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PHYSICS STD XII

IMPORTANT DERIVATIONS & LONG ANSWER QUESTIONS

I Electric Charges & Field 13. Two infinite parallel plates have uniform charge
densities + and –. Determine the electric
1. Electric field intensity at a point on the axial
field in i) the region between the plates and
(
line of a dipole. Eaxial = 1
40 r3
2p
) ii) Outside it.
2. Electric field intensity at any point along the 14. Parallel combination of capacitors,
(CP = C1 + C2 + C3)
(
equatorial line. Eequatorial =
1
40 r3
P
) 15. Series combination of capacitors,
3. Torque acting on an electric dipole, when held
in a uniform field, ( = PE Sin)
( 1 = 1 + 1 + 1
CS C1 C2 C3 )
q 16. Energy stored in capacitance, (U = ½CV2=
4. (
Proof of Gauss’s Theorem; E = 
0
) ½QV = Q2/2C)
5. Using Gauss’s theorem, derive an expression 17. Derive the expression for energy density or
for the electric intensity due to an infinitely workdone per unit volume of a parallel plate

(

long straight wire, E = 2 r
0
) capacitor, ( U = ½0E2 )

6. Also derive an expression for the E at a III Current Electricity
point near thin infinite plane sheet of charge,
  18. Derive the relation between drift velocity and
( E = 2 ) (
electric field Vd = m
eE
)
0

7. Derive the E due to a uniformly charged 19. Derive the relation between current and drift
spherical shell at a point (i) Outside (ii) On velocity, I = nAeVd.
the shell (iii) Inside the shell
 1 q    20. Derive an expression for the resistivity () of a
( i) E = 4 r2 ; ii) E = 
0 0
iii) E = 0 ) conductor in terms of number density and
m
relaxation time, = ne2

II Electrostatic Potential and Capacitance 21. Deduce the relation between current density
( J ) and conductivity () of conductor.
8. Electric potential due to a point charge,    
1 q J = E or E = J.
V = 4
r
0
22. Prove that, internal resistance r = E – 1 R.
( )
9. Electric potential difference between two points V

V = 4
q
[
1
rA –
1
rB
] 23. Series combination of cells, eq = 1 +2 + 3 +
0 ......... ; req = r1+ r2 + r3 + ....... rn.
10. Electric potential due to a dipole, eq 1 2
1 P cos 24. Parallel combination of cells, r = r + r +
V = 4 (r2 – a2 Cos2) eq 1 2
0 n
........ + r
11. Electric potential energy of a dipole in an n
external electric field U = PE (Cos1 – Cos2) 1 1 1
= r + r + .......... + 1
12. Derive an expression for capacitance of parallel req 1 2 rn
plate capacitor (C = A0/d.) 25. (
Derive wheat stone bridge principle, Q = S
P R
)
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IV Magnetic Effects of Electric Current VII Alternating Current
26. Using Biot-Savats law, deduce an expression 42. Derive the relation between rms value or
for the magnetic field on the axis of a circular effective value and peak value of a.c.
current loop. I
Irms = Ieff = 0 or 0.707 I0.
27. Using Ampere’s law, to derive the formula for 2
the magnetic field due to an infinitely long 43. Prove that the voltage and current always vary
straight current carrying wire. in the same phase in an a.c circuit containing
28. Expression for the magnetic field inside a long resistance only or A.C through resistor.
solenoid (B = 0nI) 44. A.C circuit containing only an inductor phasor
29. Using Ampere’s circuital law, find the magnetic diagram.
field both inside and outside of a toroid, 45. A.c circuit containing only a capacitor.
B = 0nI.
46. A.C through series LCR circuit.
30. The motion of charged particle in a uniform
magnetic field with initial velocity (i) parallel 47. Power in an a.c ckt. Pav = rms Irms Cos
to the field (ii) er to the magnetic field 1
48. Derive the resonant frequency, fr =
(iii) at an arbitrary angle with the field 2LC
direction. 49. Principle, Construction, Working of
31. Derive a mathematical expression for the force transformer.
acting on a current carrying straight conductor
kept in a magnetic field, F = BIL Sin. VIII Ray Optics
32. Force between two parallel wires carrying 50. Prove, radius of curvature is twice the focal
currents in the same direction. length, f = R/2.
1 1 1
33. Torque on a current loop in a uniform magnetic 51. Derivation of mirror formula, u + v = f
  
field = m × B.
52. Derive the refraction at a spherical surface,
34. Principle, Construction, Working of a moving n2 n n -n
coil galvanometer. Also define current – 1 = 2 1
v u cos r
sensitivity and voltage sensitivity. 53. Derive the len’s marker’s formula for a double
1
35. Conversion of galvanometer into ammeter. convex lens; f = (n – 1) 1 – 1[ ]
R1 R2
Conversion of galvanometer into voltmeter. 54. Derive equivalent focal length and power of two thin
lenses in contact 1 = 1 + 1 or P = P1 + P2
V Magnetism and Matter F f1 f2
36. Derive an expression for the magnetic field (A + Dm)
Sin 2
along the axis of a solenoid or bar manget. 55. Derive the prism formula, n =
 2m Sin A/2
Baxial = 0 r3 56. Explain the working of a simple microscope
4
37. Dervie an expression for potential energy of a and show that its magnification ‘m’ is given by
magnetic dipole in a uniform magnetic field, m = 1 + D/f
 
U = –mBCos = –m . B. 57. Explain the formation of image in a compound
microscope. Derive an expression for its
VI Electro Magnetic Induction magnifying power, m = f
–L
1+ f( D
e
)
38. Derive the motional emf from Faraday’s law, 0
58. Explain the formation of image in an
E = Blv.
astronomical telescope for a distant object.
39. Deduce an expression for the self inductance Derive its magnifying power.
of a long solenoid of N turns. (L = 0N2A/l) fe
40. Derive on expression for the mutual inductance
–f
m= 0 1+ D
fe
( )
of two long co-axial solenoids (M = 0n1 n2 Al)
41. Theory of A.C generator. Also principle and
working.
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IX Wave Optics
59. Deduce the Laws of reflection on the basis of
Huygen’s Wave theory.
60. Deduce the Snell’s law of refraction using
Huygen’s wave theory.

X Dual Nature of radiation and matter

61. Derive Einstein’s photo-electric equation. Use
this equation to explain the laws of phot electric
emission.

XI Atoms
62. Using Bohr’s postulates, derive an expression
for the radii of the permitted orbits in the
hydrogen atom. Also obtain an expression for
the total energy of an electron in nth orbit of an
atom. Also calculate the speed, frequency of
electron.

XIII Semi Conductor Devices

[Important connection diagrams and working
of devices]
63. Explain briefly with the help of a circuit
diagram, how V – I characteristics of a n
junction diode are obtained in (i) forward
bias (ii) reverse bias. Draw the shape of the
curves obtained.
64.. With the help of a circuit diagram, explain how
a Pn junction diode can be used as a half wave
rectifier. Draw the waveforms of input and
output voltage.
65. With the help of a labelled circuit diagram,
explain the use of junction diodes as a full wave
rectifier. Draw the input and output waveform.