiometer. The resistance of voltmeter is high but not infinity to work as an ideal voltmeter. 4. The internal resistance of a cell can be measured with the help of potentiometer.
MOVING CHARGES & MAGNETISM Magnetic Field:- Produced by magnet, moving charge, Vector quantity. Unit:- Tesla (weber/m2 ), gauss (maxwell/cm2 ) IT = 104 G Oested Experiment:- Current carrying conductor produces magnetic field. Bio Savart Law:- It gives M.F. at a point around current carrying conductor. idl sin dB r = 0 2 4 TmA − − = 0 7 1 10 4 μ0 – Permeability of free space Direction of B:- Perpendicular to dl and r. B = 0 if sin θ = 0 B = max sin θ = 1 θ = 90o Vector Form idl r dB r = 0 3 4 Ampere’s Circuital Law:- B.dl i = 0 The line integral of magnetic field B for any closed circuit is equal to μ0 times current i threading through this closed loop and this closed loop is called Amperian loop. B. Due to Infinitely Long Wire:- Magnetic field at P due to wire B.dl i = 0 B dl i = 0 B(2πr) = μ0i l B r = 0 2 4 Direction:- Right Hand Thumb Rule curly finger gives field direction if thumb of right hand points current outside Mag. Field At Centre of Coil:- o idl sin dB r = 0 2 90 4 i B dB dl r = = 0 2 4 ( ) i r r = 0 2 2 4 i B r = 0 2 or Ni B r = 0 2 Direction:- Right Hand Thumb Rule. B. due to Solenoid:- Bdl B.dl cos = N – Total Turns d a B.dl i = 0 ( ) b c d a a b c d B.dl B.dl B.dl B.dl Ni + + + = 0 ( ) b a B.dl Ni + + + = 000 0 b a B. dl Ni = 0 B.L ni =0 ⇒ ∴ B = μ0ni N n L = (Turns per unit Length) On Axis of Coil:- o idl sin dB x = 0 2 90 4 = B dB sin i a ( ) a . x x = 0 2 2 4 ( ) / Nia B a r = + 2 0 3 2 2 2 2 Force on charge in Electric field:- F = qE (both for rest & motion) Magnetic Field:- F = qV Bsin θ (only for moving charge) B. Due to Toroid:- (Closed solenoid) B.dl Ni = 0 B r Ni ( = ) 2 0 Ni N B n r r = = 0 2 2 B ni =0 [at P] Lorentz Force:- F = qE + qvB sin θ = q (E + vB sin θ) Cyclotron:- Used to accelerate charge Particles. Principle:- The repeated motion of charged particles under mag. & ele. field accelerates it. E.F. provides energy while M.F. changes direction. Construction:- Dees, Sources, M.F., R.F. Oscillator Working:- Max KE mv = max 1 2 2 qBr m m = 2 1 2 q B r K.E. m = 2 2 2 1 2 Force b/w 2 parallel current carrying wire:- Force acting on a due to b. o i F i l sin r = 0 1 2 2 90 4 i i F r = 0 2 1 2 4 (For unit Length) By Flemings LHR force is of attraction for same direction of current and force of repulsion for opposite direction of current. if i i A, r m. 1 2 = = = 1 1 then F = 2 × 10–7 N. Current Sensitivity:- Deflection per unit current s BAN I i C = = Radian Ampere Moving Coil Galvanometer:- Device to detect & measure electric current. Principle:- Current loop experience torque in uniform M.F. Construction:- Light Coil, concave magnetic Poles → radial field. Theory:- Deflecting torque = Restring force (torque) B × i × N × A × sin θ = CØ (θ = 90o ) as field is radial ∴ B AiN = CØ ⇒ C i ABN = Torque Experienced By a Current loop in uniform Magnetic Field:- τ = F × ⊥ distance = Bil × bsin θ τ = Bi A sin θ For N Turns:- τ = BiNa sin θ Voltage Sensitivity:- Deflection per unit voltage s s I BAN V R V iR CR = = = = Radian Volt Limitation:- Only charged particles can be acceleration For circular path:- mv qvB r = 2 ⇒ mv r qB = ⇒ r ∝ v q B r K.E. m = 2 2 2 1 2 Time period = Distance / Velocity = 2πr / v ⇒ T = 2πm / qB Frequency of Revolution:- f = 1/T = qB/2πm Application:- For nuclear reaction & other research purpose.
Conversion of Galvanometer into Ammeter:- (i – ig)S = ig.G g g i .G S i i = − {For Ideal Ammeter R = 0} Conversion Into Voltmeter:- By connecting high resistance in series {For Ideal voltmeter, R = ∞} ( ) V i R G = + g ( ) g V R G i = + ELECTROMAGNETIC INDUCTION (E.M.I) The phenomena of producing induced current due to change in magnetic flux is called electromagnetic induction. Faraday Law:- (i) Change in magnetic flux induces current which last till there is change. (ii) d e dt − = Lenz’s Law:- Induce current opposes the factor due to which it is produced. acc. to law of conservation of energy. Method of producing emf:- d dBAcos e dt dt − − = = Induced current / charge:- d e d dq d e ,i , dt R Rdt dt Rdt − − − = = = = d dq R − = Motional emf:- The emf induced due to motion of a conductor in M. field. Motional emf:- d e dt − = dB.A dt − = BdA Bldx dt dt − − = = e Bvl = − Direction = Anticlockwise Force:- Bvl i R = Bvl F Bil B l R = = − B vl F R − = 2 2 Power:- P = Fv B v l P R − = 2 2 2 Rotating rod:- d e dt − = dBA e dt − = BdA e dt = B L e = 2 2 e B L = 1 2 2 or e B R = 1 2 2 No. of spokes is increased emf remain same. Eddy Current:- The circulating induced current in a oscillating metallic block kept in magnetic field. In can be reduced by using laminated core, or cutting slots in block. Application:- (i) Magnetic brakes (ii) Induction furnace (iii) Dead beat galvanometer Self – Induction:- Change in current in a coil, induced current is produced which opposes the change in same coil. Unit:- L = 1 Henry (H) Dimension Formula:- [ML2T –2A –2 ] Solenoid:- ϕ = Li ϕ = BAN = (μ0niA) × N Li = μ0n 2 × i × A × l (n = N/l) L = μ0n 2Al Mutual – Induction:- when the change in current in primary coil induces current in secondary coil. ϕ ∝ i ϕ = Mi Unit – Henry ∈0 = Farad/m μ0 = Henry/m Solenoid:- B2 = μ0n2i2 ϕ = B2AN1 ϕ = (μ0n2i2)AN1 ϕ = Mi2 Mi2 = μ0n1n2Ali2 M = μ0n1n2Al *No. of turns is double than inductance become four times ( L ∝ n 2 ). Electrical Resonance:- F LC = 1 1 2 Power in A.C. circuit:- P V i cos = 0 0 1 2 V i P cos = 0 0 2 2 P V i Cos = RMS RMS R Cos Z =
MAGNETISM & MATTER Properties of Magnet: 1. Magnets have north pole and south pole. 2. Likes poles repel & unlike attract each other. 3. Freely suspended magnet rests in N – S direction. 4. Monopole do not exist. 5. Mag. Length is eq to 0.84 times of their geometric length. Permanent Magnets are made up of steel: Hysteresis Loop / curve: The graph plotted b/w external field (H) & mag. induction (B) is called “BH curve ‘or hysteresis Loop. Energy Loss: Work done (energy loss) in magnetization and demagnetization is eq. to area of BH curve. Magnetic Material: Paramagnetic 1. odd no of e– in outer most orbit & possess net dipole moment. Diamagnetic 1. Even no of e– and possess net dipole moment is 0. Ferromagnetic 1. Ferromagnetic materials have some unpaired electrons so their atoms have a net magnetic moment. They get their strong magnetic properties due to the presence of magnetic domains. Magnetic Dipole Moment: N →2l S M = m2l unit: Am2 m → pole Strength. M → Magnetic Dipole Moment Elements of Earth’s magnetic field: 1. Angle of Dip: Angle b/w horizontal line & mag. meridian as a freely suspended magnet. 2. Angle of Declination: Angle b/w geographical meridian & mag. meridian is called Angle of Declination 3. Horizontal Intensity of Earth Mag. The horizontal component of to. Earth’s field at any point is called horizontal intensity ( ) 2 V 2 2 H V H B Bsin tan ,B (B ) B B Bcos = = = + 2 2 B B B = + H V M. Due to Current Loop: When current is passed through a loop it, behaves like a magnet. (M = iA) = current × Area, M = NiA ⸫ M ( r) q evr 2 t 2 = = {for e- , v = 2r/t} Magnetic Dipole Moment of a revolving: ( ) M iA r q 2 t = = = evr 2 {for e- , v = 2r/t} 2. Aligns || to field & get weakly magnetized along ext. field. 2. Align ⊥ to ext. field. 2. When a magnetizing force is applied, the domains become aligned to produce a strong magnetic field within the part. Magnetic Field Intensity due to magnetic Dipole: 1. On Axial line: 0 3 2M B 4 r = 2. On Equatorial line: 0 3 M B 4 r = Magnetic Field of Earth: Torque Acting on dipole in Mag. field: = f dis. = mB2 l sin = m2 lBsin = MBsin ⸫ = MBsin →Torque is ⊥ to mag. field and mag. dipole moment (M) → max = MB (sin = 1), = 90° {Due to torque rotation motion or liner. } → min = 0 = (sin = 0) , = 0 3. Mag. field pass through substance 4.Increase with decrease in temp. 3. Mag. field repelled by substance. 4. Increase with increase in temp 3. Temp. at which ferromagnetic substance becomes paramagnetic called curie Temperature. Work done in Rotating the Dipole: W = MB [cos1 – cos2] Electromagnets: Are prepended by passing electric current in a solenoid. The magnet lasts till the current is passed. It can be increased by: 1. Increasing number of turns. 2. Increasing current. 3. using soft iron core.
ALTERNATING CURRENT (A.C) TRANSFORMER: - It is a device use the change AC voltage. Principle: It is based on principle of mutual induction. Construction: two coil primary & secondary Step up: Increase voltage (k>1) and decrease current. Step down: decrease voltage (k < 1) and increase current. Theory: s S p p p s V N i K V N i = = = 100% output input = A.C. Generator :- It is a device which convert mechanical energy into electrical energy. Principle: It is based on principle of electromagnetic induction. Construciton: (i) Arumature coil. (ii) Field magnet (iii) Slip ring (iv) Brushes . d e dt − = – cos dBA t e dt = e = BA(–ωsinωt) e = BAN ωsin ωt emax = e0 = BANω e = e0sinωt Alternating Current: - D.C – Direction & magnitude are fixed. A.C – Change in both magnitude and direction. HALF– CYCLE: 0 V Vavg. = avg 0 0 1 V . V sin d = av 0 0 1 V V cos = − 0 av V V cos cos0 − = − 0 0 av av 2V 2I V or I = = Full Cycle: Vav = 2 0 1 Vd 2 2 avg 0 0 1 V V sin d 2 = ( ) 2 0 avg 0 V V cos 2 = −( ) ( ) 0 0 avg V V V cos2 cos 1 1 2 2 = − + = − + V 0 or I 0 avg avg = = Root mean Square: 2 2 RMS 0 1 V V 2 = 2 2 2 2 2 2 RMS 0 0 0 1 1 V V V sin d 2 2 = = 2 2 2 2 0 0 RMS V V 1 cos2 V ( ) sin 2 2 2 − = = = 0 0 RMS RMS V I V or I 2 2 = = A.C. Circuit: - Pure Resistive Circuit: (Circuit containing resistance) V V0 sin t R R = i i sin t V V sin t = = 0 0 V I Resistance is independent frequency of A.C. Pure capacitor circuit (circuit containing capacitor only) Q = CV d dV C dt dt = , d i C dt = (V0 sinωt) 0 d i CV sin t dt = ωCV0 cosωt V0 i sin( t / 2) 1 C = + V0 i 1 C = Pure inductive circuit: V = V0 sin ωt Ldi V dt = Vdt di L + = V sin tdt 0 di L = ( ) V V 0 0 di sin t dt cos t L L = = − Series LCR circuit: - 2 2 2 R v V (Vc Vc) = + − 2 2 2 L C (IZ) (IR) (IX IX ) = + −2 Z R (X X ) = + − 2 L C 2 2 1 Z R L C = + − 1 L C tan R − = ⇒ X X L C tan R − =
RAY OPTICS Reflection of Light: i = r, Magnitization m = I o = −v u −real inverted. + virtual erect. → Convex Mirror +f, m < 1 and negative m > 1 (enlarged) m < 1(small) → Concave Mirror −f , m > 1, < 1,= 1 both +& − Refraction of Light: μ = sin i sin r , 1μ2 = μ2 μ1 = v1 v2 = λ1 λ2 = 1 1μ2 = 2μ1 Total Internal Reflection (i) Denser → Rarer (ii) i > ic sin ic = ( 1 μd ) Mirror formula: Object AB image A ′ B ′ △ AFB ≈△ PFN AB PN = AB A′B′ = FB PF = u − f f − (i) ΔA ′B ′F ≈ ΔMFP MP A′B′ = AB A′B′ = PF FB′ = f v − f − (ii) from eq− (i) and (ii). u −f f = f v −f By sing convention u, v, f are -ve. f 2 = (u − f)(v −f) f 2 = uv− uf − fv+ f 2 uv = uf +vf. Dividing by uvf uv uvf = uf uvf + vf uvf 1 f = 1 v + 1 u m = I/0 = −v/u Thin lens formula: △ ABP ≈△ A ′B ′P AB A′B′ = PB PB′ = u v − (i) △ MPF ≈△ A ′B ′F PM A′B′ = PF FB′ = f v− f − AB A′B′ = v v− f −(ii) From eq (i) and (ii) f v −f = u v Since u = −ve sign convention vf = (−u)v −(−u)f vf = −uv+ uf uv = uf − vf Dividing by uvf 1 f = 1 v − 1 u Refraction through Spherical Surface: ASSUMPTION: (Since i & r are very small) 1. Small Aperture 2. Point size object By snell's law μ = sin i sin r = i r i = μr △ COM α = i + γ ∴ i = α −γ △ CIM β = r + γ ∴ r = β − γ. α− γ = μ(β − γ) PM −u − PM −R = μ (PM −v − PM) −R 1 u − 1 R = μ v − μ R ⇒ μ v − 1 u = μ R − 1 R μ v − 1 u = (μ −1) R Lens maker formula: By Refraction through first surface μ v′− 1 u = μ − 1 R1 ⋯ (1) I ′ acts as an object for second surface so that final image is formed at I, so for second surface. 1/μ v − 1 v′ = 1/μ −1 R2 1 v − μ v ′ = 1 − μ R2 − (ii) adding eq (i) & (ii). 1 v − 1 u = (μ − 1) ( 1 R1 − 1 R2 ) 1 f = (μ − 1) ( 1 R1 − 1 R2 ) Power of Lens: P = 1 f( m) = 100 f( cm) Diopter. Combined focal length: - First lens forms image I ′ of 0 1 f1 = 1 v′− 1 u − (i) I' acts as object for second lens and final image is formed at I, so for second leans. 1 f2 = 1 v − 1 v ′− (ii) Adding eq (i) & (ii) 1 v − 1 u = 1 f1 + 1 f2
Refraction through a Prism: i = r1 +x e = r2 + y } vertically opposite Angles. i +e = (r1 +r2 )+ (x + y) –-----(1) δ = x + y exterior angle is equal to sum of interior angles ∠P = 180 −(r1 + r2 ). In quadrilateral AMPN. ∠A+ 90∘ + ∠P +90∘ = 360∘ A+ 90∘ + 180 − (r1 + r2 )+ 90 = 360 A = (r1 + r2 )− − −(2) i +e = A+ δ At minimum deviation δm ie, r1 = r2 = r 2i = A+ δm ∴ i = (A +δm) 2 − −− − − (3) A = 2r ∴ r = ( A 2 )− − − −(4) By snell’s Low μ = sin i sin r μ = sin ( A+ δm 2 ) sin ( A 2 ) For then prism μ = A+ δm 2 A/2 δm = (μ − 1)A A-Prism Angle μ =Refractive Index. Angular Dispersion: θ = δV −δR = (μV − μR )A Dispersive Power: ω = θ δy = δv−δR δy = (μv−μR)A (μy−1)A ⟹ ω = (μv−μR) (μy−1) Scattering of light: δ ∝ 1 λ4 (Rayleigh) (RAYLEIGH LAW) OPTICAL INSTRUMENTS: Simple Microscope: Convex lens of low focal length and high power. i) Image at D.: Object placed blow Focus and tens. Magnifying Power. m = 1+ D fe m = β α = Angle made by image angle made by object when kept in position of image. ii) Image at ∞ Object placed on focus. magnifying Power m = D f Compound Microscope: Objective - (convex lens of low focal length and small aperture). Eyelens - (convex lens of high focal length and large aperture). i) Image at D.: Final virtual inverted Image. m = m0 × me = v0 −u0 (1 + D fe ) ≈ 1 fe (1 + D fe ) ii) Image at infinity ∞ Final Image at Infinity. m = − v0 u0 ( D fe ) ≈ L f0 ⋅ D fe Length of tube L = v0 + fe Astronomical Telescope: Objective - (convex lens of high focal length & large aperture.) Eyelens - (Convex tens of low focal length & small aperture.) Danger signals Red. sky appears blue. Reddish appearance of sun-rise, sunset. N
i) Image at Infinity m = f0 fe L = f0 + fe (Length of tube) Length of the Tube L = f0 + ue ii) Image at D m = f0 fe (1 + fe D ) R. P = D 1.22λ D-Diameter of objective Reflecting Telescope: Concave mirror acts as an objective. ADVANTAGES: 1) Bright Image is formed. 2) Image free from chromatic aberration. Resolving Power:- The ability of optical instrument to form distinct image of two object situated close to eachother. Resolving Power of Microscope Telescope [(R ⋅ P)m = 2μ sinθ λ ] [(R ⋅ P)T = D 1.22λ] (R ⋅ P) ∝ 1 limit of resolution Polarisation: C = E0 B0 Brewsters law tan ip = μ Malus law: Iθ = I0 cos2θ
WAVE OPTICS • A wavelet is the point of disturbance due to propagation of light. • A wavefront(w.f.) is the locus of points having the same phase of oscillation. • A line perpendicular to a wavefront is called a 'ray'. HUYGEN'S PRINCIPLE:- Find the shape of wavefront at any particular instance. The two postulate are- (i) Each paint on primary w. f. acts as a source of secondary w.f. which travel in all direction with speed of light. (ii) The forward envelope or common tangent of secondary w. f. give shape of new wavefronts. Reflection by Huygen’s Principle Refraction by Huygen’s Principle MPN and MQN , MN = MN common side = = = o P Q 90 ,PN MQ (dist. covered by light in same time) MPN MQN (by SAS) 90 i 90 r − = − i r = PN = V t1 MQ = V t2 = = = 0 sini PN / MN PN μ sinr MQ / MN PQ 1 1 0 2 t v t v μ = = v t v INTERFERENCE OF LIGHT: - Variation of intensity of light due to overlapping of two light waves. Constructive: - Resultant increase and bright light is formed. Path diff.:- Δx = 0, λ, 2λ, . . . . . ,3λ Destructive:- Path diff.:- λ 3λ λ x , , .....,(2n 1) 2 2 2 = − Phase diff.:- Δϕ = 0,2π, 4π, 6π, . . . . . ,2nπ Phase diff.:- Δϕ = π, 3π, 5π ⋯ (2n − 1)π Δϕ = 2π λ × Δx Destructive:- Resultant is minimum. Young's double slit Experiment (YDS):- A monochromatic light beam is incident in double slit the pattern obtain on screen consist alternate bright and dark bands called fringes. Expression for Interference Pattern: Expression for fringe width: i S′2 S′1 (M-1)
Let, two interference wave y = a,sin 1 ωt y = a (sin( 2 2 ωt + )) = phase diff. by Principle of Superpositiony = y + y 1 2 y = a sin 1 2 ωt +a sin(ωt + ) y = a sin 1 2 2 ωt +a sinωt cos +a cosωt sin y = sinωt (a +a cos )+a cosωt sin 1 2 2 1 2 2 a +a cos = Rcosθ a sin = Rsinθ y = Rsinωt cosθ+cosωt Rsinθ y = Rsin(ωt +θ) a +a cos +a sin = Rcosθ+Rsinθ 1 2 2 Square both side 2 2 2 2 2 2 2 2 2 1 2 2 a + a cos + a sin = R cos θ+ R sin θ 2 2 2 2 2 2 2 1 2 1 2 a + a cos + sin ) = R sin ( ( θ+ cos θ)-2a a cos = 2 2 2 1 2 1 2 a + a +2a a cos R = 2 2 R a + a +2a a cos 1 2 1 2 º R =(a +a ) = 0 max 1 2 − º R =(a a ) = 180 min 1 2 I ∝ a 2 ∝ ω 2 2 1 S M = S P-S P from 2 S PC 2 2 2 2 S P = D +(x + d / 2) from 1 1 S BP 2 2 2 1 S P = D +(x - d / 2) 2 2 2 1 S P -S P = 2xd 2 1 2 1 (S P-S P)(S P+S P)= 2xd 2 1 (S P-S P)(D+D)= 2xd 2 1 (S P-S P)(D+D)= 2xd 2 1 2xd S P -S P = 2D From bright fringe for path difference, λ 2 1 S P-S P = n β = − n+1 n x x = λ xd n D β = (n+1)λD d − nλD d λ n = nD x d λ β = D d λ = D x d For destructive interference: xd λ = (2n -1) D 2 β x x = − n 1 n + n = − λD x (2n 1) 2d − = + − − λD (2n 1)λ D β (2(n 1) 1) 2d 2d = λD β d Interference pattern the intensity of all bright band is equal. • Coherent Source - The two light source behave like coherent source if they belong to same parent source. • Diffraction - It is bending of light at sharp corners or edges. • Fresnel’s distance - df = d 2 /λ
Single slit diffraction – • dark band or minima - dsinθ = n λ • maxima - dsinθ = (2n+1) 2 λ Intensity distribution curve: Linear width of central maxima: = arc angle raclius , β θ D 0 = 0 = λD β d
DUAL NATURE Of MATTER AND RADIATION Photoelectric emission: The emission of electron due to action of light of suitable energy is called photoelectric emission. The e −emitted are called photoelectrons. Properties of Photon- (a) Photon is a bundle of energy- E = n0 ⇒ E = hc/λ (b) Photon travel with speed of light. (c) Rest mass of photon is zero. (d) momentum of photon is p = E/C. Photoelectric effect → The of e − from a metal surface when light of suitable frequency is incident on it is called photoelectric effect. Alkali metals like Li,Na, K show photoelectric effect with visible light metal like Zn, mg, Ca respond to ultraviolet light, Laws of Photoelectric emission - (a) minimum energy required called threshold energy or work function. The freq. corresponding to threshold energy called threshold freq. E = f = hν0 ν0 =threshold frequency Work function(E = f) (b) Every photon interact with a single electron. (c) increasing the energy of incident photon the Kinetic energy of e −emitted increase. Effect of Intensity:- Effect of frequency: Determination of Plank's constant:- frequency From Einstein Photoelectric equation – hν = hν0 +K ⋅ E eν0 = K ⋅ E hν = hν0 +ev0 Einstein Phataelectric Equation: Photoelectric effect was explained using quantum theory by Einstein. E = ϕ + K ⋅ E hν = hν0 + 1 2 mv 2 hν −hν0 = 1 2 mv 2 h(ν −ν0 ) = 1 2 mv 2 Dual Nature of Matter: De-broglie Hypothesis – Acc. to De-Broglie a wave is associated with every moving particle. This wave is called matter wave and its wavelength is known as de-Broglie wavelength. In terms of wavelength:- h ( c λ − c λ0 ) = 1 2 mv 2 hc ( 1 λ − 1 λ0 ) = 1 2 mv 2 I1 > I2 (Freq. = constant) Voltage
Expression for : By particle nature, E = mc 2 By wave nature E = hν equate both the energy mc 2 = hν m = hc λc 2 m = h λc λ = h mc λ = h p In term of Energy: P = mv 2 E = 1 2 mv 2 2E = mv 2 2mE = m2v 2 2mE = p 2 P = √2mE Therefore λ = h P = h √2mE ( P = momentum) In term of charge & potential: E = qV λ = h √2qVm For electron:- λ = h √2meV λ = 12⋅3 A o √V Temp:- λ = h √3mKT E = 3 2 kT K =Boltzmann constant Davisson & Germer Experiment:- (i) Electron gun - producers a fine beam of e −of high speed. (ii) Nickel crystal - It is used to diffract the e −beam. (iii) Detector - It is used to find the intensity of diffracted e −beam. Theory/ working:- A high energy e −beam is incident on a nickel crystal which diffracts this e −beam. The intensity of diffracted beam in various direction is measured with help of detector mounted on circular scale. At 54 volt a clear hump (maxima) at angle of 50∘ , then by bragg's law for diffraction by crystal. 2dsin θ = nλ 0.91 × sin 65∘ = 1 × λ ∴ λ = 1.65Å by de-Broglie hypothesis λ = h p = 1.66Å
ATOM & NUCLEI Rutherford -particle scattering Exp: Exp. Setup: OBSERVATIONS: (i) Most of the α-particle passed underiated. (ii) Few α-particle scattered at angle θ N ∝ 1 sin 4 ( θ 2 ) (iii) Very few retraces their path. RUTHERFORD’S MODEL OF ATOM: (1909) i) Most of the part of atom is hollow. ii) The central core is (+) very charged called nucleus (10-15m) e − revolves around the nucleus & radius of orbit decreases due to decrease in energy (dement). Distance of closest approach: 1 2 mv 2 = 1 4πεo (2e)(ze) r0 ∴ r0 = 2ze2 4πεo ( 1 2 mv2) Impact parameter: It is perpendicular distance of the velocity vector when α−particle from centre of nucleus when α particle is far away from atom. b = 1 4πεo 2ze2 mv2 cot θ 2 smaller is b’ larger is angle of scattering θ cot θ 2 = 2b r0 for θ = 180∘ (rebounds) b = 0 BOHR’S MODEL: (1913) 1. The e − can exist in certain orbit without radiating energy. mv2 r = 1 4πεo ze2 r 2 2. Only those orbit are allowed for which the angular momentum (mvr) is integral multiple of h/2π. mvr = nh 2π n = 1, 2, 3…. Quantum No. 3. Electrons Reboring in their stationary orbit do not radiate energy (non-radiative orbits or BOHR’S orbits) 4. If the e– goes from orbit of energy E1 to other orbit of energy E2 then a photon of energy hv is radiated such that hv = E2– E1 Radius of Bohr orbit: = 2 2 o n 2 n h r me z for hydrogen z = 1 ENERGY OF BOHR ORBITS:- E = KE + PE = 1 2 mv 2 + ze(−e) 4πεor = 1 2 ze 2 4πεor − ze2 4πεor ( mv2 r = 1 4πεo 2e 2 r ) En = −Ze 2 8πεorn For H Atom En = −e 2 8πεorn = −13.6 n 2 eV HYDROGEN SPECTRUM:- Hydrogen spectrum consist of group of radiation emitted by a h-atom whose wavelength is given as –1 2 Rydberg constant 2 2 R 1.09 107. m 1 2 1 1 1 Rz – n n = = En = −e 2 8πεorn Lyman Series: Electron jump from higher orbit to first orbit. n L, n 2,3, 4........ = = 2 1 2 2 1 2 2 2 2 1 2 1 1 3 v R, – R n n 4 Ultra Voilet Region 1 1 8 v R – R n n 9 = = = = BALMER: Visible Region Paschen, Brackett, P Fund :- Far Infrared
Nucleons = Protons + Neutrons A = Z + N. Mass = Atomic + No. of No. Neutrons. Nuclear force • strong • short range • spin dependent • charge independent Nuclear volume ∝ Mass No. 4 3 πR 3 ∝ A OR R = ROA 1/3 R0 = 1.4 × 10−15 m 1 Fermi = 10−15 m. 1 amu = 1 12( 6 12C) = 1.66 × 10−22 kg Electron volt (ev) – unit of energy 1 eV = 1.6 × 10−19 J. 1 amu = 931MeV NUCLEAR DENSITY: 1017 kg/m3 Independent of mass no. and same For all elements e = m ⋅ A 4/3πR0 3A = 3m 4πR0 3 Isotopes: Same protons (Z) but different(A) Ex ∶ 1H 1 , 1H 2 , 1H 3 ; 2H 3 , 2H 4 , 2H 6 No. of Neutron. Isobars: Same (A) but different (2) Ex ∶ 11Na22; 10Ne22; 20Ca40; 18Ar40 Isotones: Same no. of neutrons. Ex: 1H 3 ; 2He4 ; 8O 16; 6C 14 Mass Energy Relation: E = Δmc 2 Energy & mass are interconvertible. Mass Defect: Difference in masses. of nucleons & nucleus. Δm = [ZMp + (A − Z)Mn] −[mass of ZX A nucleus] Binding, Energy: Energy equivalent. to mass defect. B. E.= ΔM ⋅ C 2 Packing Fraction: B.E per nucleon. P. F = B ⋅ E/A Variation in B.E/Nucleon with mass no. 1. B. E/A is very less for A = 8 and then increases up to A = 60∘ 2. Decreases after A = 120∘ 3. Maximum 10.8mev for Range A = 30∘ to A = 120∘ 4. Peak for 2He4 , 6C 12 , 8O 16 etc indicate more stability 5. More is B. E/A, more is stability of a nucleus. NUCLEAR FISSION: Splitting of heavy nucleus. 92U 255 + 0n 1 → 56BC141 + 36Kr92 + 3 0n 1 + θ(200Mev) NUCLEAR FUSSION: Fusing two or more lighter nuclei. 1H 1 + 1H 1 → 1H 2 + e + + v RADLOACTIVITY: Spontaneous emission of radiation (α, β, γ) from radioactive nuclei. Laws of Radioactive Decay: 1. Spontaneous. 2. Rate of dis integration is directly proportional to no. of atom at that time. 3. Independent of temperature, pressure etc. 4. α− β not emitted simultaneous N = N0e −λt Half life: T1/2 = 0.693 λ = loge 2 λ N = N0 ( 1 2 ) t T1 2 t = total time Average life = 1 λ = 1.44T1/2 Charge = Mass = Infield = Speed = α( 2He4 ) 2 × 1.6 × 10−19C 4 × 1.67 × 10−27 kg Deflected by electric Or Mag. Field Less than β β (electron) −1.6 × 10−19C 9.1 × 10−31 kg Less than γ γ (photon) 0 Rest mass 0 No effect Speed of Light Unit of Radioactivity • Curie () − 3.7 × 1010 decay /sec (activity of 1g radiurn). • Becquerel () − 1 decay/sec (S.I. unit of radioactivity) • Rutherford ()− 106Decay/sec.
ELECTRONIC DEVICES Intrinsic semiconductor: Pure semiconductors: Extrinsic semiconductor: (Impure semiconductor) P-Type: (Acceptor type) trivalant (B, Al, In, Ga) Majority carrier holes N-Type: (Donor Type) Pentavalent (Bi, P, Ar, Sb) Majority carrier electrons. Doping: Mixing suitable impurity in Ai, Ga. NET CHARGE ON PURE OR IMPURE SEMICONDUCTOR IS 0 ZERO. PN Junction: • Depletion layer: Layer near- junction having no free charge (10−6 m) • Width of Depletion layer decreases with F.B. and Vice Versa • Potential Barrier: Potential Developed across junction. Rectifiers: conversion of a.c into d.c Principle: Diode conduct in RB and do not conduct in P.B. Zener: Diode Used in reverse biased as voltage stabilize Amplifier: (CE Mode) Voltage Gain: = v0 vi = β RL Rin Current Gain = Ic/Rb Principle: Small change in input current in result in large change in O/PIC ∗ LED Light emitting Diode : used in FB light produced due to e− h combination. ∗ PHOTODIODE RB. e− h pairs generated due to incident photon hv > Eg. ∗ SOLAR CELL convert solar energy into electrical energy properties → [Eg ≈ 1.5ev. high optical absortion electrical conductivity Transistor Action: ie = ib + ic ib = 5% of ie Base region is very thin and regulates of O/p current Logic Gates: Electronic devices which give one O/P for one or more I/P Basic logic Gate: AND, OR, NOT UNIVERSAL GATE: NAND, NOR OR AND NOT NAND NOR Symbol Truth Table A B 0 0 0 1 1 0 1 1 A + B 0 1 1 1 A . B 0 0 0 1 A̅ 1 0 A̅. B̅ 1 1 1 0 A̅ +B̅ 1 0 0 0 Reverse current induce to minority charge carriers µA