1.
Which of the following statements is true? A.
The wavelength of microwaves is greater than that of UV-rays
B.
The wavelength of IR rays is lesser than that of UV-rays
C.
The wavelength of microwaves is lesser than that of IR rays
D.
Gamma rays has largest wavelength in the electromagnetic spectrum.
Answer :
Gamma rays has largest wavelength in the electromagnetic spectrum.
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$$G > X > U > V > I > M > R\,\left[ {{\text{frequency}}\,{\text{order}}} \right]$$
2.
The velocity of electromagnetic radiation in a medium of permittivity $${\varepsilon _0}$$ and permeability $${\mu _0}$$ is given by A.
$$\sqrt {\frac{{{\varepsilon _0}}}{{{\mu _0}}}} $$
B.
$$\sqrt {{\mu _0}{\varepsilon _0}} $$
C.
$$\frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }}$$
D.
$$\sqrt {\frac{{{\mu _0}}}{{{\varepsilon _0}}}} $$
Answer :
$$\frac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }}$$
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The velocity of electromagnetic waves in free space is given by
3.
In an apparatus, the electric field was found to oscillate with an amplitude of $$24\,V/m.$$ The magnitude of the oscillating magnetic field will be A.
$$6 \times {10^{ - 6}}T$$
B.
$$2 \times {10^{ - 8}}T$$
C.
$$8 \times {10^{ - 8}}T$$
D.
$$12 \times {10^{ - 6}}T$$
Answer :
$$8 \times {10^{ - 8}}T$$
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$$\frac{E}{B} = C \Rightarrow B = \frac{E}{C} = \frac{{24}}{{3 \times {{10}^8}}} = 8 \times {10^{ - 8}}T$$
4.
Given below is a list of electromagnetic spectrum and its mode of production. Which one does not match? A.
Gamma rays - Radioactive decay of the nucleus
B.
Ultraviolet rays - Magnetron valve
C.
Radio wave - Rapid acceleration and deceleration of electrons in conducting wires
D.
X-rays - coolidge tube
Answer :
X-rays - coolidge tube
5.
Which of the following has/have zero average value in a plane electromagnetic wave? A.
Both magnetic and electric fields
B.
Electric field only
C.
Magnetic field only
D.
Magnetic energy
Answer :
Both magnetic and electric fields
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Both magnetic and electric fields have zero average value in a plane $$e.m.$$ wave.
6.
In an apparatus, the electric field was found to oscillate with an amplitude of $$18\,V/m.$$ The magnitude of the oscillating magnetic field will be A.
$$4 \times {10^{ - 6}}T$$
B.
$$6 \times {10^{ - 8}}T$$
C.
$$9 \times {10^{ - 9}}T$$
D.
$$11 \times {10^{ - 11}}T$$
Answer :
$$6 \times {10^{ - 8}}T$$
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$$c = \frac{E}{B} \Rightarrow B = \frac{E}{c} = \frac{{18}}{{3 \times {{10}^8}}} = 6 \times {10^{ - 8}}T.$$
7.
In a plane electromagnetic wave propagating in space has an electric field of amplitude $$9 \times {10^3}\,V/m,$$ then the amplitude of the magnetic field is A.
$$2.7 \times {10^{12}}T$$
B.
$$9.0 \times {10^{ - 3}}T$$
C.
$$3.0 \times {10^{ - 4}}T$$
D.
$$3.0 \times {10^{ - 5}}T$$
Answer :
$$3.0 \times {10^{ - 5}}T$$
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$${B_0} = \frac{{{E_0}}}{c} = \frac{{9 \times {{10}^3}}}{{3 \times {{10}^8}}} = 3 \times {10^{ - 5}}T.$$
8.
If $${\lambda _v},{\lambda _x}$$ and $${\lambda _m}$$ represent the wavelengths of visible light, X-rays and microwaves respectively, then A.
$${\lambda _m} > {\lambda _x} > {\lambda _v}$$
B.
$${\lambda _v} > {\lambda _m} > {\lambda _x}$$
C.
$${\lambda _m} > {\lambda _v} > {\lambda _x}$$
D.
$${\lambda _v} > {\lambda _x} > {\lambda _m}$$
Answer :
$${\lambda _m} > {\lambda _v} > {\lambda _x}$$
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Wavelength order of given rays are listed below
Waves
Wavelength (in $$\mathop {\text{A}}\limits^ \circ $$)
Visible light
4000 - 7000
X-rays
$${10^{ - 3}} - {10^2}$$
Microwaves
$${10^7} - {10^9}$$
So, $${\lambda _m} > {\lambda _v} > {\lambda _x}$$
9.
Which of the following is the correct equation for magnetic field as a function of $$x,$$ and $$t$$ where a plane electromagnetic wave propagating in the $$x$$-direction has a wavelength of $$5.0\,mm$$ ? The electric field is in the $$y$$-direction and its maximum value is $$30\,V{m^{ - 1}}.$$ A.
$$B = {10^{ - 3}}\sin \left[ {\frac{{2\pi }}{{5 \times {{10}^{ - 3}}}}\left( {ct - x} \right)} \right]$$
B.
$$B = {10^{ - 7}}\sin \left[ {\frac{{2\pi }}{{5 \times {{10}^{ - 3}}}}\left( {ct - x} \right)} \right]$$
C.
$$B = {10^{ - 5}}\sin \left[ {\frac{\pi }{{1.5 \times {{10}^{ - 3}}}}\left( {ct - x} \right)} \right]$$
D.
None of these
Answer :
$$B = {10^{ - 7}}\sin \left[ {\frac{{2\pi }}{{5 \times {{10}^{ - 3}}}}\left( {ct - x} \right)} \right]$$
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$$\eqalign{
& E = {E_0}\sin \omega \left( {t - \frac{x}{c}} \right);B = {B_0}\sin \omega \left( {t - \frac{x}{c}} \right) \cr
& {I_d} = {I_0}\sin \left( {\omega t + \frac{\pi }{2}} \right) = I\,{\text{and}}\,\omega = 2\pi v = \frac{{2\pi }}{\lambda }c \cr
& {E_0} = 30\sin \left[ {\frac{{2\pi }}{{5 \times {{10}^{ - 3}}}}\left( {ct - x} \right)} \right]\,{\text{and}}\,{B_0} = \frac{{{E_0}}}{C} = {10^{ - 7}}T, \cr
& B = {B_0}\sin \left[ {\frac{{2\pi }}{\lambda }\left( {ct - x} \right)} \right] \cr
& = {10^{ - 7}}\sin \left[ {\frac{{2\pi }}{{5 \times {{10}^{ - 3}}}}\left( {ct - x} \right)} \right] \cr} $$
10.
Which of the following waves have the maximum wavelength A.
X-rays
B.
I.R. rays
C.
UV rays
D.
Radio waves
Answer :
Radio waves
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$${\lambda _{{\text{Radiowave}}}} > {\lambda _{{\text{IR}}\,{\text{ways}}}} > {\lambda _{{\text{UV}}\,{\text{rays}}}} > {\lambda _{{\text{x - rays}}}}$$