Electromagnetic Waves Test - 12

Since both electric and magnetic fields are vectors, the direction of propagation of EM waves is obtained from the right-hand rule.

Let the electric field be denoted by \(\vec{E}\) and magnetic field be denoted by \(\vec{B}\).

According to the rule - If the fingers of the right hand are curled so that they follow a rotation from \(\vec{E}\) to \(\vec{B}\), then the thumb will point in the direction of the vector product i.e., the direction of EM waves.

Therefore, the direction of EM waves is found from the cross product of the electric field and magnetic field.

Hence, the correct option is (C).

Visible spectrum lies between infrared spectrum and ultra violet rays.

• The increasing order of frequency of EM waves are given as Radio, Microwave, Infrared, Visible, Ultraviolet, X Rays, and Gamma Rays.
• From the above, it is clear that the visible spectrum lies between infrared spectrum and ultraviolet rays.

Electromagnetic spectrum is the arrangement of electromagnetic radiations according to their frequency or wavelength.

• ​The electromagnetic spectrum has a range of frequencies, wavelengths, and photon energies.
• Typically, electromagnetic waves travel at the speed of light in a vacuum.  

The velocity of an electromagnetic wave (c) in a vacuum is related to its wavelength (λ) and frequency (f) as follows:

f = cλ 

As we go from gamma rays to radio waves, the frequency decreases, and the wavelength increases.

Therefore, the velocity (c = 3 × 10⁸ m/s) is constant.

Hence, the correct option is (C).

The concept of displacement current was proposed by Maxwell.

• We know that, it is the current that comes into existence, in addition to the conduction current, whenever the electric field and hence the electric flux changes with time.
• To modify Ampere’s law, Maxwell followed a symmetry consideration.
• By Faraday’s law, a changing magnetic field induces an electric field, hence a changing electric field must induce a magnetic field.
• As currents are the usual sources of the magnetic field, a changing electric field must be associated with the current.
• Maxwell called that current as displacement current.

To maintain the dimensional consistency, the displacement current is added in ampere’s law: 

\( \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I+\mu_{0} \epsilon_{0}\left(\frac{d \phi_{E}}{d t}\right)\)

Where, \(\epsilon_{0}\left(\frac{d \phi_{E}}{d t}\right)\) is the displacement current.

From the above, it is clear that the concept of displacement current was proposed by Maxwell.

Hence, the correct option is (D).

Infrared electromagnetic wave is used for thermal imaging.

• The electromagnetic spectrum is the arrangement of electromagnetic waves, in the order of their respective wavelength.
• Infrared rays are a type of electromagnetic waves which are emitted by hot bodies.
• Within the electromagnetic spectrum, infrared waves occur at frequencies above microwaves below the wavelength of visible red light, that this type of electromagnetic waves termed infrared.
• Thermal imaging is the technique in which thermal energy and infrared radiation are used to gather information about objects.
  

Hence, the correct option is (C).

The correct match is:

The Magnus effect is not related to electromagnetic waves.

• The force exerted on a rapidly spinning cylinder or sphere moving through air or another fluid in a direction at an angle to the axis of spin is called the Magnus effect.
• This force is responsible for the swerving of balls when hit or thrown with spin.

The Doppler effect is the change in the observed frequency of an (electromagnetic) wave due to relative motion of the source and observer.

Interference occurs when several waves are added together provided that the phase differences between them remain constant over the observation time.

Diffraction takes place with sound; with electromagnetic radiation, such as light, X-rays, and gamma rays; and with very small moving particles such as atoms, neutrons, and electrons, which show wavelike properties.

Therefore, Magnus effect is our required answer.

The phase difference between the electric field and the magnetic field in the electromagnetic wave is zero.

• The electric field and the magnetic field components of an electromagnetic wave oscillate in such a way that they have their peak at the same time and also become zero at the same time.
• Since there is no time difference between the peaks of the electric and the magnetic field, so the phase difference between the electric and the magnetic field of the electromagnetic wave is zero.

Displacement Current:

• The idea of displacement current was firstly developed by famous physicist James Maxwell. 
• The displacement current produces due to the change in electric flux (number of electric field lines through a cross-sectional area of a closed-loop) with respect to time.
• The SI unit of displacement current is Ampere.  
• The magnitude of displacement current is zero in the case of steady electric fields in conducting wire.
• The idea of displacement current was introduced to the current for making ampere circuital law consistent.

Therefore, out of all the given statements, Only the statement of option (C) is incorrect.

Hence, the correct option is (C).

Spectrum of X-rays is continuous and linear. 

• In an X-ray tube, when high-speed electrons strike the target they penetrate to the target.
• The electrons lose their kinetic energy and come to rest inside the metal.
• The electron before finally being stopped makes several collisions with the atom in the target. At each collision, one of the following two types of X-rays get formed
• Continuous X-rays
• Characteristic X-rays
• ​Due to continuous X-rays, the spectrum will be continuous.
• ​Due to characteristic X-rays, the spectrum will be linear.

So, the spectrum of X-rays is continuous and linear.

Electromagnetic waves: It is a transverse wave defined as composed of oscillating electrical and magnetic fields perpendicular to each other.

The speed of electromagnetic waves is the same as of speed of light, i.e., \(c=3 \times 10^{8}\) \({m} / {s}\)

Mathematically, 

Speed of \(E M W=\frac{1}{\sqrt{\epsilon_{0} \mu_{0}} }=3 \times 10^{8} {~m} / {s}\)

Or, the relation between the speed of electromagnetic wave and dielectric constant and vacuum permeability is:

Speed of \(E M W=\frac{1}{\left(\epsilon_{0} \mu_{0}\right)^{\frac{1}{2}}}\)

where,

\(\epsilon_{0}=8.854 \times 10^{-12} {~F} / {m}\) (vacuum permittivity or dielectric constant)

\(\mu_{0}=4 \pi \times 10^{-7} {H} / {m}\) \((\frac{\text{vacuum permeability}}{{\text{magnetic constant}}})\)

Hence, the correct option is (B).

Electromagnetic spectrum:

• It is a collection of a range of different waves in sequential order from radio to gamma electromagnetic waves.
• Frequency (ν) = speed of light (c)/wavelength (λ)

Infrasonic waves: 

• The frequency range of these types of a wave is below 20Hz. Humans cannot detect it.
• Example: Sound produced by Earthquake, Volcanic eruption and ocean waves, etc.

Radio waves:

• The lowest frequency portion comes in radio waves generally, has wavelengths range between 1mm to 100km or frequencies between 300 GHz to 3 kHz.
• There are several subcategories in between these waves like AM and FM radio.

Visible Light: 

• A portion in the spectrum of electromagnetic waves that is visible to the human eye, ranging roughly between 400 nm to 700 nm.
• Red has the longest wavelength and lowest frequency in this visible spectrum.
• Violet has the smallest wavelength and highest frequency in the visible spectrum.

X-rays: 

• It is an electromagnetic wave with wavelength range 0.1Å – 100Å.
• The wavelength of X-rays is small in comparison to the wavelength of the light. Therefore, they carry more energy.

Electromagnetic waves are the transverse waves.

Transverse Waves: 

• Those waves whose direction of propagation and direction of disturbance is always perpendicular, are known as transverse waves.
• These waves produced in a medium that can sustain shearing strain.
• Example: Electromagnetic Waves, Ripples on the surface of water, Vibrations in a guitar string.

Hence, the correct option is (B).

When heat radiation falls on a surface, then it gives energy and exerts pressure.

• Heat radiation is thermal energy carried in the form of electromagnetic waves.
• Since it is a form of electromagnetic radiation, they also exert radiation pressure on the surface on which it falls.
• Therefore, heat radiation gives energy and exerts pressure as well.

Radio waves are readily diffracted around building where as light waves are negligibly diffracted around buildings. This is because radio waves have much longer wavelengths than light waves.

• From the electromagnetic spectrum, it is inferred that the radio waves have higher-order wavelengths comparable to the size of the buildings.
• Visible light rays have wavelengths lesser than that of radio waves.
• Since the wavelength of radio waves is comparable to the size of the building, diffraction occurs readily. While visible light has shorter wavelengths and thus, diffraction is negligibly small.

Hence, the correct option is (C).

Given: 

Change in an electric field, \(\frac{d E}{d t}=5 \times 10^{12} {Vm}^{-1} s^{-1}\), 

Side of the plate (I) \(=2\) \({cm}=2 \times 10^{-2} {~m}\), 

and \(\epsilon_{0}=8.85 \times 10^{-12} C^{2} N^{-1} {~m}^{-2}\)

The area of the plate is:

Area of square \(=(\text{side})^2\)

\( A=2 \times 10^{-2} \times 2 \times 10^{-2}=4 \times 10^{-4} {~m}\)

We know that displacement current is given as:

\( I_{d}=\epsilon_{0} A \times \frac{d E}{d t}\)

\( I_{d}=8.85 \times 10^{-12} \times 4 \times 10^{-4} \times 5 \times 10^{12}\)

\( I_{d}=177 \times 10^{-4} A\)

\( I_{d}=17.7 {~m}\)

Hence, the correct option is (B).

Radio waves, infrared rays, visible light, ultraviolet rays, X-rays, and gamma rays are all types of electromagnetic radiation.

• Radio waves have the longest wavelength, and gamma rays have the shortest wavelength.
• After radio waves, infrared waves has the longest wavelength among the others.

Hence, the correct option is (D).

The idea of displacement current was introduced to the current for making ampere circuital law consistent.

\( \oint \vec{B} . d \vec{l}=\mu_{0}\left(i_{c}+i_{d}\right)\)\(\quad\) (Modified Ampere circuital law)

Where, \(\mu_{0} \) is the permittivity of free space, \({i}_{d}\) is the displacement current, and \({i}_{c}\) is the conduction current. \(\oint \vec{B} \cdot d \vec{l}\) is line integral of the magnetic field over the closed-loop. 

The expression for displacement current is given by,

\( i_{d}=\epsilon_{0} \frac{d \phi_{E}}{d t}\)

Where \(\phi_{{E}} \) is the flux of the electric field through the area bounded by the closed curve, \({i}_{{d}} \) is the displacement current, and \(\epsilon_{0} \) is the permittivity of free space.

Hence, the correct option is (C).

Given: 

\(\phi_{E}=\left(50 t^{2}+10 t+2\right) V m\)

We know that:

The expression for displacement current is given by,

\( i_{d}=\epsilon_{0} \frac{d \phi_{E}}{d t}\)

\( i_{d}=\epsilon_{0} \frac{d\left(50 t^{2}+10 t+2\right)}{d t}\)

\( i_{d}=\epsilon_{0}(100 t+10)\)

For t = 2 sec,

\( i_{d}=\epsilon_{0}(100 \times 2+10)\)

\( i_{d}=\epsilon_{0}(200+10)=210 \epsilon_{0}\)

\( i_{d}=210 \epsilon_{0} {~A}\)

Hence, the correct option is (A).

Electromagnetic waves are generated by accelerated charge.

• An accelerating charge produces a changing electric field which in turn produces a magnetic field. These alternatively changing magnetic and electric field give rise to electromagnetic waves.
  
• Whereas, the static force generate only electric field and moving particle generates only magnetic field.
  

Electromagnetic waves or EM waves: The waves that are formed as a result of vibrations between an electric field and a magnetic field and they are perpendicular to each other and to the direction of the wave is called an electromagnetic wave.

Electromagnetic waves do not require any matter to propagate from one place to another as it consists of photons. They can move in a vacuum.

Properties of electromagnetic waves:

• Not have any charge or we can say that they are neutral.
• Propagate as a transverse wave.
• They move with the velocity the same as that of light i.e., \(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\).
• It contains energy and they also contain momentum.
• They can travel in a vacuum also.

From above, it is clear that, electromagnetic waves do not require any matter to propagate from one place to another as it consists of photons. Therefore, statement in option (A) is correct.

In an electromagnetic wave, the electric field and magnetic field vary continuously with maxima and minima at the same place and same time. Therefore, statement in option (B) is correct.

The energy in an electromagnetic wave is divided equally between electric and magnetic fields. Therefore, statement in option (C) is correct. 

An electromagnetic wave is a perpendicular variation in both the electric field (E) and Magnetic field (B). Therefore, statement in option (D) is incorrect.

Hence, the correct option is (D).

Infrared waves are called waves of heat energy.

• The infrared waves present in the light ray coming from the sun is responsible for the heat energy.
• Thus, infrared waves are called as waves of heat energy. 
• The Radio waves, Ultraviolet waves and Microwaves don’t have the heat energy. 

For free-space transmission, it wouldn't be good to use "high" energy radiation such as gamma rays, ultraviolet rays, and x-rays because they could be dangerous for people's health. Also, the air can scatter high-energy radiation (we see a blue sky because of this scattering of blue and violet light for instance).

• Radio waves have a wavelength varying from a millimeter to 10 km.
• The higher the frequency of the electromagnetic wave, the more it penetrates into the atmosphere.
• The frequency of the radio waves is less than \(3 \times 10^{11} \mathrm{~Hz}\).
• The frequency of the microwaves is varies from \(3 \times 10^{11} \mathrm{~Hz}\) to \(10^{13} \mathrm{~Hz}\).
• Since low-frequency radio waves are stopped by the earth's atmosphere, and some radio waves are reflected back by the part of the earth's atmosphere.

So, Microwaves are preferred in order to communicate with the artificial satellites which are orbiting the earth at a particular height from the surface of the earth. Microwaves are preferred because they can penetrate through the Earth's atmosphere very easily and reach the target satellite.

Hence, the correct option is (B).

In the case of a steady electric field, the electric field does not change with time. Therefore, the electric flux density through a closed-loop will be constant.

This results in zero change in electric flux with respect to time i.e.,

\( \frac{d \phi_{E}}{d t}=0\)

The displacement current will be:

\( i_{d}=\epsilon_{0} \frac{d \phi_{E}}{d t}=0\)

Hence, the correct option is (B).

Infrared radiation was discovered in 1800 by William Herschel.

• He did so with a simple experiment in which he dispersed sunlight through a prism and placed a thermometer at the location of each colour. 
• He noticed that the thermometer temperature increased when he did this, which was not really unexpected since sunlight carries warmth.
• However when he placed the thermometer past the red end of the spectrum – where there was no visible sunlight – the thermometer’s temperature still increased! 
• Herschel had discovered infrared radiation – radiation beyond the red end of the visible spectrum. 
• Wavelength: 700 nanometers to 1 millimeter. 

Given: 

Capacitance, (C) \(=1 \mu {F}\), 

Rate of change in voltage, \(\frac{d V}{d t}=10^{6} {~V} / {s}\)

The expression for displacement current \({i}_{{d},}\) in the case of capacitance is given as:

\( i_{d}=\frac{d q}{d t}\)\(\quad\).....(i)

As we also know that, the charge on the capacitor is:

\( {q}={CV}\)

Where q = charge on the capacitors

On substituting the value of q = CV in equation (i), we get,

\( i_{d}=C \frac{d V}{d t}\)\(\quad\).....(ii)

On substituting the given values in equation (ii), we get,

\( i_{d}=\left(10^{-6} \times 10^{6}\right) A\)

\( {i}_{{d}}=1 {~A}\)

Hence, the correct option is (A).

Given: 

\(\phi_{E}=\left(10 t^{2}-20 t+5\right) V m\)

We know that:

The expression for displacement current is given by,

\( i_{d}=\epsilon_{0} \frac{d \phi_{E}}{d t}\)

\( i_{d}=\epsilon_{0} \frac{d\left(10 t^{2}-20 t+5\right)}{d t}\)

\( i_{d}=\epsilon_{0}(20 t-20)\)

For t = 1 sec,

\( i_{d}=\epsilon_{0}(20 \times 1-20)\)

\( i_{d}=\epsilon_{0}(20-20)=0\)

\( i_{d}=0\)

Hence, the correct option is (D).

Light waves have the the wavelength range of 700 nm to 400 nm.

• Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that can be perceived by the human eye. 
• Visible light is usually defined as having wavelengths in the range of \(400-700\) nanometers \(({nm})\), or \(4.00 \times 10^{-7}\) to \(7.00 \times 10^{-7} {~m}\), between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths). 
• This wavelength means a frequency range of roughly \(430-750\) terahertz \(({THz})\). 

Wavelength table of electromagnetic spectrum:

As the frequency is inversely proportional to the wavelength, so, the decreasing order of the wavelength and increasing order of the frequency of different rays are as followed:

Radio waves < Microwaves < Visible Light < Ultra Violet

Infrared rays:

• It is a part of the EM spectrum and has wavelengths range from about 700 nanometers (nm) to 1 millimeter (mm).
• it has longer wavelengths than visible light.
• Infrared cameras and telescopes or night-vision goggles etc, use infrared waves to sense or measure the heat radiated by the object.
• Infrared energy radiated from the hot objects can be detected and then converted into an electronic signal to produce a visual image by cameras telescopes.