33 Years NEET-AIPMT Chapterwise Solutions - Physics 2020
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Electromagnetic WavesTelegram @unacademyplusdiscounts73Speed of light, c = 3 × 10 8 m s –12. (a) : Here, R = 100 W, X c = 100 WArea, A = 15 cm 2 = 15 × 10 –4 m 2 as perpendicular to the direction of propagation of wave.2 2For a perfectly reflecting surface, the average forceNetimpedance, Z = R + X C = 100 2 Ωexerted on the surface isPeak value of displacement current= Maximum conduction current in the circuitIAF = = × × 4 −2 × × −4 22 2 25 10 Wm 15 10 mεc8 −1= 0 220 23×10 ms= = 22 . AZ 100 2= 250 × 10 –8 N = 2.50 × 10 –6 N3. (c) : Energy received in 1 minute = Intensity × Area 10. (b) : Frequency of electromagnetic wave does not× TimeE = (20 W/cm 2 ) × (20 cm 2 ) × (1 × 60 s) = 24 × 10 3 Jchange with change in medium but wavelength andvelocity of wave changes with change in medium.4. (b) : Energy of electromagnetic wave is equally Velocity of electromagnetic wave in vacuumdistributed in the form of electric and magnetic field 1energy, so ratio U =UE c =B 1 .∈ = υλ vacuum...(i)µ 0 0Velocity of electromagnetic wave in the medium5. (a) : Given : relative permittivity, e r = 1.44 and relativecvmedium permeability, m r = 11µ r ∈∈ = 0µ 0 r µ r ∈rεNow, as we know that, εr= ⇒ ε=εrε0where m r and ∈ r be relative permeability and relativeε0µpermittivity of the medium.and µ r = ⇒ µ = µ rµ0µFor dielectric medium, m r = 10cwhere, e and m are the permittivity and permeability of ∴ vmedium=the medium.∈ r\ Velocity of light in the medium will beHere, ∈ r = 4.0v =81 1 c 3×10c c= = =∴ v = =...(ii)mediumµε µµεε r 0 r 0 µε r r 1×1.444 2Wavelength of the wave in medium= 25 . × 10 8 m/svmediumc λvacuumλmedium= = =6. (b) : Velocity of em wave in a medium is given byυ 2υ2 (Using (i) and (ii))v = E×B∴ vi ̂= Ej ̂( ) × ( B) [ ∵ E 11. (a) : Compare the given equation with= Ej ̂ ( Given)]E = E 0 cos(kz – wt)As ̂i ̂j k̂= × , so B=Bk̂we get, w = 6 × 10 8 s –18 −1ω 6×10 sDirection of oscillating magnetic field of the em wave−1Wave vector, k = == 2 mwill be along +z direction.c 8 −13×10 ms7. (a) : Given: E rms = 6 V m –112. (b) : The amplitude of magnetic field and electricfield for an electromagnetic wave propagating in vacuumErmsErms= c or Brms=are related asBrmscE 0 = B 0 c6B rms = = 2× 10− 8Twhere c is the speed of light in vacuum.3 ×810B01∴ =BSince, Brms= 0 E0c13. (a) : The electromagnetic wave is propagating along2the +z axis.where B 0 is the peak value of magnetic field.Since the electric and magnetic fields are perpendicular−8∴ B0= Brms2 = 2× 10 × 2Tto each other and also perpendicular to the direction ofB 0 ≈ 2.83 × 10 –8 Tpropagation of wave.8. (b) : An accelerating charge is used to produceAlso, E× B gives the direction of wave propagation. ^ ^ ^ ^ ^oscillating electric and magnetic fields, hence the ∴ E= E0 i, B= B0j ( ∵ i × j=k)electromagnetic wave.14. (c) : In an electromagnetic wave both electric and9. (b) : Here, Energy flux, I = 25 × 10 4 W m –2magnetic vectors are perpendicular to each other as well
Telegram @unacademyplusdiscounts74 NEET-AIPMT Chapterwise Topicwise Solutions Physics15. (d) : As givenE = 10cos(10 7 t + kx)...(i)Comparing it with standard equation of e.m. wave,E = E 0 cos(wt + kx)...(ii)Amplitude E 0 = 10 V/m and w = 10 7 rad/s c = υλ =ωλ 2π82πc2π× 3×10or λ = == 188.4 mω 7107ω ω 10−1Also, c = or k = = = 0.033 mk c 3 ×810The wave is propagating along –x direction.16. (b) : Ey = N ⎡⎛× 6 rad ⎞ ⎛ −2rad ⎞ ⎤25 . ⎢t x⎝⎜2π10⎠⎟ − ×⎝⎜π10⎠⎟C⎥⎣ ms ⎦E z = 0 and E x = 0The wave is moving in the positive direction of x.This is the form E y = E 0 (wt – kx)w = 2p × 10 6 or 2pu = 2p × 10 6 ⇒ u = 10 6 Hz2π2π−= k ⇒ = π× 10 2 ⇒ λ= 2× 10 2 = 200 mλ λ17. (a) : The velocity of electromagnetic radiation in1vacuum isµε , where m 0 and e 0 are the permeability and0 0permittivity of vacuum.18. (c) : In electromagnetic wave, electric and magneticfield are in phase and perpendicular to each other andalso perpendicular to the direction of the propagation ofthe wave.19. (b) : According to Maxwell, the electromagneticwaves are those waves in which there are sinusoidalvariation of electric and magnetic field vectors at rightangles to each other as well as at right angles to thedirection of wave propagation.If the electric field ( E ) and magnetic field ( B ) arevibrating along Y and Z direction, propagation ofelectromagnetic wave will be along the X-axis. Therefore,the velocity of electromagnetic wave is parallel to E× B.20. (b) : λ= × 83 106= 3×10 m100 Hz121. (b) : c =µε (freespace)0 0v = 1 µε (medium) ∴ µ = c= µεv µε 0 022. (b) : The wave length of radiation used should beless than the size of the particlecSize of particle = λ = υ10−43 10143× 10 = × or υ = 10 hertzυHowever, when frequency is higher than this, wavelengthis still smaller. Resolution becomes better.23. (c) : As λ= hcEwhere the symbols have their usual meanings.Here, E = 15 keV = 15 × 10 3 eV and hc = 1240 eV nm∴ λ =1240 eV nm= 0.083 nm315 × 10 eVAs the wavelength range of X-rays is from 1 nm to10 –3 nm, so this wavelength belongs to X-rays.24. (c) : In microwave oven, the frequency of themicrowaves must match the resonant frequency of watermolecules so that energy from the waves is transferredefficiently to the kinetic energy of the molecules.25. (a) : The decreasing order of wavelength of thegiven electromagnetic waves is as follows:l Microwave > l Infrared > l Ultraviolet > l Gamma rays26. (b) : l m > l v > l x .In spectrum X-rays has minimum wavelength andmicrowave has maximum wavelength.27. (a) : Every body at all time, at all temperatures emitradiation (except at T = 0), which fall in the infraredregion.28. (c)29. (a) : As the electromagnetic radiations from Sunpass through the atmosphere, some of them are absorbedby it while other reach the surface of earth. The range ofwavelength which reaches earth lies in infrared region.This part of the radiation from the sun has shorterwavelength and can penetrate through the layer of gaseslike CO 2 and reach earth surface. But the radiation fromthe earth being of longer wavelength can escape throughthis layer. As a result the earth surface gets warm. This isknown as green house effect.30. (a) : The ozone layer absorbs the harmful ultravioletrays coming from sun.31. (a)32. (d) : The range is from 380 nm to even 200 nm to120 nm.33. (b) 34. (d)35. (b) : X-rays are used for the investigation ofstructure of solids.36. (d) : Radiations Wavelength [Range in m]X-rays 1 × 10 –11 to 3 × 10 –8g-rays 6 × 10 –14 to 1 × 10 –11Microwaves 10 –3 to 0.3Radiowaves 10 to 10 4vvv
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74 NEET-AIPMT Chapterwise Topicwise Solutions Physics
15. (d) : As given
E = 10cos(10 7 t + kx)
...(i)
Comparing it with standard equation of e.m. wave,
E = E 0 cos(wt + kx)
...(ii)
Amplitude E 0 = 10 V/m and w = 10 7 rad/s
c = υλ =
ωλ 2π
8
2πc
2π
× 3×
10
or λ = =
= 188.
4 m
ω 7
10
7
ω ω 10
−1
Also, c = or k = = = 0.
033 m
k c 3 ×
8
10
The wave is propagating along –x direction.
16. (b) : Ey = N ⎡⎛
× 6 rad ⎞ ⎛ −2
rad ⎞ ⎤
25 . ⎢
t x
⎝
⎜2π
10
⎠
⎟ − ×
⎝
⎜π
10
⎠
⎟
C
⎥
⎣ m
s ⎦
E z = 0 and E x = 0
The wave is moving in the positive direction of x.
This is the form E y = E 0 (wt – kx)
w = 2p × 10 6 or 2pu = 2p × 10 6 ⇒ u = 10 6 Hz
2π
2π
−
= k ⇒ = π× 10 2 ⇒ λ= 2× 10 2 = 200 m
λ λ
17. (a) : The velocity of electromagnetic radiation in
1
vacuum is
µε , where m 0 and e 0 are the permeability and
0 0
permittivity of vacuum.
18. (c) : In electromagnetic wave, electric and magnetic
field are in phase and perpendicular to each other and
also perpendicular to the direction of the propagation of
the wave.
19. (b) : According to Maxwell, the electromagnetic
waves are those waves in which there are sinusoidal
variation of electric and magnetic field vectors at right
angles to each other as well as at right angles to the
direction of wave propagation.
If the electric field ( E ) and magnetic field ( B ) are
vibrating along Y and Z direction, propagation of
electromagnetic wave will be along the X-axis. Therefore,
the velocity of electromagnetic wave is parallel to E
× B
.
20. (b) : λ= × 8
3 10
6
= 3×
10 m
100 Hz
1
21. (b) : c =
µε (freespace)
0 0
v = 1 µε (medium) ∴ µ = c
= µε
v µε 0 0
22. (b) : The wave length of radiation used should be
less than the size of the particle
c
Size of particle = λ = υ
10
−4
3 10
14
3× 10 = × or υ = 10 hertz
υ
However, when frequency is higher than this, wavelength
is still smaller. Resolution becomes better.
23. (c) : As λ= hc
E
where the symbols have their usual meanings.
Here, E = 15 keV = 15 × 10 3 eV and hc = 1240 eV nm
∴ λ =
1240 eV nm
= 0.
083 nm
3
15 × 10 eV
As the wavelength range of X-rays is from 1 nm to
10 –3 nm, so this wavelength belongs to X-rays.
24. (c) : In microwave oven, the frequency of the
microwaves must match the resonant frequency of water
molecules so that energy from the waves is transferred
efficiently to the kinetic energy of the molecules.
25. (a) : The decreasing order of wavelength of the
given electromagnetic waves is as follows:
l Microwave > l Infrared > l Ultraviolet > l Gamma rays
26. (b) : l m > l v > l x .
In spectrum X-rays has minimum wavelength and
microwave has maximum wavelength.
27. (a) : Every body at all time, at all temperatures emit
radiation (except at T = 0), which fall in the infrared
region.
28. (c)
29. (a) : As the electromagnetic radiations from Sun
pass through the atmosphere, some of them are absorbed
by it while other reach the surface of earth. The range of
wavelength which reaches earth lies in infrared region.
This part of the radiation from the sun has shorter
wavelength and can penetrate through the layer of gases
like CO 2 and reach earth surface. But the radiation from
the earth being of longer wavelength can escape through
this layer. As a result the earth surface gets warm. This is
known as green house effect.
30. (a) : The ozone layer absorbs the harmful ultraviolet
rays coming from sun.
31. (a)
32. (d) : The range is from 380 nm to even 200 nm to
120 nm.
33. (b) 34. (d)
35. (b) : X-rays are used for the investigation of
structure of solids.
36. (d) : Radiations Wavelength [Range in m]
X-rays 1 × 10 –11 to 3 × 10 –8
g-rays 6 × 10 –14 to 1 × 10 –11
Microwaves 10 –3 to 0.3
Radiowaves 10 to 10 4
vvv