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Question 12 Marks
Write characteristics of electro magnetic waves.
Answer
Characteristics of EM waves are as follows :
(1) In EM wave, the electric field, magnetic field and direction of wave propogation are mutually perpendicular.
(2) Relationship between the values / magnitudes of electric field and magnetic field in EM wave is :
$\frac{ E _0}{B_0}=c \text { or } \frac{ E _{ rms }}{ B _{ rms }}=c$
(3) EM waves are transverse and non-mechanical waves.
(4) Velocity of EM waves in vacuum, $c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$
where, $\mu_0$ - permeability of free space
$\varepsilon_0$ - permittivity of free space
 →Velocity of EM waves in medium, $v=\frac{1}{\sqrt{\mu \varepsilon}}$ where, $\mu$ - permeability of medium $\varepsilon$ - permittivity of medium
(5) As demonstrated by scientist Hertz, the EM waves experience diffraction, refraction and polarisation.
(6) EM waves are polarized.
(7) EM waves possess and carry energy, which is known as radiation energy.
(8) When an EM wave strikes (/ is incident) on a surface, it exerts pressure, which is called radiation pressure.
(9) Direction of $\vec{E} \times \vec{B}$ shows the direction of propogation of wave.
(10) In the region of space far from the source, the oscillations of electric field and magnetic field vectors are in phase.
(11) Energy density in EM wave, $\varrho=\varepsilon_0 E _{\text {rms }}^2$ and $\varrho=\frac{ B _{\text {rms }}^2}{\mu_0}$.
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Question 22 Marks
Write Maxwell's equations.
Answer
→(1) $\oint \overrightarrow{ E } \cdot \overrightarrow{d A}=\frac{ Q }{\varepsilon_0}$ (Gauss's Law for electricity)
(2) $\oint \overrightarrow{ B } \cdot \overrightarrow{d A}=0$ (Gauss's Law for magnetism)
(3) $\oint \overrightarrow{ E } \cdot \overrightarrow{d l}=\frac{-d \phi_{ B }}{d t}$ (Faraday's Law)
(4) $\oint \overrightarrow{ B } \cdot \overrightarrow{d l}=\mu_0 i_c+\mu_0 \varepsilon_0 \frac{d \phi_{ E }}{d t}$
(Ampere - Maxwell Law)
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Question 32 Marks
Write a short note on Infrared waves.
Answer
$\rightarrow IR ($Infrared$)$ waves are produced by hot bodies and molecules.
$\rightarrow I.R$. waves are sometimes referred to as heat waves. This is because water molecules present in most materials readily absorb infrared waves. $($many other molecules, for example, $CO_2, NH_3$ also absorb infrared waves$)$ After absorption, their thermal motion increases, that is, they heat up and heat the surroundings.
$\rightarrow$ Range of wavelength from $7 \ mm$ to $700 \ nm.$
$\rightarrow$ Infrared lamps are used in physical therapy.
$\rightarrow$ Infrared radiation also plays an important role in maintaining the earth's warmth or average temperature through the greenhouse effect.
$\rightarrow I.R$. detectors are used in Earth satellites, both for military purposes and to observe growth of crops.
$\rightarrow$ Electronic devices $($semiconductor $LEDs)$ also emit infrared and are widely used in remote switches of household electronic systems such as, $TV$ sets, Video recorders and hi$-$fi systems.
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Question 42 Marks
Write a short note on Ultra violet rays.
Answer
$\rightarrow$ Wave length range: from $4 x 10^{-7} m (400 \ nm) to 6 \times 10^{-10} m (0.6 \ nm)$
$\rightarrow U.V. (or UV)$ radiation is produced by special lamps and very hot bodies.
$\rightarrow UV$ light in large quantities has harmful effects on humans.
$\rightarrow$ Exposure to $UV$ radiation induces the production of more melanin, causing tanning of the skin, which is known as Sunburn.
$\rightarrow$ The Ozone layer in the atmosphere at an altitude of about $40-50 \ km$ absorbs the $UV$ rays coming from the sun. In this way, it acts as a protecting shield for humans. Depletion of Ozone layer by chlorofluoro carbons $(CFCs$) gas $($such as freon$)$ is a matter of concern.
$\rightarrow$ Welders wear special glass goggles or face masks with glass windows to protect their eyes from large amount of $UV$ produced by welding arcs. $($Because $UV$ radiation is absorbed by ordinary glass.$)$
$\rightarrow UV$ radiations can be focused into very narrow beams for high precision applications such as $LASIK ($Laser assisted in situ keratomileusis.$)$ eye surgery.
$\rightarrow UV$ lamps are used to kill germs in water purifiers.
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Question 52 Marks
Write a short note on radio waves.
Answer
→Radio waves are produced by the accelerated motion of charges in conducting wires.
→They are used in radio and television communication systems.
→Frequency range: from 500 kHz to about 1000 MHz.
→Range of frequencies for different bands:
(i) AM (Amplitude Modulated) band: from 530 kHz to 1710 kHz
(ii) SW band: Up to 54 MHz
(iii) TV waves band: 54 MHz to 890 MHz
(iv) FM (Frequency Modulated) radio band: 88 MHz to 108 MHz
(v) UHF (Ultra High Frequency band: 300 MHz to 3000 MHz.
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Question 62 Marks
Explain some of the far reaching consequences of displacement current.
Answer
→The displacement current has some far reaching consequences.
→One key thing that can be noticed is that the laws of electricity and magnetism now seem (and can be represented) more symmetrical, though they are not perfectly symmetrical.
→Because the source of electric field are electric charges, which exist independently. Electric Mono poles (either positive or negative) exist independently. Unlike electric monopoles, magnetic mono poles do not exist. The source of Magnetic field are magnetic poles (North-N or South-S), but independent North pole or South pole doesn't exist.
→Faraday's law of induction states that there is an induced emf equal to the rate of change of magnetic flux. Now, since the emf between two points 1 and 2 is the work done per unit charge in taking it from 1 to 2, the existence of emf implies the existence of electric field.
→So, we can rephrase Faraday's law of electromagnetic induction by saying that, 'A magnetic field, changing with time, gives rise to an electric field. Then the fact that an electric field changing with time gives rise to a magnetic field, is the symmetrical counter part, and is a consequence of the displacement current being a source of magnetic field. Thus, time-dependent electric and magnetic fields give rise to each other.
→Faraday's law of electromagnetic induction and Ampere-Maxwell law give a quantitative expression of this statement.
→One very important consequence of this symmetry is the existence of electro magnetic waves.
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Question 72 Marks
Write a brief history of Electro Magnetic waves.
Answer
→Danish physicist Hans Christian Oersted was the first one to discover / notice that moving charges or Electric Current creates / produces magnetic field.
→Faraday discovered that emf and current is induced in a conductor, if the magnetic flux associated with it changes.
→As per the opinion of James Clerk Maxwell, not only an electric current but also a time-varying electric field generates magnetic field.
→When a capacitor is connected with a time- varying current, magnetic field is created in the region outside the capacitor.
→While applying the Ampere's circuital law to find magnetic field at a point outside capacitor, he found an inconsistency in the law. →To remove the inconsistency he suggested existence of an additional current, called by him, the 'displacement current.'
→Maxwell formulated a set of equations involving electric and magnetic fields, and their sources, the charge and current densities.
→These equations are knwon as Maxwell's equations.
→The most important prediction to emerge from maxwell's equations is the existence of electro-magnetic waves, which are (coupled) time-varying electric and magnetic fields that propogate in space.
→The speed of the waves, according to these equations, turned out to be very close to the speed of light $\left(3 \times 10^8 m / s \right)$. This led to a remarkable conclusion that light is an electro magnetic wave.
→Thus, Maxwell unified the domains of electricity, magnetism and light.
→In 1885, Hertz experimentally demonstrated the existence of electro magnetic waves. Their technological use has led to a revolution in the field of communication.
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Question 82 Marks
Write a short note on visible rays.
Answer
→Visible rays are the part of the EM spectrum which is detected by human eye.
→Frequency range: 4 $\times$ $10^{14}$ Hz to about 7 $\times$ $10^{14}$Hz.
→Wavelength range: About 700-400 nm (or 7000 A° to 4000 A°).
→The visible light emitted or reflected from objects around us provide us information about the world.
→Different animals are sensitive to different range of wave lengths. For example, Snakes can detect infrared waves, and the 'visible' range of many insects extends well into the ultra violet.
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Question 92 Marks
Write (or mention) the achievements of Maxwell's Electro Magnetic wave theory and Hertz's experiment.
Answer
→After Hertz's experiment, other scientists were also successful in generating electromagnetic waves of different frequencies.
→Seven years after Hertz, Jagdish Chandra Bose, working at Calcutta succeeded in producing and observing electro magnetic waves of shorter wave length (5 mm to 25 mm).
→At around the same time, Marconi in Italy succeeded in transmitting electromagnetic waves over distances of many kilometres.
→Marconi's experiment was the beginning of the field of communication using EM waves.
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Question 102 Marks
Explain the physical effect of displacement current.
Answer
→The displacement current has the same physical effect(s) as the conduction current.
→In some cases, for example steady electric fields in a conducting wire, the displacement current will be zero, since the electric field E does not change with time.
→In other cases, for example the charging capacitor above, both conduction and displacement currents may be present in different regions of space.
→In most of the cases, they both may be present in the same region of space, as there exists no perfectly conducting or perfectly insulating medium.
→Most interesting, there may be large regions of space where there is no conduction current, but there is only a displacement current due to time-varying electric fields. In such a region,we expect a magnetic field, through there is no (conduction) current source nearby.
→For example, a magnetic field at a point between the plates of a capacitor is seen to be the same as field at a point just outside the capacitor plates.
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Question 112 Marks
Provide brief information about electro- magnetic spectrum.
Answer
→At the time when Maxwell predicted the existence of EM waves, the only familiar EM waves were the visible light waves.
→The existence of ultraviolet waves (u.v.) and infrared (I.R.) waves was hardly established. By the end of the nineteenth century, x-rays and gamma rays had also been discovered.
→We now know that, EM waves include visible light waves, x-rays, gamma rays, radio waves, micro waves, ultraviolet and infrared waves.
→The classification of EM waves according to frequency is called Electro magnetic spectrum, which is shown in the figure.
Image
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Question 122 Marks
Write a short note on $X-$rays.
Answer
$\rightarrow$ The region of electro magnetic spectrum beyond the $UV$ region is called $X-$ray region.
$\rightarrow$ Range of wave length: $10^{-8}m(10 nm)$ to $10^{13}m (10^{-4}nm).$
$\rightarrow X-$rays can be generated by bombarding a metal target by high energy electrons.
$\rightarrow X-$rays are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer.
$\rightarrow$ Because $X-$rays damage $($or destroy$)$ living tissues and organisms, care must be taken to avoid unnecessary or over exposure.
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Question 132 Marks
Write a short note on Gamma rays.
Answer
$\rightarrow$ Frequency of the Gamma rays is the highest in the electro magnetic spectrum.
$\rightarrow$ Wave length range from $10^{-10} m$ to less than $10^{-14} m.$
$\rightarrow$ This high frequency radiation is produced in nuclear reactions and also emitted by radio active nuclei.
$\rightarrow$ They are used in medicine to destroy cancer cells.
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Question 142 Marks
How are electro magnetic waves produced ?
Explain.
Answer
→Neither stationary charges nor charges in uniform motion (steady currents) can create electromagnetic waves.
→Because the static electric charges produce only electro static fields, while charges in uniform motion produce magnetic fields.
→As per Maxwell's theory, accelerated charges radiate electromagnetic waves.
→An oscillating charge, which is an example of an accelerating charge, produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn, is a source of oscillating electric field and so on.
→The oscillating electric and magnetic fields thus regenerate each other, as the wave propogates through the space.
→The frequency of the EM wave is equal to the frequency of oscillation of the charge.
→An electro magnetic wave propogates in space with speed of light. In an electro magnetic wave, the Electric field, Magnetic field and direction of propogation all three are mutually perpendicular.
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Question 152 Marks
Write down the equation of displacement current and derive the Ampere$-$Maxwell's law.
Answer
$\rightarrow $ Displacement Current $i_d=\varepsilon_0 \frac{d \phi_E}{d t}$ but $\phi_{ E }= AE$
$\therefore i_d=\varepsilon_0 A \frac{d E }{d t}$
Image
$\rightarrow $ Fig. shows the electric and magnetic fields inside the parallel plate capacitor discussed above. At point $M$ shown in the fig., both these fields are normal to each other.
$\rightarrow $ As per the generalisation made by Maxwell, the source of magnetic field is not just the conduction electric current due to flowing charges, but also the time rate of change of electric field.
$\rightarrow $ Which means, the total current $i$ is the sum of conduction current $\left(i_{ c }\right)$ and the displacement
$\begin{array}{l}\text { current }\left(i_{ d }\right)\left(\text { where } i_{ d }=\varepsilon_{ o } \frac{d \phi_E}{d t}\right) \text {. } \\\quad i=i_{ C }+i_{ d } \\\therefore i=i_{ C }+\varepsilon_{ o } \frac{d \phi_E}{d t} \\\therefore i=i_{ C }+\varepsilon_{ o } A \frac{d E }{d t}......(1)\end{array}$
$\rightarrow $ Eq. $(1)$ can be interpreted as follows :
Outside the capacitor plates, we have only conduction current $i_{ c }=i$ and no displacement current $i_{ d }=0$. On the other hand, inside the capacitor, there is no conduction current, i.e. $i_{ c }=0$, and there is only displacement current, so that $i_{ d }=i$.
$\rightarrow $ The generalised (and correct) form of Ampere's circuital law is
$\oint \overrightarrow{ B } \cdot \overrightarrow{d l}=\mu_0 i(t)$
$($But there is a difference; "The total current passing through any surface of which the closed loop is the perimeter" is the sum of the conduction current and the displacement current.$)$ Generalised law is :
$\begin{array}{l}\therefore \oint \overrightarrow{ B } \cdot \overrightarrow{d l}=\mu_0\left(i_c+i_{ d }\right) \\\therefore \oint \overrightarrow{ B } \cdot \overrightarrow{d l}=\mu_0\left(i_c+\varepsilon_0 \frac{d \phi}{d t}\right) \\\therefore \oint \overrightarrow{ B } \cdot \overrightarrow{d l}=\mu_0 i_c+\mu_0 \varepsilon_0 \frac{d \phi}{d t}\end{array}$
$\rightarrow $ This equation is known as Ampere$-$Maxwell law.
$\rightarrow $ Ampere-Maxwell law : "The total current passing through any surface of which the closed loop is the perimeter, is the sum of conduction current and the displacement current."
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Question 162 Marks
Represent the Electric field and Magnetic field seen in the Electro magnetic waves $(EM$ waves$)$ in the form of equation.
Answer
Image
$\rightarrow$ As shown in the fig., suppose, a wave $($a plane $EM$ wave$)$ is propogating in the direction of positive $z-$axis.
$\rightarrow$ Here, the electric field, $E _x$ is along the $x-$axis and varies sinusoidally with $z$, at a given time.
$\rightarrow$ The magnetic field $B _y$ is along the $y-$axis and again, varies sinusoidally with $z$, at a given time.
$\rightarrow$ Here, as the electric field is along the direction $x-$axis, it only has $x-$component, whereas its $y$ and $z$ components are zero. $\left( E _y= E _z=0\right)$
$\rightarrow$ Equation of electric field
$E _x= E _0 \sin (k z-\omega t)$
$\rightarrow$ Similarly, because the magnetic field is along the direction of $y-$axis, it only has $y-$component and its $x$ and $z-$components are zero. $\left( B _x= B _z=0\right.$ )
$\rightarrow$ Equation of Magnetic field $B _y= B _0 \sin (k z-\omega t)$
$\rightarrow$ In vector form,
$\overrightarrow{ E }= E _x \hat{i}= E _0 \sin (k z-\omega t) \hat{i}$
$\overrightarrow{ B }= B _y \hat{j}= B _0 \sin (k z-\omega t) \hat{j}$
$\rightarrow$ Where $\omega$ is angular frequency, $k=\frac{2 \pi}{\lambda}$ is known as wave vector $($Also known as Angular wave number, or propogation constant.$) c =\frac{\omega}{k}$ is the speed of wave$-$propogation.
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Question 172 Marks
Give the explanation of the velocity of $E M$ wave and derive the equation of refractive index $n=\sqrt{\mu_r K }$.
Answer
$\rightarrow $ Velocity of the $EM$ waves in vacuum,
$c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$
$\rightarrow $ This equation was first derived by Maxwell using equations of electro magnetism.
Where, $\mu_0=4 \pi \times 10^{-7} \frac{ Tm }{ A } ($or $\frac{ N }{ A ^2} )$ known as permeability of free space / vacuum.
$\varepsilon_0=8.85 \times 10^{-12} \frac{ c ^2}{N m^2}$ known as the permittivity of free space.
$\rightarrow $ Substituting above values in the equation, and on simplifying, we get $c =3 \times 10^8 m / s$,
This value is equal to the speed of light in vacuum.
$\rightarrow $ Velocity of $EM$ waves in some medium,
$v=\frac{1}{\sqrt{\mu \varepsilon}}$
where, $\mu=$ permeability of medium
$\varepsilon=$ permittivity of medium
$\rightarrow $ But, relative permeability $\mu_r=\frac{\mu}{\mu_0} $
$\therefore \mu=\mu_r \mu_0$ Relative permittivity,
$\varepsilon_r=\frac{\varepsilon}{\varepsilon_0}=K ($where $K=$ die$-$electric constant of given medium $)$
$\therefore \varepsilon=\varepsilon_0 K$
$\rightarrow $ From eq. $(1),$
$v=\frac{1}{\sqrt{\mu_0 \mu_r \varepsilon_0 K}}=\frac{1}{\sqrt{\mu_0 \varepsilon_0}} \cdot \frac{1}{\sqrt{\mu_r K}}=\frac{ c }{\sqrt{\mu_r K}}$
$\rightarrow $ Hence, refractive index of medium,
$n=\frac{ c }{ v }=\frac{ c }{\frac{ c }{\sqrt{\mu_r K}}}=\sqrt{\mu_r K}$
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Question 182 Marks
Write a short note on Micro waves.
Answer
→Micro waves (short-wavelength radio waves), with frequencies in the giga hertz (GHz) range, are produced by special vacuum tubes (called klystrons, magnetrons and Gunn diodes).
→They are used in radar systems used in aircraft navigation, due to their short wave lengths.
→Radar also provides the basis for the speed guns used to time fast balls, tennis serves and automobiles.
→Microwave ovens are an interesting domestic application of these waves. In such ovens, the frequency of the microwaves is selected to match the resonant frequency of water molecules so that energy from the waves is transferred efficiently to the kinetic energy of the molecules.
→This raises the temperature of any food containing water.
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