Chap Wise Derivations Physics class 12

{\rtf1\ansi\ansicpg1252\deff0\deflang16393{\fonttb l{\f0\fnil\fcharset0 Calibri;}{\f1\fnil\fcharset16 1 Calibri;}{\f2\fnil\fcharset204 Calibri;}{\f3\fni l Calibri;}{\f4\fnil\fcharset2 Symbol;}} {\*\generator Msftedit 5.41.21.2509;}\viewkind4\uc 1\pard\sa200\sl276\slmult1\lang9\b\f0\fs22 Electro statics-I\b0\par 1.State Gauss\u8223?s law and use this law to deriv e the electric filed at a point \par from an infinitely long straight uniformly charged wire.\par \lang1033 2.Derive an expression for electric fiel d intensity at a point on the axial line \par and on the equatorial line of an electric pole. \pa r 3.Derive an expression for torque acting on an elec tric in a uniform \par electric filed\par 4.Derive an expression for total work done in rotat ing an electric dipole \par through an angle \'84\f1\'e8\u8223? in uniform elec tric field.\f0 \par 5.State Gauss\u8223?s theorem in electrostatics. U sing this theorem, derive an expression for the \p ar electric field intensity due to a charged metallic spherical shell\par (i)point outside sphere.\par (ii)point inside sphere.\par 6. Using Gauss\u8223? theorem obtain an expression for the electric field intensity at a distance r \par from an infinitely long line of charge with unifor m linear charge density \f1\'eb Cm-1\par \f0 7.\f1 On the basis of Gauss\u8223? theorem pro ve that, for a point outside a charged spherical s hell it \par behaves as a point charge.\par Ans: If E = 0\f0 , V= constant\f1 E=-dV/dr\par \f0 8\f1 . An electric dipole is held in uniform e lectric field.\f0 \f1 Show that net force acting on it is zero.\par

\f0 9\f1 . Derive an expresion for the strength of electric field intensity at a point\par on the axis of a uniformly charged circular coil of radius R carying charge\par \f0 '\f1 Q\f0 '\par 24 State the theorem which relates total charge enc losed within a closed surface 5\par and the electric flux passing through it. Prove it for a single point charge. \f1\par \lang9\b\f0 Electrostatics-II\b0\par 1.Derive an expression for capacitance of parallel plate capacitor, when a \par di\f1 lectric slab of dielectric constant k is par tially introduced between \par the plates of the capacito\lang1033\f0 r\par 2.Derive the expression for energy(or electrostatic potential energy) stored in a \par parallel plate capacitor from the capacitor.\par 3. Derive the expression for \lquote Energy Densit y\rquote in a parallel plate capacitor.\par 4. Derive Energy stored in series combination of ca pacitors.\par 5. Derive the Energy stored in parallel combination of capacitors. \par 6. Derive the relation for the loss of energy whil e sharing of charges when two capacitors are \par connected in parallel.\par 7. Derive the expression for the potential due to a dipole\par Derive an expression for the potential energy of a system of two electric charges in an \par external electric field.\par 8.Derive the formula for the capacitance of a para llel plate capacitor having a dielectric \par slab of thickness \'84t\rquote the plates.\par 9. Derive the relation between \f1\'d8\f0 E and \u 8712? r\par 10. Show that at a point where the electric field i ntensity is zero, electric \par potential need not be zero.\par 11.Show that the potential of a charged spherical c onductor, kept at the \par

Centre of a charged hollow spherical conductor is a lways greater than \par that of the hollow spherical conductor, irrespectiv e of the charge \par accumulated on it\par \b Ans\b0 : Va-Vb=(q/4\f1\'f0\f2\'ba) (1/r-1/R)(PRI NCIPLE OF VAN DE-GRAFF \par GENERATOR IS DELETED)\par \f0 12\f2 . Show that the force on each plate of a parallel plate capacitor has a magnitude equal to (1/2) QE, \par where Q is the charge on the capacitor and E is th e magnitude of EF between the plates\par \f0 13.\f2 Show that electric field is always perp endicular to the \par equipotential surface\par 14. . Show that work done in carrying electric cha rge on an equipotential surface is zero.\par Show that electric field at a point is equal to th e negative \par of the potential gradient at that point.\lang9\f0\p ar \b \b0 15.With the help of an example, show that F arad is a very large unit of\par capacitance.\par 16. Derive an expresion for potential at any point distant r from the centre O\par of dipole making an angle with the dipole.\par \b Current ELectricity\b0\par \lang1033 1.\f1 Derive the principle of wheatstone bridge using Kirchoff\u8223?s law.\par \f0 2\f1 .Derive the relation between Drift Velocit y & Current.\par \f0 3\f1 . Derive Ohm\u8223?s law in terms of mate rial constant or expression for resistivity in ter ms of \par material constant\f0 ,\f1 number density\f0 \f1 of fre\f0 e\f1 electrons and relaxation time.\b\p ar \b0\f0 4\f1 . Derive the relation for the internal resistance of a cell in terms emf and terminal po tential \par

difference.\par \f0 5.\f1 Obtain an expression for the \par potential difference per unit length of the potenti ometer wire.\par \f0 6\f1 . Obtain the equivalent emf of cells group ed in series and in parallel.\par \f0 7\f1 . Obtain the relation for the combination of resistances in Series: -\par \f0 8\f1 .Obtain the relation for the combination o f resistances in parallel: -\par \f0 9.\f1 A voltmeter of resistance RV is connecte d across a resistor R which is to be measured. An \par ammeter of resistance RA is in series with this com bination. The arrangement is then \par connected across a battery and the ratio of the re adings in the meters give a value R\f0 '\f1\par for R. Show that R and R\f0 '\f1 are related as 1/R = 1/R\f0 '\f1 - 1/RV\par \f0 10.\f1 Derive the expresion for the potential e nergy of the dipole and show\par diagrammaticaly the orientation of the dipole in th e field for which the\par potential energy is (i) maximum (i) minimum.\par \f0 11.\f1 Obtain an expression for resistance Rg of the galvanometer in terms of R, S and n. To\par what form does this expression reduce when the val ue of R is very large as compared to\par S? 3\lang9\f0\par \b Magnetic force and things\par \lang1033\b0 1.\f1 Derive an expression for the fo rce experienced by a current carrying straight \pa r conductor placed in a magnetic field. Under what co ndition is this force \par maximum? \par \f0 2.\f1 Derive the expression for \par the magnetic moment when an electron revolves at a speed \'84v\u8223? around an orbit \par of radius r in hydrogen atom\par \f0 3.S\f1 tate Ampere\u8223?s Circuital Law. Deri ve an expression for the magnetic field at a \par

point due to straight current carrying conductor.\p ar \f0 4.\f1 Derive an expression for the magnetic fi eld at a point along the axis of an air \par cored solenoid using a Ampere\u8223?s circuital law .\par \f0 5.\f1 Derive an expression for torque acting o n a rectangular current carrying loop \par kept in a uniform magnetic field B. Indicate the di rection of acting on \par the loop\par \f0 6.\f1 Derive an expression for: (i) induced emf & (ii) induced current when, a \par conductor of length is moved into a uniform velocit y v normal to a uniform \par magnetic field B. Assume resistance of conductor to be \par \f0 7\f1 . Derive an expression for magnetic field on a point on the axial \par of circular \f0 coil\f1 .\par \f0 8\f1 . Derive an expression for Force per unit length due to two straight current carrying wires \par \lang9\f0 9. Using Biot-Savart law, derive an expr ession for the Magnetic field due to a current \pa r carrying circular loop at its centre\par 10. Obtain an expression for the magnetic field due to a toroid carrying the current.\par 11. Obtain an expression for torque experienced by a current carrying conductor placed in \par uniform magnetic field.\par 12. State and prove Ampere\u8223?s Circuital law.\p ar \pard{\pntext\f4\'B7\tab}{\*\pn\pnlvlblt\pnf4\pnin dent0{\pntxtb\'B7}}\fi-360\li720\sa200\sl276\slmul t1 13.Show that cyclotron frequency does not depen d \par \pard\sa200\sl276\slmult1 upon the speed of particl es. Write its two limitations\par 14. Show that the average energy density of the ele ctric field E equals the\par

average energy density of the magnetics fields B?\p ar 15. Derive an expresion for the torque on a magneti c dipole placed in a\par magnetic field and hence define magnetic moment.\pa r 16. Derive an expresion for magnetic field intensit y due to a bar magnet\par (magnetic dipole) at any point (i) Along its axis ( i) Perpendicular to the axis.\par 17. Derive an expresion for the torque acting on a lop of N turns of area A\par of each turn carying curent I, when held in a unifo rm magnetic field B.\par 15. Prove that the magnetic moment of a hydrogen at om in its ground state\par is eh/4(pi).m. Symbols have their usual meaning.\pa r 16.Apply this law to obtain an expression for the induced emf when one \lquote rod\rquote of a\par rectangular conductor is free to move in a uniform , time independent and \lquote normal\rquote\par magnetic field.\par \b EMI\par \lang1033\b0 1.\f1 Derive an expression for the \pa r mutual inductance of two long \par solenoids of same length wound over \par the other.\par \f0 2.Derive an expression for the \par mutual inductance of two long coaxial solenoids of same length wound over \par the other\par 3.Derive an expression for the \par mutual inductance of two long coaxial solenoids of same length wound over \par the other.\par 4.Derive an expression f Derive an expression for self inductance of a long, air-cored solenoid of length l, radius r, and having N number of turns\p ar 5.What is the power dissipated in the pure inductor

circuit & derive the equation \par for energy stored in an inductor?.\par 6.Prove that the total inductance of two coils con nected in parallel is\par (1/L\b t)=\b0 (1/L1)+(1/L2)\par 7.Show that LENZ LAW is in accordance with the law of conservation of \par energy. \par 8. SI unit of magnetic flux - show that it equals v olt -second \par \lang9 9.Derive an expresion for mutual\par inductance of a system of two concentric and coplan er circular lop P and\par Q of radi a and b and number of turn N1\par or N2\par respectively (a