Important Question Of Physics
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1. Define linear harmonic motion and angular harmonic motion. Derive the equation of simple harmonic motion.
2. A meter stick suspended from one end swings as a compound pendulum; (a) what is the period of oscillation, (b) what would be the length of the simple pendulum that would have the same period.
3. What is the time period of a particle executing simple harmonic motion? Discuss the theory of spring-mass system and derive an expression for its time period and frequency.
4. Why is really S.H.M rare? Deduce the expression for the time period of a compound pendulum and establish the interchangeability of center of oscillation and suspension.
5. Distinguish between simple and compound pendulum. Deduce the time period of a compound pendulum and show that it is minimum when the length of the pendulum is equal to radius of gyration.
6. Derive an expression for the time period of simple pendulum and show that the energy of a body in simple harmonic motion is conserved.
7. Define compound pendulum. Show that the point of oscillation lies beyond the center of gravity. 8. Derive the equation of plane progressive wave in differential form.
9. What is wave motion and what are the types of waves according to their origin, explain in short? Derive an expression for average power transmitted due to wave travelling in a stretched string.
10. Derive the speed of wave on a stretched string.
11. Derive the energy, power and intensity of plane progressive wave, also show that the power and intensity are directly proportional to square of amplitude.\
12. Explain the relation between particle velocity and wave velocity.
13. Show that the reverberation time is inversely proportional to velocity of sound and absorption coefficient.
14. Explain ultrasonic wave with its properties, method of production and application.
15. Define reverberation, reverberation time and absorption coefficient. Derive the Sabine’s reverberation relation in FPS system with physical meaning and significance.
16. What is stimulated emission? Describe working principle of ruby laser and He-Ne laser.
17. Write down the requirements for a good acoustics hall and derive a relation for the reverberation time.
18. Obtain relation between transition probabilities for spontaneous and stimulated emissions of radiation.
19. Write down the principles of laser action and explain the construction and working principle of He-Ne laser and Ruby laser.
20. Write down the characteristics of laser beam. Also, explain the main applications of laser in various fields.
21. What is optical fiber? Describe the working principle and its main application in various fields.
22. What are single mode and multimode fibers? What are the advantages of cladding on a fiber and graded index fibers?
23. What is thin film, explain the phenomenon of interference in thin film by reflected and refracted rays.
24. What are Newton’s rings? How are they produced? Find the wave length of refracted light by this method.
25. Define coherent waves, Give the necessary theory, the Newton’s rings method for the determination of wave length of monochromatic light.
26. Discuss the analytical treatment of interference and energy distribution in Young’s double slit experiment.
27. Show that the spacing between rings goes on decreasing with increased order in Newton’s ring due to reflected system.
28. What do you mean by plane diffraction grating? Give the theory of plane transmission grating with intensity diagram.
29. Explain Fraunhofer’s diffraction pattern obtained with a narrow slit and illuminated by a parallel beam of monochromatic light.
30. Define the phenomena of interference and diffraction of light? Give the necessary theory for the diffraction of light from plane transmission grating.
31. What do you mean by plane diffraction grating?
32. Give the necessary theory of plane transmission grating with intensity diagram.
33. State Brewster’s law. Explain polarization by reflection and discuss Malus law of polarization.
34. What is plane polarized light? Explain the phenomenon of double refraction. Describe the construction and working of Nicol prism.
35. What is optical activity and specific rotation? What is specific rotation of light? Explain how it is determined in laboratory.
36. Explain Gauss law in free space. Apply Gauss law of electrostatics for two different cases.
37. Derive the relation of three vectors in dielectrics.
38. Explain the atomic view of resistivity and show that; ⍴ = π ππ 2π , where symbols carry their usual meaning.
39. Show that, π½ = ππΈ. Explain why resistivity of a conductor increases with temperature.
40. Two concentric spheres with same charge density () of radii x and y carry charges q1 and q2 respectively. Show that, the electric potential at the common centre is; V = π (π₯+π¦) ∈0 .
41. What is electric field intensity? Show that electric field due to dipole along axis is double than that of electric field along equatorial line?
42. What is electric potential? Show that, π ∝
1π1, π ∝1π2 and π ∝1π3for electric
monopole, dipole and quadrupole respectively.
43. What is electric field intensity? Show that, E ∝
12, πΈ ∝1π3 and πΈ ∝1π4for electric
monopole, dipole and quadrupole respectively.
44. Derive the expression for the electric field intensity at any point due to electric
dipole and specify for a point at axial line and at equatorial line.
45. Show that electric potential due to quadrupole along axis is double than that of
electric potential along equatorial line in magnitude?
46. Write the circuit equation for a charging and discharging of RC circuit. Solve it to
find charge and current. Provide quantitative sketch for the charge and current
varying with time.
47. What is capacitor? Derive the expression of capacitance of cylindrical capacitor
with inner and outer electrode r1 and r2 respectively.
48. What is energy density? Determine an expression for energy stored on a charged
capacitor.
49. State and discuss Biot and Savart law for magnetic field strength due to a current
carrying circular coil with its special cases.
50. Among Ampere’s law and Biot-Savart’s law, which do you prefer? Obtain the
expression for the magnetic field due to a current circular solenoid using both law.
51. Describe about Hall-effect with its application. Derive an expression for Hall
coefficient, Hall Voltage and establish the relation with mobility of charge carriers
and conductivity of the material of wire.
52. Derive an expression for the growth and decay of current in LR circuit. Explain the
meaning of inductive time constant.
53. Show that the current through the circuit never exceed saturation current?
54. Show that the magnetic field strength at the center of a rectangular loop of wire of
length l and width b, carrying current I is given by, π΅π =
2 π0πΌ √π2+π2πππ.
55. A straight wire segment of length L carries a current I. Show that the magnetic field
B associated with this segment at a distance R from the segment along a
perpendicular bisector is given by =
Β΅0πΌ2ππ πΏ√πΏ2+4π 2. Show that this results to an expected result as πΏ → ∞ .
56. Derive the expression for force per unit length between two parallel current carrying
conductors.
57. Explain Faraday’s law and Lenz’s law of electromagnetic induction. Discuss the
concept of self-induction and mutual induction.
58. Define Lorentz force with its examples.
59. Write the circuit equation for a charging RC circuit. Solve it to find charge and
current with qualitative sketch varying with time. Provide the meaning of capacitive
time constant.
60. Derive the differential equation of the driven oscillation of RLC circuit with ac the
expression for the current amplitude for ac current source.
61. Write the Maxwell's equation in differential form and their significance. Using
Maxwell's equations.
62. Starting from; ∇ × π΅ = π0( π½ + π0ππΈππ‘ ), prove that ∇. πΈ =π∈0.
63. Starting from Maxwell’s third equation, derive second equation in free space.
64. “Ampere’s law cannot justify the continuity equation”, Explain this. Also explain
its modification.
65. Define pointing vector. Show that the intensity of electro-magnetic wave equals the
Average magnetic energy density times the speed of light.
66. Distinguish between the particle velocity and wave velocity. Also obtain the
relation between them.
67. Show that the electromagnetic wave is travelling with the velocity of light.
68. Write set of Maxwell equations and derive them starting from integral form with
their physical significance.
69. Derive electromagnetic wave equation in free space and dielectric medium.
70. Define displacement current.
71. Starting from Maxwell equation derive the equation of continuity.
72. What is wave function? Derive the expression for time dependent and independent
SchrΓΆdinger equation.
73. A particle is in motion along a line between x = 0 and x = l with zero potential
energy. At points for which x < 0 and x > l, the potential energy infinite. Using this
condition, derive an expression for the energy and the normalized wave function
for the particle in the nth state.
74. An electron is trapped in an one dimensional infinite potential well having width
“l” such that;
π= ∞ πππ π₯ ≤ 0 πππ π₯ ≥ l
π=0 πππ 0 < π₯ < l
75. Prove that the energy levels are quantized, when the electron is confined in an
infinite potential well of width “a”.
76. What are superconductors? Define their type.
77. Explain the distinction between superconductors using Meissner effect and BCS
theory.
78. Explain the classification of solids on the basis of band theory.
79. What do you mean by semiconductors? Explain the term intrinsic and extrinsic
semiconductors.
80. How superconductors differ from perfect conductors? Give basic properties and
uses of superconductors.
81. A physical pendulum consists of a meter stick that is pivoted at a small hole drilled
through the stick at a distance x from the cg. The period of oscillation is observed
to be 2.5 sec. Find the distance x. [5.57 cm]
82. A body of mass 0.3 kg executes SHM with a period 2.5 sec and amplitude of 4 cm.
Calculate the amplitude, velocity, acceleration and kinetic energy.
[v = 0.1 m/s, a = 0.252 m/s2and 1.5 x 10-3Joule]
83. A meter stick suspended from one end swings as a physical pendulum. Calculate
the frequency of oscillation. [0.61 Hz]
84. The equation of transverse wave travelling in a rope is given by y =10sin (0.01x – 2t)
centimeters. Find the amplitude, frequency, velocity and wave length of the wave. [ 10 cm,
2 m/s, 1 Hz and2 m]
85. A wire has a torsional constant of 2 Nm/rad. A disk of radius 5 cm and mass 100
gm is suspended at its center. What is the frequency of torsional oscillations? [20.12
Hz]
86. A solid sphere of mass 2 kg and diameter 0.30 m is suspended on a wire. Find the
period of angular oscillation for small displacements of torque constant of wire is 6
x 10 -3 Nm/rad. [10.9 sec]
87. A body of mass 100 gm is suspended from a spring of negligible mass and is found
to stretch the spring 1 cm. a) What is the force constant of spring? b) What is the
period of oscillation of the body if pulled down and released? [98 N/m
and 0.2 sec]
88. A small body of mass 0.1 kg is undergoing a SHM of amplitude 0.1 m and period
2 sec. a) What is the maximum force in the body? b) If the oscillations are produced
in the spring, what should be the force constant? [0.0986 N and 0.986 N/m]
89. A block is in SHM on the end of a spring with position is, π₯ = π₯π sin(ππ‘ + π) .
If π =π5
radian, then at t = 0 what percentage of the total mechanical energy is
potential energy? [34.54 %]
90. A sinusoidal wave travels along a string. The time for a particular point to move
from maximum displacement to zero is 0.17 S. What are the, a) period and
frequency and b) if the wavelength is 1.40m, what is the wave speed? [1.47 Hz
and 2.05 m/s]
91. The speed of a transverse wave on a string is 170 m/s when the string tension is 120
N. To what value must the tension be changed to raise the wave speed to 180 m/s?
[134.5 N]
92. A wave travelling along a string is described by π¦(π₯,π‘) = 0.00327 π ππ(72.1π₯ −
2.72π‘) in which the numerical constants are in SI units (0.00327 m, 72.1 rad/m, and
2.72 rad/s). a) What is the amplitude of this wave? b) What are the wavelength,
period, and frequency of this wave? c) What is the velocity of this wave? d) What
is the displacement y at x = 22.5 cm and t = 18.9 S? [3.27 mm, 8.71 cm, 2.31 S
0.433 Hz, 3.77 cm/S and displacement 1.92 mm]
93. A string has linear density Β΅ = 525 g/m and tension = 45 N. We send a sinusoidal
wave with frequency f = 120 Hz and amplitude ym = 8.5 mm along the string. At
what average rate does rate do the wave transport energy? [100 W]
94. The volume of a room is 980 m2. The wall area of the room is 150 m2, ceiling area 95 m2and floor area is 90 m2. The average sound absorption coefficient a) for wall is 0.03, b) for ceiling is 0.80 and c) for the floor is 0.06. Calculate the average sound absorption coefficient and reverberation time. [ 85.76 metric Sabines and 1.80 sec]
95. A room has dimensions 6 x 4 x 5 m. Find a) the mean free path of the sound wave
in the room. b) Number of reflections made per sec by sound waves with the walls
of the room. Given velocity of sound in air = 350 m/s. [3.242 m and 108]
96. In an experiment on Newton’s rings the light has a wavelength of 600 nm. The lens
has a refractive index of 1.5 and a radius of curvature of 2.5 m. Find the radius of
5th bright fringe. [2.6x10-3 m]
97. A beam of monochromatic light of wavelength 5.82 x 10-7 m falls normally on a
glass wedge with the wedge angle of 20 seconds of an arc. If the refractive index of
glass is 1.5, find the number of dark interference fringes per cm of the wedge length.
[ 5 fringes per cm]
98. Light of wavelength 600 nm falls normally on a thin wedge-shaped film of
refractive index 1.4 forming that are 2 mm apart. Find the angle of wedge. [1.07
x 10-4
rad]
99. Two identical sinusoidal waves moving in the same direction along a stretched
string interfere with each other. The amplitude of each wave is 9.8 mm and the
phase difference between them is 1000
. What is the amplitude of resultant wave?
[12.6 mm]
100. In Newton’s ring experiment the diameter of the 10th ring changes from 1.4 to
1.27 cm when a liquid is introduced between the lens and the plate. Calculate the
refractive index of the liquid. [1.215]
101.In Newton’s ring experiment the radius of 4th and 12th rings are 0.26 cm and 0.37
cm respectively. Find the diameter of 24th dark ring. [0.912 cm]
102.Newton’s rings formed by sodium light between a flat glass plate and a convex
lens are viewed normally. What will be the order of the dark ring which will have
double the diameter of 40th ring? [160]
103.A thin film ( =1.5) suspended in air is 0.41 m thick and is illuminated with
white light incident perpendicularly on its surface. At what wavelength will
visible light that is reflected from the two surfaces of the film undergo fully
constructive interference? [82 x 107 m]
104.A beam of parallel rays is incident at an angle of 300 with the normal on a plane
parallel film of thickness 4 x 10 -5 cm and refractive index 1.5. Show that the
reflected light whose wavelength is 7.539 x 10-5 cm, will be strengthened by
reinforcement. [Show, (2n-1) = 3]
105.In Young’s double slit experiment, the separation of two slits 0.2 mm apart and
third bright fringe is at 7.5 mm from the central fringe on a screen 1 m away from
the slits. Find the wavelength of light. [5.0 x 10 – 7 m]
106.In a Newton’s rings experimental the diameter of 20th ring was found to be 0.590
cm and that of the 10th ring was 0.336 cm. If the radius curvature of the planoconvex lens is 100 cm. Calculate the wavelength of light used. [5.88 x 10 – 5
cm]
107.In a Newton’s ring experiment, the light has a wavelength 600 nm. The lens has a
refractive index 1.5 and a radius of curvature 2.5 m. Find the radius of 5th bright
fringe. [2.6 x 10 – 3 m]
108.Newton’s rings are observed in reflected light of wavelength 5900 A0. The
diameter of 10th dark ring is 50 mm. Find the radius of curvature of lens and
thickness of air film. [2.95 x 10 – 4
cm]
109.Calculate the second order angles for the light of wavelength 400 nm and 700 nm,
if the grating contains 10,000 lines/cm. [53.10
and impossible]
110. A parallel beam of sodium light is incident normally on a diffraction grating. The
angle between the two first order spectra on either side of the normal is 27042’.
Assuming that the wavelength of light is 589.3 nm, find the number of lines per
mm on the grating? [406 lines/mm]
111.Light of wavelength 600 nm is incident normally on slit of width 0.1 mm. Calculate
the intensity at angle of diffraction of 0.20. [0.28I0]
112.Determine the angular separation between central maxima and first order
maximum of the diffraction pattern due to a single slit of width 0.25 mm, when
light of wavelength 5890 A0is incident on it normally. [0.130]
113.How wide is the central diffraction peak on a screen 3.5 m behind a 0.01 mm slit
illuminated telescope by 500 nm light? [0.35 m]
114.Light of wavelength 5500A0
falls normally on a slit of width 25 x 10-5
cm. Calculate
the angular position of first two minima on either side of central maxima. [12.70 and 260]
115.How many lines per cm are there in a grating which gives an angle of diffraction of 300
in first order spectrum of light of wavelength 6 x 10-5
cm. [8333]
116.How many orders will be visible if the wavelength of incident radiations is 4800 A0
and
the number of lines on the grating is 2500 per inch. [Approx. 21]
117.Deduce the missing orders for a double slit Fraunhofer diffraction pattern, if the slit widths
are 0.16 mm and they are 0.8 mm apart. [The orders 6, 12, 18, … will be missed]
118.A 200 mm long tube and containing 48 cm3 of sugar solution produces an optical
rotation 110 when placed on a saccharimeter. If the specific rotation of sugar
solution is 660
, calculate the quantity of sugar contained in the tube in the form of
solution. [4 gm]
119.Find the specific rotation of a sample of sugar solution if the plane of polarization
is turned through 460. The length of the tube containing 20 % solution is 20 cm.
[1150]
120.The thickness of calcite plate to produce plane polarized light is 8.56 x 10-5
cm, the principal refractive indices are Β΅0 = 1.658, Β΅E = 1.486 and = 5890 A0
. Find the type of wave plate. [quarter wave]
121.A sugar solution produces an optical rotation of 9.90when placed in a tube of length 20 cm. If the specific rotation of sugar is 660, find the concentration of sugar in gram per liter. [75 gm/liter]
122.Calculate the polarizing angle for the light travelling from water, of refractive
index 4/3 to glass of refractive index 3/2. [63.430
]
123.A beam of light is incident at polarizing angle on a piece of transparent materials
of refractive index 1.62. What is the angle of refraction for the transmitted beam?
[31.70]
124. 80 gm of impure sugar when dissolved in a liter of water, gives an optical rotation
of 9.90, when placed in a tube of length 200 mm. If the specific rotation of sugar is
66 degree/dm/(gm/cc), find the percentage purity of sugar sample. [93.75%]
125.What is the transition rate for the neon atom in a He-Ne laser, if the energy drop
for the 632.8 nm emission is 1.96 eV and the power output is 1.0 mW?
[3x1015/sec]
126.What is the magnitude of point charge chosen so that the electric field 50 cm away
has magnitude of 2 N/C? [5.5 x 10-11 C]
127.The electric potential V (in volts) varies with x (in meter) according to the relation
V = 5 + 4x2
. Calculate the force experienced by a negative charge of 2 x 10-6 C
located at x = 0.5 m. [8 x 10-6 N]
128.What will be the potential at the center of the square of side 23 cm, if the charges
1 Β΅C, -2 Β΅C, -3 Β΅C and 4 Β΅C are placed at the corners. [0 volts]
129.If the charge on a capacitor is increased by 2 C, the energy stored in it increased
by 21%. Find the original charge on the capacitor. [20 C]
130.Show that the capacitance due to a charged sphere of radius ‘r’ is 40r. The total
charge on the sphere is supposed to be concentrated at the center.
131.A capacitor of capacitance C is discharged through a resistor of resistance R. After
how many time constants is the stored energy becomes one fourth of the initial
value. [t = 0.693]
132. A capacitor of capacitance C is charged through a resistor of resistance R.
Calculate the time at which the potential across the resistor is equal to the potential
across the capacitor. [t = 0.693RC]
133.Two capacitors 2 Β΅F and 4 Β΅F are connected in parallel across 300 volts pd.
Calculate the total energy in the system. [0.27 Joule]
134.Obtain the charging time constant of a capacitor in a RC circuit such that current
through the resistor is decreased by 50 % of its peak value in 5 seconds. [7.21 sec]
135.If a dielectric is inserted into a space between charged capacitor having field E0
and charge density , prove that the induced charge density on the dielectric will
be ππ = (π−1π) π. Where k is the dielectric constant. [where k is greater than 1 and so π > ππ]
136.The relative permittivity of distilled water is 81. Calculate refractive index and
velocity of light in it. [3.33x107 m/s and 9.0]
137.Show that in a given volume, the magnetic energy density is equal to the electric
energy density.
138. Calculate the drift speed of electrons when 10 A current is supplied through a
copper wire of cross-sectional area 1 mm2
and electron density is 1028m-3
.
[6.25 x 10-3 m/sec]
139.What are, the a) mean time between collusions? b) the mean free path of free
electron in copper? (Given, n = 8.4x 1028 m-3
, = 1.7 x10-8 m, vavg = 1.6 x 106
m/s). [2.49 x 10-14sec and 3.98 x 10-8m]
140.In a Hall experiment a current of 3A is sent length wise through a conductor 1 cm
wide, 4 cm long and 10 micro meter thick produces a transverse (across the width)
Hall voltage of 10 micro volts, when a magnetic field of 1.5 T is passed
perpendicularly through the thickness of conductor. From these data find i) the
drift velocity of charge carriers ii) the number density of charge carriers.
[6.67 x 10-4m/sec and 2.8 x 1029electrons/ m3]
141.A copper strip 2 cm wide and 1 mm thick is placed in a magnetic field of 1.5 T. If
a current of 200A is set up in the strip, calculate i) Hall voltage ii) Hall mobility if the number of electrons per unit volume is 8.4 x 1028/m3and resistivity is 1.72 x 10-8 Ohm-m. [2.23 x 10-6 V and 231.12 m2v-1S-1]
142.A certain radio station broadcasts at a frequency at a frequency of 1020 kHz. At a
point some distance from the transmitter, the maximum magnetic field of the
electromagnetic wave if emits is found to be 1.6 × 10-6 T. (i) What is the speed of
propagation of wave? (ii) What is the wavelength? (iii) What is the maximum
electric field? [3x108 m/s, 294.12 m and 4.8 x 104 V/m]
143.An observer is at a distance of 1 m from the point source of light, whose power
output is 1 kW. Calculate the maximum value of electric and magnetic fields.
[0.82 x 10-6 T and 244.5 V/m]
144.An observer is at a distance of 1m from a source, which emits energy in the form
of monochromatic electromagnetic wave. The power of emission of 1000W and is
emitted with equal probability in all directions. Calculate the peak values of
electric intensity and magnetic flux density. [0.82 x 10-6 T and 244.5 V/m]
145.A certain radio station broadcasts at a frequency at a frequency of 1020 kHz. At a
point some distance from the transmitter, the maximum magnetic field of the
electromagnetic wave if emits is found to be 1.6 × 10-4 T. i) What is the speed of
propagation of wave? ii) What is the wavelength? iii) What is the maximum
electric field? [3 x 108 m/s, 294.12 m and 4.8 x 104 V/m]
146.A certain plane electromagnetic wave emitted by a microwave antenna has a
wavelength of 3 cm and a maximum magnitude of electric field of 2 x10 – 4 V/cm.
a. What is the frequency of wave?
b. What is maximum magnetic field?
c. What is maximum energy density?
d. What is the intensity of wave?
[1010 Hz, 0.67 x 10-10 T, 1.77 x 10-15 Joule and 5.33 x 10-7 W/m2]
147.A solenoid has an inductance of 100 mH and a resistance of 50 β¦. If it is connected
to a 2 V battery, how long will it take for a current to reach one half its final
equilibrium value? [1.386 x 10-3sec]
148.A circular loop of wire 5 cm in radius carries a current of 5 Amp. What is the
energy density at the center of the loop? [1.58 x 10-3Joule/m3]
149.How many time constant must we wait for the current in LR circuit to build up to
with in 0.1% of it’s equilibrium value. [t = 0.693]
150.A solenoid of inductance L and resistance R is connected to a battery. After how
many time constants the magnetic energy fall to one fourth of it’s maximum value.
[t = 0.693]
151.A 45 V potential difference is suddenly applied to a coil with L = 50 mH and R =
180. At what rate is the current increasing after 1.2 ms? [11.97 A/Sec]
152.A solenoid 1.3 m long and 2.6 cm in diameter carries a current of 18 A. The
magnetic field inside the solenoid is 23 mT. Find the length of the wire forming
the solenoid. [108 m]
153.What is the initial rate of increase of current and final saturation current in RL
circuit with L=15 mH, R=24 Ohm and emf = 10 volts? [666.67 A/S and 0.417 A]
154.A circuit has C =10 F, L=10 mH. How much resistance should be added to the
circuit, so that the frequency of oscillation will be 1% less than that of LC
oscillation? [63.25 Ohm]
155.The quality factor of an LCR circuit is 10,000 and its frequency is 100 Hz. What
will be the energy after 15.92 secs? [U = 0.34U0]
156.A 40 mH inductor and 1000 F capacitor from an oscillating circuit. What is the
peak value of current if the initial charge is 40C? [ 6.32 mA]
157.A football of 500 gm is confined between two impenetrable walls of a Futsal that
can be modeled as a box of length 100m. Calculate the minimum speed of the ball.
[6.63 x 10-36 m/s and so considered to be at rest]
158.Calculate the permitted energy levels of an electron in one dimensional potential
well of width 2 A0
. [1.5 x 10-8
n
2
Joules]
159.Sun light just outside the Earth’s atmosphere has an intensity of 1.4 kW/m2
.
Calculate maximum electric and magnetic fields for sun light, assuming it to be a
plane wave. [1.03 kV/m and 3.43 micro tesla]
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