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 Physics Short Notes CHAPTER 1: UNIT AND MEASUREMENT  Fundamental Units : Sr. No. Physical Quantity SI Unit Symbol 1 Leng...

 Physics Short Notes CHAPTER 1: UNIT AND MEASUREMENT  Fundamental Units : Sr. No. Physical Quantity SI Unit Symbol 1 Length Metre m 2 Mass Kilogram Kg 3 Time Second S 4 Electric Current Ampere A 5 Temperature Kelvin K 6 Luminous Intensity Candela Cd 7 Amount of Substance Mole mol  Supplementary Units : B Sr. No. Physical Quantity SI Unit Symbol 1. Plane Angle Radian r 2 Solid Angle Steradian Sr (1). Distance of an object by parallax method, D  U Basis Parallax angle PH (2). Absolute error = True value – Measured value  [ an ] (3). True value = Arithmetic mean of the measured values a1  a2 ....  an amean  EX n amean (4). Relative error in the measurement of a quantity  amean amean (5). Percentage error   100 amean (6). Maximum permissible error in addition or subtraction of two quantities (A  A) and (B  B) :  A  B ap  bq z a b C (7). When z  , then maximum relative in z is p q r r z a b C c 2  Physics Short Notes CHAPTER 2: MOTION IN A STRAIGHT LINE (1). For objects in uniformly accelerated rectilinear motion, the five quantities, displacement x, time taken t, initial velocity v 0 , final velocity v and acceleration a are related by a set of kinematic equations of motions. These are v  v 0  at 1 x  v 0t  at2 2 v 2  v 02  2ax B The above equations are the equations of motion for particle. If the position of the particle at t = 0 is 0. If the particle starts at x  x0 i.e. if it is at x 0 at t = 0, then in the above equation x is replaced by (x  x0 ). U (2). The relative velocity of an object moving with velocity v A w.r.t. an object B moving with velocity vB PH is given by v AB  v A  vB EX CHAPTER 3: MOTION IN A PLANE if  P  Q then R  P2  Q2  2PQ cos  (1). Law of cosines, R Here,   angle between P and Q Q cos  (2). Direction of R  tan   :   angle between R and P P  Q sin  (3). Position of an object at time t, if it is initially at r0 , having initial velocity v0 and moving with constant acceleration a , is 3  Physics Short Notes 1 r  r0  v 0t  a2 2 CHAPTER 4. LAWS OF MOTION dp dv dm dv (1). Force: F  m v , when m is constant F  m  ma dt dt dt dt B (2). Conservation of linear momentum:  pi   p j U (3). For motion of a car on level road maximum safest velocity is v max  sRg  (s  tan )  PH (4). For motion of a car on banked road maximum safest velocity is v max  Rg   1  s tan   1 v2 Angle of banking:   tan rg EX CHAPTER 5. WORK ENERGY AND POWER (1). The work-energy theorem states that for conservative forces acting on the body, the change in kinetic energy of a body equal to the net work done by the net force on the body. K f  Ki  Wnet Where Ki and Kf are initial and final kinetic energies and Wnet is the net work done. 4  Physics Short Notes (2). For a conservative force in one dimension, Potential energy function V(x) is defined such that dV(x) F(x)   dx (3). Average power of a force is defined as the ratio of the work, W, to the total time t taken. W  Pav  t (4). The instantaneous power is defined as the limiting value of the average power as time interval dW approaches zero. P  dt Power can also be expressed as B dr P  F  Fv here, dr is displacement vector. dt (5). Work done by Constant Force : W  FS U PH (6). Work done by multiple forces  F  F1  F2  F3 ..... W  [F]  S …i W  F1  S  F2  S  F3  S ........ EX Or W  W1  W2  W3 ..... (7). Work done by A variable force dW  F  ds (8). Relation between momentum and kinetic energy P2 K and P  2 m K ; P  Linear momentum 2m (9). Potential energy U2 r2 r2  dU    F  dr i.e., U2  U1   F  dr  W U1 r1 r1 r U    F  dr  W  5  Physics Short Notes (10). Conservative Forces U F r (11). Work-Energy theorem WC  WNC  WPS  K (12). Modified Form of work-Energy Theorem WC  U WNC  WPS  K  U WNC  WPS  E B (12). Power W The average power (P or Pav ) delivered by an agent is given by P or pav  P F  dS dt F dS dt  Fv U t PH EX CHAPTER 6. SYSTEM OF PARTICLES AND ROTATIONAL MOTION (1). According to the theorem of perpendicular axes moment of inertia of a body about perpendicular axis is Iz  Ix  I y' Where Ix ,I y ,Iz , are the moment of inertia of the rigid body about x, y and z axes respectively x and y axes lie in the plane of the body and z-axis lies perpendicular to the plane of the body and passes through the point of intersection of x and y. (2). According to the theorem of parallel axes I  IC  Mdc Where IC is the moment of inertia of the body about an axis passing through its centre of mass and d is the perpendicular distance between the two axes. Table 1: Moment of inertia of some symmetrical bodies 6  Physics Short Notes Body Axis Figure M.I. (1) Rod (Length L) Perpendicular to rod, at the ML2 midpoint centre of mass 12 (2) Circular ring (radius R) Passing through centre and MR2 perpendicular the plane (3) Circular ring (Radius Diameter MR 2 R) 2 B (4) Circular Disc (radius R) Perpendicular to the disc at MR 2 centre 2 U PH (5) Circular Disc (radius R) Diameter MR 2 4 (6) Hollow cylinder Axis of cylinder MR2 EX (radius R) (7) Solid cylinder (radius Axis of cylinder MR 2 R) 2 (8) Solid sphere (radius R) Diameter 2 MR 2 5 7  Physics Short Notes (9) Hollow sphere (radius Diameter 2 R) MR 2 3 (3). Relation between moment of inertia (I) and angular momentum L is given by L  l  (4). Relation between moment of inertia (I) and kinetic energy of rotation is given by 1 K.E.rotation  l2 2 (5). Relation between of inertia (l) and torque ( )    l B (6). If no external torque acts on the system, the total angular momentum of the system remains unchanged l11  l22 U (7). Position vector of centre of mass of a discrete particle system PH n m1 r1  m2 r2 ......  mn rn  mi ri i1 rCM   m1  m2 ......  mn n  mi i1 Where mi is the mass of the ith particle and r1 is the position of the ith particle corresponding EX xCM  y CM and z CM co-ordinates are n n n  mn i i  mi y i  mizi l1 i1 i1 xCM  n , y CM  n , z CM  n  mi  mi  mi i1 i1 i1 n  miv i (8). Velocity of centre of mass, v CM  i1  mi n  miai (9). Acceleration of CM, aCM  i1 n  mi i1 8  Physics Short Notes n  (10). Momentum of system, P  P1  P2 .....  Pn    mi  v CM  i1    (11). Centre of mass of continuous mass distribution rCM   dmre , xCM   x dm , y CM   y dm , z CM   zdm dm  dm  dm  dm (12). Given below are the positions of centre of mass of some commonly used objects. B S.No. Object Location of centre of mass i. L x CM  , y  0 , zCM  0 U 2 CM PH ii. 2R xCM  0 , y CM  , zCM  0  EX iii. 4R xCM  0 , y CM  ,z 0 3 CM iv. 2R 2R xCM  , y CM  , zCM  0   9  Physics Short Notes v. 4R 4R xCM  , y CM  ,z 0 3 3 CM vi. R xCM  0 , y CM  ,z 0 2 CM vii. B 3R xCM  0 , y CM  , zCM  0 8 U PH (13). Head-on collision EX Velocity of bodies m1 ,m2 after collision are  m  em2  m2 (1  e)  m  em1  m1 (1  e) v1   1  u1  u2 ; v 2   2  u2  u  m1  m2  m1  m2  m1  m2  m1  m2 1 Here e is coefficient of restitution. 1 m1m2 Loss in kinetic energy, KE  (u  u2 )2 (1  e2 ) 2 m1  m2 1 (14). For elastic collision KE  0 and e = 1, then velocities after collision are  m  m2   2m2   m  m1  2m1 v1   1  u1    u2 ; v 2   2  u2  u  m1  m2   m1  m2   m1  m2  m1  m2 1 (15). For perfectly inelastic collision, e = 0, then velocities after collision are 10  Physics Short Notes m1u1  m2u2 1 m1m2 v1  v 2  and loss in kinetic energy is KE  (u1  u2 )2 m1  m2 2 m1  m2 CHAPTER 7. GRAVITATION Gm1m2 (1). Ne to s u i e sal la of g a itatio F  r2 B Gm1m2 In vector form, F   (r ) r2 (2). According to Keple s IInd law dA  dt 2m L U PH 4 2 3 (3). A o di g to Keple s IIIrd law T  2 R  T2  R 3 GM Where, T = Time period of revolution, and R = Semi-major axis of the elliptical orbit. Gm1m2 EX Ne to s u i e sal la of gravitation F  r2 GMe. A ele atio due to g a it g is g  R 2e 2  R  (5). Variation of g at altitude h is gh  g  e  Re  h   2h  If h < < R then, gh  g 1    Re   d (6). Variation of g at depth d is gd  g 1    Re  11  Physics Short Notes 1 1 (7). Gravitational potential energy U  WAB  GMm     r2 r1  GMm If, r1  , r2  r  U   r CHAPTER 8. MECHANICAL PROPERTIES OF SOLIDS B gL2 MgL (1). Elongation produced in rod of length ‘L’ due to its own weight is L   2Y 2AY (2). Thermal Stress Y   (3). Elastic potential energy density U  1 U (stress)  (strain) PH 2 P 1 (4). Bulk modulus, B  V (5). Compressibility  V B r 4 r / r (6). Restoring couple per unit twist  (7).    L / L EX 2 9BS (8). Relation between Y,B,S  Y  (9). Relation between Y,B,  , Y  3B(1  2) 3B  S 3B  2S (10). Relation between Y,S Y  2S(1  ) (11). Poisso s ‘atio   6B  2S Wt3 (12). Depression at the middle of a beam y  4Ybd3 Fh 2S(1  ) (13) Sheer Modulus S  (14) Relation between B,S, , B  Ax 3(1  2) 12  Physics Short Notes CHAPTER 9. MECHANICAL PROPERTIES OF FLUIDS substance (1). Relative density of a substance rel  water at 4o C (2). Gauge pressure Pg  gh (3). Apparent weight of a body of density  in a fluid of density    W '  W  1   , W = weight of the body in air   (4). Equation of continuity Av = constant B Here, A = cross-sectional area of pipe and v = fluid velocity. Be oulli s e uatio : At any point in a streamline flow 1 P  gh  v 2  constant 2 U PH Here, P= pressure, v = fluid velocity and  is density. F (6). Coefficient Of viscosity   vA Here, F = Viscous force, = Separation between two lamina, A = Area of each lamina and v = Relative EX velocity of two lamina (7). According to Stokes la F  6av Here, a = radius a ball or drop and v = velocity of ball or drop 2a2 (8). Formula for Terminal velocity is v T  (  )g 9 Where,  = density of falling body,  = density of fluid and  = coefficient of viscosity vd (9). Reynolds number. R e  where, d = diameter of the pipe  2S (10). Excess pressure inside a liquid drop or a cavity of radius R is  Pi  P0  where S is surface R tension 13  Physics Short Notes 4S (11). Excess pressure inside an air bubble is Pi  P0  R 2S cos  (12). Height of a liquid in a capillary tube is h  rg Where,  = angle of contact,  = density of the liquid and g = acceleration due to gravity B CHAPTER 10. THERMAL PROPERTIES OF MATTER (1). Conversion of temperature from one scale to other. U PH 5 9 (a) From C  F tC  (tF  32), & tF  tC  32 9 5 (b) From C  K T  tC  273.15, & tC  T  273.15 9 5 (c) ) From F  K tF  T  459.67, & T  tF  255.37 EX 5 9 Where T, tC , tF , stand for temperature reading on Kelvin scale, Celsius scale, Fahrenheit scale respectively. (2).   2,   3 (Relation between  , ,  ) kA(T1  T2 )t (3). (a) Q  x Where Q is the amount of heat that flows in time t across the opposite faces of a rod of length x and cross-section A. T1 and T2 are the temperatures of the faces in the steady state and k is the coefficient of thermal conductivity of the material of the rod.  dT  dT (b) Q  kA  t Where represents the temperature gradient.  dx  dx 14  Physics Short Notes dQ  dT  (c) H   kA   H is called the heat current. dt  dx  Q1 (4). (a) Coefficient of reflectivity is r  Q Q2 (b) Coefficient of absorptivity a  Q Q3 (c)Coefficient of transitivity t  Q Where Q1 is the radiant energy reflected, Q2 is the radiant energy absorbed and Q3 is the radiant energy transmitted through a surface on which Q is the incident radiant energy B (T1  T0 ) (5). (a) ln  Kt (T2  T0 ) (b) (T1  T2 ) t T T   K  1 2  T0   2  U PH The a o e t o e uatio s ep ese ts Ne to s la of ooli g. He e, t is the ti e take a ody to cool from T1 to T2 in a surrounding at temperature T0. EX CHAPTER 11. THERMODYNAMICS (1). First law of thermodynamics Q  U  W (2). Work done, W  PV  Q  U  PV (3). Relation between specific heats for a gas Cp  Cr  R. Fo isothe al p o ess, i a o di g to Bo le s la PV = constant According to Charles law (For volume) V  T constant and Charles law (for pressure) P  T 15  Physics Short Notes V2 V And (ii) Work done is W  RT ln  2.303 RT log 2 V1 V1 Cp. Fo adia ati p o ess, i A o di g to Bo le s la PV  = constant Where,   Cv P1V1  P2V2 R  T1  T2  And (ii) Work done is W    1  1 (6). Slope of adiabatic =  (slope of isotherm) (7). For Carnot engine, Q2 T  Q1 T1  (i) Efficiency of engine is   1  1 2    B Q1 T  Q2 T2  W (ii) And work done is W  Q1  Q2 (8). For Refrigerator U   Q1 PH Q2 Q 1 (i) Coefficient of performance is    2   Q1  Q2 W  Q1 Q1 1 (9). For Heat pump r   W Q1  Q2  EX CHAPTER 12. KINETIC THEORY OF GASES (1). Ideal gas equation is PV  RT where  is number of moles and R is gas constant 1 mM 2 Pressure exerted by ideal gas on container is P  v 3 V 16  Physics Short Notes 3kBT 8KBT (2) R.M.S. velocity vrms  (3). Average velocity v av  m m 2KBT (4). Most probable velocity vmp  m 1 (5). Mean free path ( )  2nd2 Where n = number density and d = diameter of molecule Table 2: Some important points about molecules of gas B S.No. Atomicity No. of Cp Cv CP degree of  Cv freedom 1. 2 Monoatomic Diatomic U 3 5 5 2 7 R 3 2 5 R 5 3 7 PH R R 2 2 5 3. Linear molecule (Triatomic) 7 7 5 7 R R 2 2 5 4. Non-linear molecule (Triatomic) 6 4R 3R 4 3 EX n1Cv  n2Cv (6). For mixture of gas, molar specific heat at constant volume is given by Cv(mix)  1 2 n1  n2 Where n1 and n2 are number of moles of two gases mixed together C v and C v are molar specific 1 2 heat at constant volume of 2 gas. (7) For mixture of gases with n1 ,& n2 moles the following relation holds true. n1  n2 n n  1  2  1 1  1  2  1 17  Physics Short Notes CHAPTER 13. OSCILLATIONS (1) Displacement equation for SHM x  A sin (t  ) Or x  A cos[t  ]  where A is amplitude and t    is phase of the wave (2). Velocity in SHM v  A cos t and v   A  x 2 2 (3). Acceleration in SHM is a   A sin t and a   x 2 2 B (4). Energy in SHM is (i) Potential energy U  1 2 m2x2 U (ii) Kinetic energy K  1 2 m2 (A2  x2 ) PH 1 (iii) Total energy E  m2A2 2 (5). For Simple pendulum L 1 (i) Time period of pendulum is T  2 (ii) If L is large T  2 EX g 1 1  g   L R  T 1 L L (iii)  (iv) Accelerated pendulum T  2 T 2 L ga l (6). For torsional pendulum, time period of oscillation is T  2 ; where I is moment of inertia k l (7). For physical pendulum, time period of oscillation is T  2 ; where l is moment of inertia of mgd body about axis passing through hinge and, d : Distance of centre of mass from hinge (8). Damped simple harmonic motion 18  Physics Short Notes d2x dx (i) Force action on oscillation body is m   kx  b 2 dt dt u/2m k b2 (ii) Equation of motion is x  Ae cos('t  ) Where  '   m 4m2 (9). Forced oscillator md2x (i) Force acting on body is  kx  bv  F0 sin t dt2 F (ii) Equation of motion is x  A sin [wt  ] Where A  2  b  m ( 2  20 )2   B m. Supe positio of T o SHM s U PH (i) In same direction x1  A1 sin t and x2  A2 sin (t  ) Resultant amplitude is Ar  A12  A22  2A1A2 cos  EX (ii) In perpendicular direction x1  A1 sin t and y1  A2 sin(t  ) (a) Resultant motion is SHM along straight line, if   0 or     (b) Resultant motion is circular, if   and A1  A2 2  (c) Resultant motion is an (light) elliptical path, if   and A1  A2 2 19  Physics Short Notes CHAPTER 14. WAVES (1). Equation of a plane progressive harmonic wave travelling along positive direction of X-axis is y(x, t)  a sin (kx  t  ) And along negative direction of X-axis is y(x, t)  a sin(kx  t  ) Where, y(x,t) Displacement as a function of position x and time t, a Amplitude of the wave,  Angular frequency of the wave, k Angular wave number, (kx  t  ) Phase, And  Phase constant or initial phase angle B 2 (2). Angular wave number or propagation constant (k) k  (3). Speed of a progressive wave v   U   f k T PH (4) Speed of a transverse wave on a stretched string T v where, T Tension in the string, and  Mass per unit length  EX (5). Speed of sound wave in a fluid B v where, B Bulk modulus, and  density of medium  (6). Speed of sound wave in metallic bar Y v he e, Y = ou g s odulus of elasti it of etalli a . Speed of sou d i ai o gases Ne to s fo mula (connected)] v v where, P Pressure,  Density of air (or gas) and  Atomicity of air (or gas)  20  Physics Short Notes v2 1 (8). The effect of density on velocity of sound  v1 2 v1 T 273  t (9). The effect of temperature on velocity of sound   v0 T0 273 (10). If two waves having the same amplitude and frequency, but differing by a constant phase  , travel in the same direction, the wave resulting from their superposition is given by     y(x,t)  2a cos  sin  kx  t    2  2 (11). If we have a wave B y1 (x,t)  a sin(kx  t) then, (i) Equation of wave reflected at a rigid boundary U yr (x,t)  a sin(kx  t  ) Or yr (x, t)  a sin (kx  t) i.e. the reflected wave is 180o out of phase. PH (ii) Equation of wave reflected at an open boundary yr (x, t)  a sin(kx  t) i.e. the reflected wave is a phase with the incident wave. (12). Equation of a standing wave on a string with fixed ends y(x,t)  [2a sin kx]cos t nv EX Frequency of normal modes of oscillation f n  1,2,3..... 2L (13). Standing waves in a closed organ pipe (closed at one end) of length L.  1 v Frequency of normal modes of oscillation. f  n   n  1,2....  2  2L  fn  (2n  1)f1 Where fn is the frequency of nth normal mode of oscillation. Only odd harmonics are present in a closed pipe. (14). Standing waves in an open organ pipe (open at both ends) nv Frequency of normal modes of oscillation f n  1,2,3.... 2L  fn  nf1 21  Physics Short Notes Where fn is frequency of nth normal mode of oscillation. (15). Beat frequency (m) m Difference in frequencies of two sources m  (v1  v2 ) or (v2  v1 )  v  v0 . Dopple s effe t f  f0    v  v s  Where, f Observed frequency, f0 Source frequency, v Speed of sound through the medium, v 0 Velocity of observer relative to the medium B and vs Source velocity relative to the medium  In using this formula, velocities in the directions (i.e. from observer to the source) should be treated U as positive and those opposite to it should be taken as negative. PH CHAPTER 15. ELECTRIC CHARGES AND FIELDS EX q1q2 (1). Electric force between two charges is given by F  40R2 q2 And F  q1E where E  is the electric field due to charge q2 4 0R 2 q1 q2  1 1  (2) Electric potential energy for system of two charges is U  W     4 0  r1 r2  q1 q2 For r2   , U 4 0r1 22  Physics Short Notes U (3) Electrostatic potential is V  q (4). Electric field on the axis of a dipole of moment p  2aQ at a distance R from the centre is 2Rp 2p E. If R > > a then E  4 0 (R 2  a2 )2 4 0R 3 (5). Electric field on the equatorial line of the dipole at a distance R from the centre is p p E. If R > > a then E  3 4 0R 2 4 0 (R  a ) 2 2 2 (6). Torque  experienced by a short dipole kept in uniform external electric field E is B   p  E  pE sin 0 nˆ (7). Perpendicular deflection of a charge q in a uniform electric field E after travelling a straight distance x is y qEx 2 2mv 20 U , where m is mass of the charge and v0 is initial speed of perpendicular entry in the electric PH field. (8). Electric flux E  E  S  ES cos . Area vector S is perpendicular to the surface area. Q (9). Gauss law :  E  dS  . Here E is the electric field due to all the charges inside as well as outside 0 EX the Gaussian surface, while Q is the net charge enclosed inside Gaussian surface. (10). Electric field due to infinitely long charged wire of linear charge density  at a perpendicular  distance R is E  20R  (11). Electric field due to singal layer of surface charge density  is. Field due to oppositely 20  charged conducting plates is in between the gap but zero outside. 0 Q (12). Field due to a uniformly charged thin spherical shell of radius R is E  for outside points 4 0r 2 and zero inside (r is distance from the centre of shell) 23  Physics Short Notes d Q  r (13). Field due to a charge uniformly distributed in a spherical volume is E   r2   dr  4  R 3  30  0  Q for inside points and E  for outside point. 4 0r 2 3Q Here   is volume charge density and Q is total charge inside the sphere. 4 R3 B CAPACITANC CHAPTER 16. ELECTROSTATIC POTENTIAL AND CAPACITANCE (1). Electric potential : U PH (a) Potential due to a conducting sphere of radius r with charge q (solid or hollow) at a distance r from the centre  1 q  1 q V  if (r > R) or V  if (r = R)  4   4   0 r  0 R EX 1 q or V if (r < R) 4 0 R v | v | (b) Relation between electric field potential | E |     (2). Electric dipole potential: 1  p cos   (a) V    4 0  r 2  (b) Potential energy of a dipole in an external electric field U()  P  E 24  Physics Short Notes (3). Capacitors : A Capacitance of a potential plate capacitor C  0 d 1 Q2 1 2 (4). Electric field energy : (a) U  QV   CV 2 2C 2 1 (b) Energy density of energy stored in electric field u  0E2 2 (5) Combination of capacitors : 1 1 1 1 (a) When capacitors are combined in series,    ..... Ceq C1 C2 C3 B (b) When capacitors are connected in parallel. Ceq  C1  C2  C3 ...... (c) Capacitance of spherical capacitor, C  4 0 ab. (When outer shell is earthed). U or PH ba b2 C  40. (When inner shell is earthed) or ba C  40R (For a sphere of radius R) EX 20 (d) Cylindrical capacitor, C  b ln   a (6). Dielectrics :  1 Dipole moment (a) Induced charge, q'  q  1   (b) Polarization p   k Volume Electric dipole moment is p  eE e  K 1 where e is electrical susceptibility, and K is dielectric constant. 0 25  Physics Short Notes CHAPTER 17. CURRENT ELECTRICITY (1). Resistance of a uniform conductor of length L, area of cross-section A and resistivity  along its length, R   A di 1 (2). Current density j  (3). Conductance G . ds R eE i i4) Drift velocity v d  t.  (5). Current i  neAv d m neA m 1 (6) Resistivity is    where  is resistivity. B ne2 t  vd (7) A o di g to Oh (9)   ne s la j  E and V  iR U (8) Mobility of free electrons   (10). Thermal resistivity of material is T  0 [1  (T  T0 )] E PH R (11). Potential difference across a cell during discharging V    ir  R r (12). Potential difference across a cell during charging V    ir n EX (13) For n cells in series across load R, current through load i R  nt n (14). For n identical cells in parallel across load R, current through load i  nR  r (15). Wheatstone bridge network R1 R3 For balanced Wheatstone bridge  R2 R4 (16). If unknown resistance X is in the left gap, known resistance R is in the right gap of meter bridge and R balancing length from left end is l then X  100  (17) Potentiometer 27  Physics Short Notes 1   (i) Comparison of emf  1 (ii) Internal resistance of cell r   1  1  R 2  2  2  CHAPTER 18. MOVING CHARGES AND MAGNETIC FIELD S.No. Situation Formula 1. q[E  v  B] B Lorentz force 2. Condition for a charged particle to go undeflected in a cross E  3. electric and magnetic field U A charge particle thrown perpendicular to uniform magnetic B (i) Circular PH field mv (i) Path (ii) r  qB (ii) Radius 2m (iii) Time period (iii) t  qB EX 4. A charge particle thrown at some angle to a uniform magnetic (i) Helix field mv sin  (i) Path (ii) r  qB (ii) Radius 2m (iii) Time period (iii) t  qB (iv) Pitch (iv) T  v cos  5. Cyclotron frequency qB f 2m 6. Maximum kinetic energy of a charged particle in a cyclotron q2B2R 2 (With R as radius of dee) K 2m 28  Physics Short Notes 7. Force on a straight current carrying conductor in a uniform F  i( l  B) magnetic field 8. Force on a arbitrary shaped current carrying conductor in a F  i d  B  i  B uniform magnetic field 9. Magnetic moment of a current carrying loop Mi A 10. Torque on a current carrying loop placed in a uniform magnetic   M B field 11. Biot-Savart Law 0i d  r dB  4 r3 B 12. Magnetic field at a point distance x from the centre of a current 0iR 2 carrying circular loop 2(R 2  x 2 )3/2 13. U Magnetic field at the centre of a current carrying circular loop  0i PH 2R 14. Magnetic field on the axis of a current carrying circular loop far 0 2M away from the centre of the loop 4  x3 (Moment behaves as magnetic dipole) 15. EX Magnetic field on the centre of current carrying circular arc 0 i  4 t 16. A pe e s i ula la  Bd  0i 17. Magnetic field due to a long thin current carrying wire 0i B 2r 18. Magnetic field inside a long straight current carrying cylindrical 0 i conductor at a distance r from the axis. B  r 2 R 2 19. Magnetic field outside a long straight current carrying conductor 0 2i at a distance r from the axis B  4 r 20. Magnetic field inside a long solenoid B  0ni 29  Physics Short Notes 21. Magnetic field inside a toroid 0Ni B 2r 22. Force per unit length between two current carrying wire 0i1i2 F 2r 23. Current sensitivity of moving coil galvanometer  NBA  i k 24. Voltage sensitivity of moving galvanometer  NBA  V kR 25. Shunt resistance required to convert galvanometer into G rg  B ammeter of range i ( ig is the full scale deflected current of  i  galvanometer)   1  ig    26. range V U Resistance required to convert galvanometer into voltmeter of R V ig G PH EX CHAPTER 19. MAGNETISM AND MATTER (1). Bar magnet : The electrostatic Analog Electrostatics Magnetism 1 Permittivity = 0 Permittivity = 0 Charge q Magnetic pole strength (qn) Dipole Moment Magnetic Dipole Moment p  ql M  qml 30  Physics Short Notes q1q2 0 qm(1)qm(2) F F 4 0r 2 4 t2 F  qE F  qmB 2p 0 2M Axial Field E  B 4 0r 2 4  r3 p 0 M Equatorial Field E  B 4 0r 2 4 r2 Torque   p  E   M B B Potential Energy U  p  E U  M  B Work W  pE(cos 1  cos 2 ) U W  MB(cos 1  cos 2 ) PH 0 qm (2). Field due to a magnetic monopole B   rˆ 4 r2 (3). B on the axial line or end on position of a bar magnet 0 2Mr  0 2M  EX B  for r  l, B    4  (r 2  l2 )2  4 r2  (4). B on the equatorial line or broad side on position of a bar magnet 0 M  0 M  B  for r  l, B    4  (r  l2 )3/2 2  4 r3   (5). Time period angular SHM T  2 here  is moment of inertia. MB. Gauss s la i ag etis  B  ds  0 Bv (7). Fo ho izo tal a d e ti al o po e t of ea th s ag eti field,  tan  BH 31  Physics Short Notes tan  (8). tan 1  ' (9). cot2   cot2 1  cot2 2 cos  B B  (10). Magnetic intensity is H   (11). Relative magnetic permittivity is r  0  0 M 1 (12). Magnetic Susceptibility m  (13). r  1  m (14).   H (T  Tc ) CHAPTER 20. ELECTROMAGNETIC INDUCTION B (1). Average induced emf e   t       2 1   t2  t1  U PH d(t) (2). Instantaneous induced emf e(t)   dt (3). Motional emf  B v    (4). Motional emf e  de  (v  B)dl  (v  B) j d EX  (5). E  dl   dt B [ E electric (induced) field, B Magnetic flux] (6). B  Li  L self inductance of the coil di (7). Induced emf e  L (8). L  0rn2  A  i Where L coefficient of self-inductance dt di1 (9). 2  Mi1 and 2  M Where M is co efficient of mutual inductance dt (10). The emf induced (in dynamo) e(t)  BA sin t   (11). Mutual inductance M  01n1n2Ai 32  Physics Short Notes CHAPTER 21. ELECTROMAGNETIC WAVES dE d  E  ds CdV (1). Displacement current lD  0  0  dt dt dt. Ma ell s E uatio : q (a)  E  ds   (b)  B  ds  0 0 d d  dE  (c)  E  dl   dt B  dt  B  ds (d)  B  dl  0  lc  0 dt   B (3). Ey  E0 sin(t  kx) and B2  B0 sin (t  kx) c vacuum  1 0 0 ; cmedium  1 r0r 0 U PH E ERMS E (4).   c B0 BRMS B (5). Average of wave lav = Average energy density  (speed of light) E0B0 E2 cB2 Of lav  Uav    0  0 EX 20 2c0 20 1  2 B2  B2 (6). Instantaneous energy density uav   0E    0E  2 2 0  0 1 B20 0E02 B02 Average energy density uav  0E0  2   4 40 2 20 (7). Energy = (momentum), c or U  Pc I0 (8). Radiation pressure R.P.  where I0 is intensity of source (when the wave is totally absorbed) c 2I0 And R.P.  (when the wave is totally reflected) c 33  Physics Short Notes 1 1 (9). I  (for a point source) and I (for a line source) t2 r For a plane source intensity is independent of r. CHAPTER 22. RAY OPTICS AND OPTICAL INSTRUMENTS (1). The distance between the pole and centre of curvature of the mirror called radius of curvature B R f 2 (2). Mirror equation 1 1 1 U   (u is Object distance, v is Image distance and f Focal length) v u f PH size of image image distance v (3). Linear magnification m    size of object Object distance u 2 1 2  1 (4). In case of lens   v u R EX (R= Radius of curvature , 1 and 2 are refractive indices of medium) 1 1 1 (5). Relationship between u, v and focal length f is   in case lens. v u f (6). Longitudinal magnification = (Lateral magnification)2 (7) Equivalent lens 1 1 1 1 1 1 d (i) Lens in contact   (ii) Lens at a distance d,    F f1 f2 F f1 f2 f1f2 (8). Reciprocal of focal length is called as power of lens. 1 100 P  f(in metres) f(in cm) 34  Physics Short Notes 1 2 (9). For achromatic combination of two lens  0 f1 f2  A  m  sin   (10). Refractive index of material of prism    2  (m ) Minimum deviation angle A sin   2 (11). For small-angled prism d  (  1)A (where A= Angle of prism and B= Deviation angle) (12). Dispersive power of prism for two colors (blue and red)    R    v  R  B  v    d    1  (13). For simple microscope, (a) Magnification m  1  D f U (Where D= Least distance of distinct vision. and f= Focal length) PH D (b) M  for image to form at infinity f (14). For compound microscope.  ve  EX vO Magnification of objective MO  and Magnification of eye piece Me   1   uO  fe   vo  D  (a) m  mome  1   for least distance of distinct vision. ue  fe  L D (b) m   for image to form at infinite. fo fe fo (15). Magnifying power of telescope m  and length of telescope  L  fe  fo fe 35  Physics Short Notes CHAPTER 23. WAVE OPTICS sin i 2 v1 1 (1).    S ell s la sin t 1 v 2 2 max ( 1   2 )2 (2). Ratio of maximum to minimum intensity  min ( 1  2 )2 D (3). (a) Fringe width   (b) Condition of maxima   2n where n  0, 1, 2.. d (c) Condition of minima   (2n  1) where n  0, 1, 2.. B  (d) Intensity of any point of screen I  40 cos 2 2 Where   2  U x is phase difference and x is path difference PH v v . Dopple s effe t fo light   radial   v c  2 sin  (5). Resolving power of microscope  1.22  EX 1.22 f (6). Radius of central bright spot in diffraction pattern r0  2a a2 (7). Fresnel distance Z f  (8) Malus law   0 cos2   9 B e ste s la tan iB   36  Physics Short Notes MATTE CHAPTER 24. DUAL NATURE OF RADIATION AND MATTER 1. Ei stei s photoele t i ell e uatio , mv 2  hf  hf0 2 max Where f,f0 are frequencies of incident radiation. hc (2). Work function and threshold frequency or threshold wavelength, 0  hf0  0 hc E h (3). Energy of photon, E  hf  (4). Momentum of photon, P    c  B h (5). De Broglie wavelength of a material particle,   mv  12.27 V o A 1.227 V nm U (6). De Broglie wavelength of an electron accelerated through a potential V volt, PH h (7). de Broglie wavelength of a particle in terms of temperature (T),   3mkT h (8). de Broglie wavelength in terms of energy of a particle (E),   EX 2mE 37  Physics Short Notes CHAPTER 25. ATOMS Rutherford’s Model e2 Distance of closest approach r0  where E is the energy of  -particle at a large distance. 4 0E Bohr’s Model of hydroge ato 0h2n2 Postulates: (i) Radius of nth orbit, rn  me2 nh  me 4  1 13.6 (ii) Orbital speed, Vn  (iii) Energy of nth orbit, En      2 eV 2mrn  82h2  n2 n  0  B (iv) TE   KE (v) PE  2TE 1 1 ‘ d e g s o sta t 1  R 2  2  n1 n2  and U R me 4 820h3c PH CHAPTER 26. NUCLEI EX (1). Nuclear radius (R) is given by R  R0A1/3 Here R0  1.2  1015m. (2). Density of all nuclei is constant. (3). Total binding energy  [Z mp  (A  Z)mn  M]c J 2 (4). Av. BE/nucleon = Total B.E/A dN (5). Radioactivity decay law  N  N  N0et dt 0.6931 1 (6). Half life T1/2  (7). Average or mean life is Tav   1.44 T1/2.   38  Physics Short Notes CHAPTER 27. SEMICONDUCTOR ELECTRONICS  Intrinsic semiconductors : ne  nh  ni Extrinsic semiconductors: nenh  ni2  Transistors : e  b  c  E  b  c  Common emitter amplifier : c    c (i)   ; ac   c . (ii) Trans-conductance gm  b    Vi  b  vdE Rout (iii) AC voltage gain  ac  (iv) Power gain = voltage gain  Current gain Rin  Logic Gates For input X and Y , output Z be given by Z XY B OR gate Z  XY AND gate ZX NOR gate Z  (X  Y) NAND gate Z  (XY) NOT gate Z  X or Z  Y when either X or Y is present. U PH CHAPTER 28. COMMUNICATION SYSTEM (1). The maximum line of sight distance dM between the two antennas having height hT and hR , above EX the earth, is given by dM  2RhT  2RhR Am (2). Modulation index   where Am and Ac are the amplitudes of modulating signal and carrier Ae wave.  2  (3). In amplitude modulation P1  P2 1    2  (4). Maximum frequency can be reflected from ionosphere fmax  9(Nmax )1/2 1 (5). Maximum modulated frequency can be detected by diode detector fm  2R 39