KENDRIYA VIDYALAYA SANGATHAN CHENNAI REGION MINIMUM LEVEL OF LEARNING(MLL)

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1 KENDRIYA VIDYALAYA SANGATHAN CHENNAI REGION MINIMUM LEVEL OF LEARNING(MLL) XII PHYSICS (VOLUME-1) INDEX T.MURALI PGT (PHYSICS) KENDRIYA VIDYALAYA, DGQA CHENNAI-114 S.NO UNIT PAGE 1 ELECTROSTATICS CURRENT ELECTRICITY MAGNETIC EFFECTS OF CURRENT AND MAGNETISM ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS ELECTRO MAGNETIC WAVES 18-19

2 - VERY IMPOTANT UNIT-I ELECTROSTATICS 1. Electrostatics is the study of charges at rest. 2. Charges are quantized. i.e., Q= ± ne [n=1,2,3, & e=1.602 X10-19 C] 3. Coulomb s law: the force between two charges is directly proportional to their product and inversely proportional to the square of the distance between them F = kq 1q 2 r r 2 k= 1 = 9 x 10 9 Nm 2 C -2 4πε 0 ε 0 = absolute permittivity of free space. ε 0 = x N -1 m -2 C 2 Q 1Q 2<0 1/r 2 Q 1Q 2>0 5.Uniform Charge distribution: F o Linear charge density λ = q l o Surface charge density σ = q S o Volume charge density ρ = q V 6. Electric field: Force experienced by a unit positive charge. It is a vector. SI unit is NC -1. E = F q 7. Dipole: Two equal and opposite charges separated by a small distance. 8. Dipole moment: Product of magnitude of either charge and distance of separation between them. It is a vector. SI unit: Coulomb-metre, p = (Q) 2a ; direction of p is from negative charge to positive charge. 9. DERIVATION IMPORTANT: τ =p E τ =pe sin θ n - Dipole in a uniform electric field experiences no net translatory force. -Ifθ= 0 stable equilibrium; Ifθ= 180 unstable equilibrium. 10. Electric field due to a short dipole o (DERIVATION IMPORTANT) at a point on the axial line : E axial = 2kp r3 along the direction of dipole moment Page 1 of 19

3 o (DERIVATION IMPORTANT) At a point on the equatorial line: E eq = kp r3opposite to the direction of dipole moment. 11. Electric flux: It is defined as the number of field lines crossing the surface normally. = S. E =E ( S)cosθ ; It is a scalar; SI unit: N m 2 C Gauss theorem in electrostatics: It states that total electric flux passing through an enclosed surface is numerically equal to 1 / ε 0 times the net charge enclosed.. total = = q total ε APPLICATIONS OF GAUSS THEOREM: - Electric field due to infinitely long line charge (DERIVATION IMPORTANT) - Electric field due to infinite plane sheet of charge (DERIVATION IMPORTANT) - Electric field due to spherical surface of charge (DERIVATION IMPORTANT) - The graph showing the variation of electric potential with distance from the Centre of a uniformly charged shell. V r Distance 14. Electrostatic Potential: Work done to bring a unit positive from infinity to a particular point in an electric field. It is a scalar. SI unit: J/C or V V = W / q o Electric potential for a point charge: 15. As E= - dv dr If V is constant, E 1 r V = kq r and if E is constant, V r 16. Potential due to a dipole at a point (DERIVATION IMPORTANT) o on its axial line: V axial = k p o on its equatorial line: V eq = 0 k p [or] r2 r 2 cosθ Page 2 of 19

4 17. Equipotential surfaces: The surfaces on which the potential is same everywhere. Work done in moving a charge over an equipotential surface is zero. No two equipotential surfaces intersect. Electric field lines are always perpendicular to the equipotential surfaces. 18. Electrostatics of conductors (i) Inside a conductor Electrostatic field is zero (ii) On the surface E is always Normal to the surface (iii) No excess charge resides inside the conductor (iv) Charge distribution on the surface is uniform if the surface is smooth (v) Electric field is zero in the cavity of hollow conductor and potential remains constant which is equal to that on the surface. 19. Capacitor: An arrangement of two conductors separated by a small distance without any electrical contact between them is called capacitor. Q - Capacitance: C, Ratio of charge and potential difference. Scalar. SI unit: farad [F]. - V Capacitance of a parallel plate capacitor: C = ε 0 A d (DERIVATION IMPORTANT) - Capacitance of a parallel plate capacitor with a dielectric medium in-between: C m = k C Energy stored in capacitor: Q U CV QV C (DERIVATION IMPORTANT) Page 3 of 19

5 UNIT-II CURRENT ELECTRICITY 1. The rate of flow of charge through the conductor is called electric current. I = Q/t. SI Unit: Ampere (A). 2. Current density J = I/A. 3. Ohm s law: The electric current passing through a conductor is directly proportional to the potential difference at constant temperature. V α I V = IR Where R is the resistance of the conductor. 4. Resistance R = ρl/a where ρ is the resistivity of the conductor. 5. Resistivity is the characteristic property of the material which is the resistance of the conductor of unit length and unit area of cross section. It does not depend on dimension of the material. 6. Resistivity ρ = m/ne 2 τ, Where m, n, e are mass, number density and charge of electron respectively, τ-relaxation time. (DERIVATION IMPORTANT) - Relaxation time is the average time interval between two successive collisions - Conductance of the material G =1/R and conductivity σ=1/ρ 7. Drift velocity is the average velocity of all electrons in the conductor which drift in opposite direction to the applied electric field. Drift velocity V d = (ee/m) τ Also, I = neav d 8. Mobility (μ) of a charge carrier is the ratio of its drift velocity to the applied electric field V d E 9. Effect of temperature on resistivity: Metals: ρ = 1 = m σ ne 2 τ When temperature increases, the no. of collisions increases due to more internal energy and relaxation time decreases. Therefore, Resistivity increases Semiconductors: Unlike metals, the resistivity of semiconductor decreases with increase in temperature exponentially Alloys : Alloys exhibit very weak dependence of resistivity with temperature due to negligibly small value of temperature coefficient of resistivity. Due to this reason, alloy wires are used for standard resistance. Ex Manganin and constantan Combination of resistors: Rseries R1 R2... Rn,... RParallel R1 R2 Rn 11. Colour coding : Black Brown Red Orange Yellow Green Blue Violet Gray White Tolerance (i) Gold 5% (ii) Silver 10% (iii) No Color 20% Page 4 of 19

6 Example: if colour code of carbon resistor is Red Yellow and Orange with tolerance colour as silver, the resistance of the given resistor is ( ± 10%) Ω. 12. Electrical energy: The total work done by the source in maintaining the current in an electrical circuit for a given time. Electrical energy = VIt = I 2 Rt =(V 2 /R)t = Pt Electrical power: The energy dissipated per unit time is known as power. P = W = VI = t I2 R = V2 R 13. Cells: - E.M.F (E) of a cell is defined as the potential difference between its terminals in an open circuit. -Terminal potential difference (V) of a cell is defined as the potential difference between its ends in a closed circuit. - Internal resistance r of a cell is defined as the opposition offered by the cell to the flow of current. r = E V R Grouping of cells : 1 where R is external resistances. ne i) In series grouping circuit, current is given by I s, R nr me ii) In parallel grouping circuit, current is given by I p r mr Where n, m - number of cells in series and parallel connection respectively. 14. Kirchhoff s Rule: i) Junction Rule:-The algebraic sum of currents at a junction in a network is zero. I 0 ii) Loop rule:-the algebraic sum of potential differences and emfs of a closed loop in a network is zero V o 15. Wheatstone bridge is an arrangement of four resistors arranged in four arms of the bridge and is used to determine the unknown resistance in terms of other three resistances. For balanced Wheatstone bridge, P R Q S -Wheatstone bridge is most sensitive when the resistance in the four arms is of the same order - In the balanced condition of the bridge, interchanging of galvanometer and battery makes no effect on the balancing length because condition remains same. Page 5 of 19

7 16. The principle of Metre Bridge: P R Q - Slide Wire Bridge or Metre Bridge to measure unknown resistance. S P l Q 100 l P Q = l 100 l = R S S = ( 100 l ) R l 17. Potentiometer is considered as an ideal voltmeter of infinite resistance. -Principle of potentiometer: The potential drop across any portion of the wire of uniform cross section is proportional to the length of that portion provided steady current is maintained in it i.e. v α l - Smaller the potential gradient greater will be the sensitivity of potentiometer. - Same side deflection due to (i) wrong circuiting (ii) Strength of the driver battery is less than the primary cell. -To compare the e.m.f.s of two cells: Page 6 of 19

8 - To determine the internal resistance of a cell: Page 7 of 19

9 UNIT-III MAGNETIC EFFECTS OF CURRENT AND MAGNETISM 1. Magnetic field: The region around a magnet or current carrying conductor with in which it influences other magnets or magnetic material. SI unit of magnetic field intensity is Tesla (T). 2. Biot-Savart Law: It states that magnetic field strength is directly proportional to current, length of current element, sine of angle and inversely proportional to square of the distance Idlsinθ db = μ 0 4π r 2 where μ 0 =4π x 10-7 Tm/A. 3. Applications: -Magnetic field at the centre of a current carrying circular coil B= μ 0 I/2r. Magnetic field due to a small element, db = μ 0 Idlsinθ 4π r 2 since, θ = 90 sinθ = 1 db = μ 0 Idl 4π r 2 Total magmetic field, B = db = μ 0 4π B = μ 0I 2r -Magnetic field at a point on the axis of current carrying coil I r 2 dl Magnetic field due to a small element, db = μ 0 Idlsinθ 4π r 2 since, θ = 90 sinθ = 1 db = μ 0 4π Idl r equ 1 Page 8 of 19

10 Resolve db into dbsin and dbcos. Net value of dbcos is zero and effective component is dbsin. Total magnetic field,b = dbsin = μ 0 I sin dl = μ 0 I sin 2πa 4π r 2 4π r2 From the diagram, r 2 = (a 2 +x 2 ), sin = a r B = μ 0 4π I a 2πa ; B = μ 0Ia 2 r 2 r -In case of N-turns, B = μ 0NIa (a 2 +x 2 ) 3 2 ; If x = 0, then, B = μ 0I 2(a 2 +x 2 ) 3 2 2a 5. Ampere s circuital law: It states that the line integral of magnetic field around any closed path is μ 0 times the total current threading the loop. B. dl = μ o I. Applications: - Magnetic field due to straight infinitely long current carrying straight conductor. B= μ 0 I/2πr. (DERIVATION IMPORTANT) -Magnetic field due to a straight solenoid carrying current B= μ 0 n I. n= no. of turns per unit length. (DERIVATION IMPORTANT) -Magnetic field due to toroidal solenoid carrying current. B= μ 0 N I / 2πr. N= Total no. of turns. (DERIVATION IMPORTANT) 6.Force on a moving charge [Lorentz Force]: -In magnetic field magnetic Lorentz force ; F = q(v X B ). The direction of Force is given by Fleming s left hand rule. -In magnetic and electric field Lorentz force; F = q[e + (ν x B )] - F=qvBSinθ = Bqv when θ = 90 - Radius of the path followed by the moving charge in th magnetic field r = mvsinθ qb = mv qb when θ = 90 Page 9 of 19

11 7.Cyclotron: The device which is used to accelerate the charged particles based on the principle of Lorentz force is called Cyclotron. -Principle: The charged particle accelerates in uniform electric field and follows circular path in uniform magnetic field. -An ion can acquire sufficiently large energy with a low ac voltage making it to cross the same electric field repeatedly under a strong magnetic field. -Consist of two D-shaped metallic champers connected with a HF oscillator kept in a strong magnetic field acting perpendicular and inwards as shown. - Resonance condition- Rate of polarity change is equal to rate of completion of semicircular path of charged particle. - Cyclotron cannot accelerate neutral particle like neutron. 8.Force on a current carrying conductor - in uniform magnetic field, F = (I l x B ). l=length of conductor. - Direction of force can be found out using Fleming s left hand rule. - Force per unit length between parallel infinitely long current carrying straight conductors.f/l = μ o I 1 I 2 /2πd(DERIVATION IMPORTANT). - If currents are in same direction the wires will attract each other. If currents are in opposite directions they will repel each other. Page 10 of 19

12 - One Ampere: The electric current flowing through a conductor is said to be one ampere when it is separated by one metre from similar conductor carrying same amount of current in the same direction experiences a repulsive force of 2x10-7 N per metre length. - Torque experienced by a current loop in a uniform B, τ = NIBASinθ. τ = M XB Where M is the magnetic dipole moment =NIA. Its unit is Am 2 9.Moving coil galvanometer: It is a sensitive instrument used for detecting small electric currents. - Principle: A current carrying coil placed in a magnetic field experiences torque. Deflection torque = Restoring torque NIABsinθ = K equ 1 Where A-Area of the coil, N-Number of turns, K-Torsion constant, steady angular deflection Where θ- Angle made by normal to the coil with the magnetic field. In radial magnetic field, angle made by normal to the coil with magnetic field is 90 and hence sinθ= 1 Equ 1 becomes NIAB = K = NAB K I = GI whereg Galvanometer constant α I - Current sensitivity, I s= / I=NBA/K - Voltage sensitivity, Vs= /V=NBA/KR - Increasing the current sensitivity may not necessarily increase the voltage sensitivity. If N 2N then = 2 thus, current sensitivity doubles. But, N 2N makes I I corresponding change in R 2R and due to which the voltage sensitivity remains unchanged.( V = V ) Page 11 of 19

13 - Conversion of galvanometer into ammeter: A small resistance r S is connected in parallel to the galvanometer coil. r S =I g G/( I - I g) ; R A =GS/(G+r S ) - Conversion of galvanometer into a voltmeter: A high resistance R is connected in series with the galvanometer coil. R= ( V/I g ) G ; R v =G+R evr 10. Magnetic dipole moment of a atomic magnet M =. (DERIVATION IMPORTANT) Gauss s law in magnetism: φ B = B. ds = Elements of earth s magnetic field: Magnetic declination (θ); Dip (δ) (Dip is 90 at pole and 0 at equator); Horizontal component of earth s magnetic field (B H ). B H = B cos δ ; B V = B sin δ. 13. Clasification of magnetic materials: Some important terms: a. Magnetic flux density, B o = µ o / A b. Magnetizing field intensity, H = B o / µ o c. Intensity of magnetization, I = m/v (magnetic dipole moment per unit volume) - The relation among these three physical quantities is B = µ o (H + I) d. Magnetic permeability, µ = B/H; SI unit wb/m/a e. Magnetic susceptibility, χ m = I H ; It is a dimensionless physical quantity. - Relation between relative permeability and magnetic susceptibility is μ r = 1 + χ m. Page 12 of 19

14 Properties of magnetic substances DIA PARA FERRO 1. Feebly repelled by a magnet. Eg. Antimony, Bismuth, Copper, Gold, Silver, Feebly attracted by a magnet. Eg.Aluminium,Chromium, Platinum, Oxygen, etc. Strongly attracted by a magnet. Eg. Iron, Cobalt, Nickel, 2. When placed in magneticfield, When placed in magnetic field The lines of force tend to crowd into the specimen. 3. When placed in nonuniform magnetic field, it moves from stronger to weaker field (feeble repulsion). When placed in nonuniform magnetic field, it moves from weaker to stronger field (feeble attraction). When placed in non-uniform magnetic field, it moves from weaker to stronger field (strong attraction). - The magnetic flux density remained in the ferromagnetic substance even after removing the magnetizing field intensity is called Retentivity. - The magnetizing field intensity required to reduce the residual magnetism in ferromagnetic substance to zero is called coercivity. Page 13 of 19

15 UNIT-IV ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS 1. The phenomenon of production of induced emf in a coil/circuit when electric flux linked with those changes is called electromagnetic induction. - Magnetic flux through a surface of area A placed in a uniform magnetic field B is defined as Φ B = B. A = BA Cosθ where θ is the angle between B and A. - Magnetic flux is a scalar quantity and its SI unit is Weber (Wb). 2. Faraday s laws of induction: First Law: Whenever the magnetic flux linked with the circuit/coil changes, induced emf produces across it. Second Law: The magnitude of the induced e.m.f in a circuit is equal to the rate of change of magnitude flux linked with that circuit. ε= d B = 2 1 dt t 3. Lenz law: The direction of induced current or the polarity of the induced e.m.f is in such a way that it opposes the cause that produces it. (The negative sign in Faraday s law indicates this fact.)ε= d B. Lenz law obeys the principle of energy conservation. dt 4. The induced current in a closed loop can be produced by changing the (i) magnitude of B (ii) area A of the loop (iii) its orientation in magnetic field. - The direction of induced current is obtained from Fleming s right hand rule. 5. When a metal rod of length l is placed normal to a uniform magnetic field B and moved with a velocity v perpendicular to the field, the induced e.m.f is called motional e.m.f. It produces across the ends of the rod. ε = Blv. If R is the resistance of the metal rod, the induced current is given by I=Blv/R, the force acting on the conductor in the presence of magnetic field (due to drift of charge) is given by F =B 2 l 2 v / R. The power required to move the conductor with a constant speed is given by P= B 2 l 2 v 2 /R. 6. The induced currents produced on the surface of bulk pieces of conductors when magnetic flux linked with that changes are called eddy currents. 7. The phenomenon of production of induced emf in a coil itself when electric current passing through that changes is called self induction. Self Inductance is the ratio of the flux linked to current. L = φ. Its unit is Henry(H) I 8. The changing current in a coil can induce an e.m.f in a nearby coil. Induced emf, ε = M 12 di 2 dt, shows that Mutual inductance of coil 1 with respect to coil 2 (M 12) due to changing current in coil 2. (M 12 =M 21 ). 9. The self-inductance of a long solenoid is given by L = µ 0 n 2 Al A - the area of cross-section of the solenoid, Page 14 of 19

16 l - Its length and n - the number of turns per unit length. numeral of turns =nl Total area = nal Magnetic field in a solenoid = μ 0 ni Magnetic flux linked, = B x Total area = μ 0 n 2 IAl Also, = LI From 1 & 2, L = μ 0 n 2 Al 10. The mutual inductance of two co-axial coils/solinoids is given by M 12 = M 21 = µ 0 n 1 n 2 Al n 1 & n 2 - number of turns per unit length of coils 1 & 2. A - Area of cross-section of inner solenoid and l is the length of the solenoids. I 1 -Current through the solenoid S 1 Magnetic flux linked with S 2, 21 α I 1 : 21 = M 21 I Magnetic field in S 1, B 1 = μ 0 n 1 I 1 Magnetic flux linked with each turn of S 2 =B 1 A Total magnetic field linked with S 2, 21 = B 1 A n 2 l = μ 0 n 1 n 2 I 1 Al From equ 1&2, M 21 = μ 0 n 1 n 2 Al Similarly, we can derive that, M 12 = μ 0 n 1 n 2 Al From equ 3&4, M = μ 0 n 1 n 2 Al Alternating current(ac) 11.The electric current whose magnitude changes continuously and direction changes periodically is called alternating current (AC). I = I o Sin ωt. 12. I rms = I 0 / 2 = 0.707I 0. Similarly, v rms = v 0 / 2 = 0.707v The opposition offered by resistor is called resistance (R). The non-resistive opposition offered by a device (Capacitor or Inductor) is called reactance (X). Capacitive reactancex c = 1 = 1 & Inductive reactancex ωc 2πfC L = ωl = 2πfL. The combined effect of reactance and resistance is called impedance (Z). 14.Average power loss over a complete cycle in an circuit is P = V rms I rms Cosφ Instantaneous voltage, v = v 0 sinωt Instantaneous current,i = I 0 sin(ωt + φ) Page 15 of 19

17 Instantaneous Power, P= vi =v 0 sinωt I 0 sin(ωt + φ) We can derive that P = V 0I 0 [cosφ cos(2ωt + φ)] We can prove that, cos(2ωt + φ) = 0 Equ 1 becomes, P = V 0I 0 2 I 0 cosφ = V 0 cosφ 2 2 P = V rms I rms cosφ - In a purely resistive circuit φ = 0; P = V rms I rms. - In a purely inductive circuit φ = π/2; P = 0. - In a purely capacitive circuit φ = π/2; P = The electric current in an AC circuit is said to be wattless current when average power dissipated or consumed is zero. 16. LCR resonance circuit: The following are the conditions, a) X C =X L b) V C =V L c) Z=R d) I=Maximum 1 Resonance frequency, f = 17.Graphs: 2π LC 18.AC generator: A device which converts mechanical energy into electrical energy Principle- electromagnetic induction.. Page 16 of 19

18 Magnetic flux, φ= NBACosωt Rotation of rectangular coil in a magnetic field causes change in flux. Change in flux induces e.m.f in the coil. Induced emf, ε= -dφ/dt = NBAωSinωt ε = ε 0 Sinωt Where ε 0 = NBAω -Peak value of emf Current induced, I = ε/r = ε 0 Sinωt/R. I = I 0 Sinωt 19.Transformer: A device which changes an AC voltage of one value to another of greater or smaller value is called transformer. Principle: Mutual Induction. N p & N s -Number of turns in primary and secondary coils. φ p &φ s Magnetic flux linked with primary and secondary coils If N S >N P step up. If N P >N S step down. We know that, φ p N p and φ s N s φ s = N s φ p N p Differentiate equ 1 w.r.to time, dφ s dt = (N s ) dφ p N p dt φ s = N s N p φ p 1 e s = ( N s N p ) e p For an ideal transformer, Input Power = Output Power ie, e p I p = e s I s e s e p = I p I s = N s N p e s e p = N s N p -Need for lamination- To reduce heat energy produced by eddy current. - Losses in transformer: Copper loss, Iron loss, Flux loss, Hysteresis loss, Humming loss. - Transformer cannot be used to alter the value of DC due the reason that DC cannot produce change in magnetic flux to generate induced emf. Page 17 of 19

19 UNIT-V ELECTRO MAGNETIC WAVES 1. Conduction current and displacement current together have the property of continuity. Conduction current & displacement current are precisely the same. 2. Conduction current arises due to flow of electrons in the conductor. Displacement current arises due to electric flux changing with time. Displacement current: I D = ε 0 d E dt -To prove I C = I D In case of capacitor, E = q Aε 0 φ E = EA = q Aε 0 A = q ε 0 dφ E dt = 1 ε 0 dq dt dq = ε dφ E dt 0 dt I C = I D 3. Maxwell s equations: Gauss s Law in Electrostatics: E. ds = Q ε 0 Gauss s Law in Magnetism: B. ds = 0 Faraday s law of electromagnetic induction,e = dφ B dt dφ Ampere s Maxwell law: B. dl = 0 I + E 0 0 dt 4 Electromagnetic Wave:-The electromagnetic wave consists of sinusoidal time varying electric and magnetic fields acting at right angle to each other as well as at right angle to the direction of propagation of wave. 5. Properties of electromagnetic waves: -E M Waves are transverse in nature. -They are produced by oscillating or accelerating charged particles. -They do not require any medium for their propagation. -They obey principle of superposition. -They show polarization effect. Page 18 of 19

20 - Electric field is only responsible for optical effects of EM waves. -The amplitude of electric & magnetic fields are related by E B = c -In free space they travel with the speed c = 1 ε o μ o. -The energy of EM Wave is equally divided between electric and magnetic field vectors. -EM waves also carry energy, momentum and information. 6. Electromagnetic Spectrum: The orderly arrangement of electromagnetic radiation according to its frequency or wavelength is called electromagnetic spectrum. ELECTRO MAGNETIC SPECTRUM, ITS PRODUCTION, DETECTION AND USES IN GENERAL Type Radio Wave length Range/ Frequency Range >0.1m 10 9 to 10 5 Hz Uses Radio, TV Communication Microwave Infrared Light Ultraviolet X-rays 0.1mm to10 9 Hz 1mm to 700nm to10 14 Hz 700nm to 400nm 8x10 14 Hz 400nm to 1nm 5x10 14 to 8x nm to 10-3 nm to Hz Radar, TV communication Green House effect, looking through haze, fog and mist, Ariel mapping. Photography, Illuminations, Emit & reflect by the objects. Preservation of food items, Detection of invisible writing, finger print in forensic laboratory. Determination of Structure of molecules & atoms. Study of crystal structure & atom, fracture of bones. Gamma ray <10-3 nm to Hz Nuclear reaction & structure of atoms & Nuclei. To destroy cancer cells. Page 19 of 19