Formula Sheet - General Physics II | PH 222, Study notes of Physics

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Physics General-II (PH 222) Formula Sheet: Page 1 of 7 Physical Constants and general formulas 8.85×10 -12 C 2 /N∙m 2 OR 8.85×10 -12 F/m. ./1099.8 4 1 229 0 CmN .10602.1 19 Ce ./104 7 0 AmT .10109.9 31 kgme ./458792299 smc Avogadro’s Number .1002.6 123 MolN A Molar Mass of Copper 63.54 g/mol OR 63.54×10 -3 kg/mol Area of a circle 2RA Circumference of a circle R2 Volume of a sphere 3 3 4 R Surface area of a sphere 24 R Force is related to acceleration as maF Kinetic energy of a particle is 2 2 1 mvK Centripetal force r mv F 2 Frequency T f 1 Electric Charge, Electric Field & Electric Potential Coulomb's law: Electrostatic Force F between two charges q1 and q2 separated by distance r is 2 21 04 1 r qq F Electric Field 0q F E   Field due to a point charge 2 04 1 r q E Electric Dipole moment qdp Electric field due to a dipole at a distance z is 3 02 1 z p E Force on a point charge in an Electric field is EqF  Torque on a dipole in an Electric field is Ep  Potential Energy Associated with a dipole in an electric field is EpU  Physics General-II (PH 222) Formula Sheet: Page 2 of 7 Gauss’ Law encq0 where AdE  External electric field near the surface of a charged conductor has magnitude 0 E Electric field at any point due to an infinite line of charge with uniform linear charge density has magnitude r E 02 Electric field due to a spherical shell of charge with radius R has magnitude 2 04 r q E , for Rr and 0E for Rr . Electric field inside a uniform sphere of charge is r R q E 3 04 , for Rr Work done is WUUU if Electric potential Difference is q W VVV if Finding V from electric field f i if sdEVV  If Vi = 0 (at infinity V is zero) f i i sdEV  Potential due to point charge r q V 04 1 Potential due to an electric dipole 2 0 cos 4 1 r p V For a parallel plate the electric field is related to potential difference as dVE Potential energy of a system of Point charges r qq WU 21 04 1 Capacitance: Capacitance . V q C For parallel plate capacitor d A C 0 For a cylindrical capacitor )/ln( 2 0 ab L C Spherical Capacitor ab ab C 04 For a conducting sphere RC 04 n capacitors in parallel n i ieq CC 1 Physics General-II (PH 222) Formula Sheet: Page 5 of 7 Current density J in a circular wire of radius R is 2 R i J Potential Energy Associated with a magnetic dipole in a magnetic field is BU  Induction, Inductance: Induced EMF in a coil with N turns is . t N dt d N BBE Magnetic flux dAB where B is magnetic field and A is the area. Magnetic flux in a coil with n turns per unit length is Ain)( 0 where i is the current through the coil. Faraday’s law, dt d dsE BE where E is the induced field. For a circular path around a solenoid, the induced electric field is related to change in flux as A dt dB dt d rEdsE B)2( where A is the area enclosed by circular path in which change in magnetic field is not zero. Inductance of a solenoid is given as AnL 20 Series RL circuit )1( / Lte R i E where RLL / Magnetic Flux through solenoid is Li Self induced emf E in an inductance is dt di LE Electromagnetic waves: Series RLC circuit 22 )( CL XXR I E and R XX CLtan LX L and LX L For a transformer s p ps N N II For an electromagnetic wave propagating along x-axis, the associated electric and magnetic fields are given as )sin( tkxEE m )sin( tkxBB m )cos( tkxB t B m cf 22 Velocity of an electromagnetic field is associated with maximum electric and magnetic field as c B E m m . At any instant, c B E Speed of light in vacuum is 00 1 c Power is related to energy U as t U P Physics General-II (PH 222) Formula Sheet: Page 6 of 7 Intensity of light is power per unit area A P I Intensity is related to electric field of the wave as c E c E I rmsm 0 2 0 2 2 Radiation pressure for total absorption is . c I Pr Radiation pressure for total reflection is . 2 c I Pr Reflection, refraction, Images: Law of refraction: 1122 sinsin nn Law of reflection: 12 For a spherical mirror . 111 fip Lateral magnification . p i m For a spherical refracting surface .1221 r nn i n p n For a thin lens . 111 fip Focal length of a spherical mirror of radius r is 2/rf Interference and Diffraction: Speed of light in a medium of refractive index n is n c v Wavelength and frequency are related to speed of light cf Wavelength of light in a medium of refractive index n is nn In a double slit setup, if d is the slit separation the angular position of maxima will be md sin , where .......3,2,1,0m In a double slit setup, if d is the slit separation the angular position of minima will be ) 2 1 (sin md , where .......3,2,1,0m Phase difference between the wave traveling through mediums of equal thickness L but different refractive indices is )( 2 12 0 nn L In a thin film for destructive interference the path difference in two beams should be mL , where .......3,2,1,0m Physics General-II (PH 222) Formula Sheet: Page 7 of 7 In a thin film for constructive interference the path difference in two beams should be ) 2 1 (mL , where .......3,2,1,0m If d is the thickness of a medium of refractive index n, the effective thickness can be taken as nd In diffraction due to a slit of width a, the angular location of first minima is related to wavelength sina