Electromagnetic Waves Questions and Answers AP Inter 2nd Year Physics Chapter 8

Regular practice with AP Inter 2nd Year Physics Study Material Chapter 8 Electromagnetic Waves Questions and Answers helps students stay prepared for examinations.

AP Inter 2nd Year Physics 8th Lesson Electromagnetic Waves Questions and Answers

I. Multiple Choice Questions

1. In 1885, the existence of electromagnetic waves was experimentally demonstrated by
1) Ampere
2) Maxwell
3) Gauss
4) Hertz
Answer:
4) Hertz
The existence of electromagnetic waves was experimentally demonstrated by Hertz.

Question 2.
The speed of propagation of electromagnetic wave in free space is given by
1) C = \(\sqrt{\frac{\mu_0}{\varepsilon_0}}\)
2) C = \(\sqrt{\frac{\varepsilon_0}{\mu_0}}\)
3) C = \(\sqrt{\frac{1}{\varepsilon_0 \mu_0}}\)
4) C = \(\sqrt{\varepsilon_0 \mu_0}\)
Answer:
3) C = \(\sqrt{\frac{1}{\varepsilon_0 \mu_0}}\)
The speed of propagation of electromagnetic wave in free space is given by c = \(\sqrt{\frac{1}{\varepsilon_0 \mu_0}}\)

Question 3.
In an electromagnetic wave travelling in free space, the amplitude of magnetic field is 6.0 × 10^-4 T . The amplitude of its electric field is:
1) 2 × 10⁴ V/m
2) 1.5 × 10¹² V/m
3) 1.8 × 10⁵ V/m
4) 0.3 × 10⁴ V/m
Answer:
3) 1.8 × 10⁵ V/m
E₀ = CB₀ = (3 × 10⁸) (6 × 10^-4 )= 1.8 × 10⁵ vm^-1

Question 4.
A plane electromagnetic wave propagates along the + X direction in free space. The components of the electric field, and magnetic field, vectors associated with the wave in Cartesian frame are
1) E_x, B_y
2) E_y, B_x
3) E_y, B_z
4) E_z, B_y
Answer:
3) E_y, B_z
Electric field \(\vec{\mathrm{E}}\), magnetic field \(\vec{\mathrm{E}}\) and propagation direction \(\vec{v}\) are all mutually perpendicular. If the wave moves in x direction, the field must exist in YZ planes.
In the given options we have E_y, B_z

Question 5.
Arrange the following in the ascending order of wavelength.
A) Microwaves (λ₁)
B) Infrared rays (λ₃)
C) Ultraviolet rays (λ₂)
D) X-rays (λ₄)
Choose the most appropriate answer from the options given below.
1) λ₄ < λ₃ < λ₂ < λ₁
2) λ₄ < λ₂ < λ₃ < λ₁
3) λ₃ < λ₄ < λ₃ < λ₁
4) λ₄ < λ₃ < λ₁ < λ₂
Answer:
2) λ₄ < λ₂ < λ₃ < λ₁
High frequency waves have short wavelengths. The order from shortest to longest wave length is: X rays (λ₄) < Ultraviolet (λ₂) < infrared (λ₃) < Microwaves (λ₁)

Question 6.
Which colour of the light has the longest wavelength?
1) Green
2) Blue
3) Red
4) Violet
Answer:
3) Red
In the visible spectrum (VIBGYOR), Red has lowest frequency and longest wavelength (70Qnm),.

Question 7.
Electromagnetic waves travel in a medium with speed of 1.5 × 10⁸ m/s. The relative permeability of the medium is 2.0. The relative permittivity will be:
1) 4
2) 1
3) 2
4) 5
Answer:
3) 2
Given υ = 1.5 × 10⁸ m/s; μ_r = 2 we know c = 3 × 10⁸ m/s; ε_r = ?
The speed of light in a medium is υ = \(\frac{c}{\sqrt{\mu_r \varepsilon_r}}\)
1.5 × 10⁸ = \(\frac{3 \times 10^8}{\sqrt{2 \times \varepsilon_r}}\) ⇒ \(\sqrt{2 \times \varepsilon_{\mathrm{r}}}\) = 2 ⇒ 2ε_r = 4 ⇒ ε_r = 2

Question 8.
If the frequency of an electromagnetic wave is 60 MHz and it travels in free space, the wavelength of the wave (m) is:
1) 2.5
2) 5
3) 10
4) 2
Answer:
2) 5
Given f = 60MHz = 60 × 10⁶ Hz, c = 3 × 10⁸ m/s; λ = \(\frac{c}{f}=\frac{3 \times 10^8}{60 \times 60^6}\) = 5 m

Question 9.
The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given μ_r = 1)
1) 4.33 × 10⁷ m/s
2) 2.33 × 10⁷ m/s
3) 3.33 × 10⁷ m/s
4) 5.33 × 10⁷ m/s
Answer:
3) 3.33 × 10⁷ m/s
The velocity of light in a medium, υ = \(\frac{c}{\sqrt{\mu_r \varepsilon_r}}\); ε_r = 81, μ_r = 1
υ = \(\frac{3 \times 10^8}{\sqrt{1 \times 81}}=\frac{3 \times 10^8}{9}\) = 0.33 × 10⁸
∴ υ = 3.33 × 10⁷

Question 10.
Green House effect is due to
1) absorption of Ultra-Violet radiation by Ozone layer
2) transmission of visible light by the atmosphere
3) good weather
4) reflection of infrared rays emitted by earth’s atmosphere
Answer:
4) reflection of infrared rays emitted by earth’s atmosphere
Green House effect is due to reflection of infrared rays emitted by earth’s atmosphere.

Question 11.
Ozone Layer absorbs
1) Visible light
2) UV radiation
3) Infrared radiation
4) Microwaves
Answer:
2) UV radiation
Ozone Layer absorbs harmful UV radiation.

Question 12.
Which of the following rays are not electromagnetic waves
1) Ultra violet rays
2) Visible light
3) X-rays
4) Alpha (α) rays
Answer:
4) Alpha (α) rays
Alpha (α) rays are not electromagnetic waves.

Question 13.
Which of the following waves are also called the “Heat waves”?
1) Visible light
2) X-rays
3) Infrared rays
4) Radio waves
Answer:
3) Infrared rays
Infrared rays are called heat waves, because, they trigger the atoms and molecules in an object to vibrate, increasing its internal energy and temperature upon absorption.

II. Fill in the Blanks

Question 1.
To remove the inconsistency in the Ampere’s circuital law, Maxwell suggested the existence of _________ current.
Answer:
displacement
To remove the inconsistency in Ampere’s circuital law, maxwell suggested the existence of displacement current.

Question 2.
The spectrum of electromagnetic waves stretching in order of increasing wavelength from _________ rays to long ________ waves.
Answer:
Gamma, Radio
The spectrum of electromagnetic waves stretching in order of increasing wave length from gamma rays to long radio waves.

Question 3.
In the charging capacitor both conduction current and __________ current may be present.
Answer:
displacement
In the charging capacitor both conduction current and displacement current may be present.

Question 4.
Faraday’s law of induction states that there is an induced emf equal to the rate of change of ________.
Answer:
magnetic flux
Faraday’s law of induction states that there is an induced emf equal to the rate of change of magnetic flux.

Question 5.
________ charges radiate electromagnetic waves.
Answer:
Accelerated
Accelerating charges radiate EM waves as per Maxwell’s theory.

Question 6.
The wave vector ‘K’ direction describes the direction of ___________ of the wave.
Answer:
propagation
The wave vector K describes the direction of propagation of wave.

Question 7.
Jagadish Chandra Bose succeeded in producing electromagnetic waves of ________ wavelength.
Answer:
shorter
Jagadish Chandra Bose succeeded in producing EM waves of shorter wavelength.

III. One Word Answer Questions

Question 1.
What type of electric field generates magnetic field?
Answer:
Magnetic field is generated by changing electric field (or) non-uniform electric field.

Question 2.
What is the name of the current carried by conductors due to flow of charges?
Answer:
Electric conduction current is the current carried by conductors due to the flow of charges.

Question 3.
“There is an induced emf equal to the rate of change of magnetic flux.”
It is the statement of w hich law?
Answer:
This statement refers to Faraday’s law of electromagnetic induction.

Question 4.
In a material medium of permittivity (e) and permeability (p), what is the expression for the velocity of light in that medium?
Answer:
Velocity of light c = \(\frac{1}{\sqrt{\mu \varepsilon}}\)
Here ε is the permittivity of medium and μ is the magnetic permeability

Question 5.
In cellular phones which band of radio waves are used to transmit voice communication?
Answer:
Cellular phones use UHF band (Ultra High Frequency) .
The frequency range is 300 MHz to 3 GHz.

Question 6.
Earth surface absorbs the incoming visible radiation from the sun and what type of waves it re-radiate?
Answer:
Earth re-radiates long infrared waves.

Question 7.
What type of rays can snakes detect in addition to visible rays?
Answer:
Snakes can detect infrared rays in addition to visible rays.

Question 8.
When high energy electrons bombard a metal target, what type of waves are produced?
Answer:
X-rays are produced when high energy electrons bombard a metal target.

Question 9.
Which type of electromagnetic waves are used in the treatment of cancer?
Answer:
Gamma rays and X-rays are used in radiation therapy to destroy cancer cells.

Question 10.
What is the most important prediction from Maxwell’s equations.
Answer:
The existence of electromagnetic waves is the most important prediction from Maxwell’s equations.

IV. Very Short Answer Questions

Question 1.
What is the wavelength range of X-rays?
Answer:
The wavelength range of X-rays: 10^-3 nm to 10 nm (or) 0.01 Å to 100 Å

Question 2.
If the wavelength of electromagnetic radiation is doubled, what happens to the energy of photon?
Answer:
Energy of photon E = \(\text { hc } \frac{\mathrm{a}}{\lambda}\) ⇒ Eα \(\frac{1}{\lambda}\)
Let λ₂ = 2λ₁
∴ \(\frac{E_2}{E_1}=\frac{\lambda_1}{\lambda_2}=\frac{\lambda_1}{2 \lambda_1}=\frac{1}{2}\) ⇒ E₂ = \(\frac{E_1}{2}\)
Thus, energy of photon becomes half.

Question 3.
What is the principle of production of electromagnetic waves?
Answer:
Electromagnetic waves are produced by accelerating or oscillating charged particles.
When a charged particle like an electron vibrates or changes speed, it creates oscillating electric and magnetic fields that ripple outward together as self-propagative EM waves.

Question 4.
What is the ratio of speed of infrared rays and ultraviolet rays in vacuum?
Answer:
Ratio of speed of infrared rays and ultraviolet rays in vacuum is 1:1.
Because they both travel with same speed of light in vacuum

Question 5.
What is the relation between the amplitudes of the electric and magnetic fields in free space for an electromagnetic wave?
Answer:
Velocity of light c = \(\frac{E_0}{B_0}\)
Here E₀ is amplitude of electric field, B₀ is amplitude of magnetic field in free space.

Question 6.
What are the applications of microwaves?
Answer:
Applications of microwaves:

Microwaves are used in electrical ovens for cooking and heating.
Microwaves are used in wi-fi network, satellite communication.
Microwaves are used for deep muscle pain relief.
Microwaves are used in radar systems due to their short wavelengths

Question 7.
What is the displacement current, and what is its formula?
Answer:
Displacement current (I_d) is equal to ε₀ times the rate of change of electric flux through the surface.
Formula: I_d = ε₀ \(\frac{d \phi}{d t}\) where \(\frac{d \phi}{d t}\) is the rate of change of electric flux.
The displacement current occurs when there is change in electric flux.

Question 8.
Give two uses of infrared rays.
Answer:

Infrared rays are used in remote control systems of TV
Infrared rays are used for the treatment of skin diseases.
Infrared rays are used in earth satellites.
Infrared rays are used for taking photographs where there is no visible light due to fog or mist.

Question 9.
The charging current for a capacitor is 0.6 A. What is the displacement current across its plates?
Answer:
The displacement current is 0.6 A.
Reason: The displacement current across the plates of a capacitor is always equal to charging current of the capacitor.

Question 10.
A plane electromagnetic wave of frequency 20 MHz travels in free space along the + X direction. At a particular point in space and time, the electric field vector of the wave is E_y = 9.3 V/m. Then find the magnetic field vector of the wave at that point?
Answer:
Given Electric field E_y = 9.3V/m in the direction of y-axis.
Velocity of light c = 3 × 10⁸ m/s. Waves travel along +ve x-axis
Magnetic field \(\vec{B}=\frac{E_y}{c}=\frac{9.3}{3 \times 10^8}\) = 3.1 × 10^-8 T = 3.1 × 10^-8 \(\hat{\mathrm{k}}\)T
\(\hat{\mathrm{k}}\) refers to positive z-axis as \(\vec{\mathrm{E}}, \vec{\mathrm{~B}}\) and propagation of EM waves are mutually perpendicular.

Question 11.
The energy of the EM waves is of the order of 15 KeV. To which part of the spectrum does it belong?
Answer:
The range of x-ray part in EM waves is 0.1 keV to 100 keV. So, 15 keV belongs to x-rays.

Question 12.
A beam of light travelling along X-axis ¡s described by the electric field E_y = 900 sin(t – \(\frac{\mathrm{x}}{\mathrm{c}}\)), then find the ratio of electnc force to magnetic force on a charge moving along Y-axis with a speed of 3 × 10⁸ rn/s. (Given speed of light is 3 × 10⁸ m/s).
Answer:
Force due to electric field F_E = E₀q ; Force due to magnetic field F_B = B₀qv
∴ \(\frac{F_E}{F_B}=\frac{E_0 /}{B_0 / v}=\frac{E_0}{B_0 v}=\frac{c B_0}{B_0 v}=\frac{c}{v}=\frac{3 \times 10^8}{3 \times 10^8}=\frac{1}{1}\) = 1:1 (∵ E₀ = cB₀)

V. Short Answer Questions

Question 1.
Wrilc down Maxwell’s equations of electromagnetism ill vacuum.
Answer:
Maxwell’s equations of electromagnetism in vanillin:
1) Gauss’s law for electricity: The total electric flux through any closed surface is always equal to 1/EQ times the net charge enclosed by that surface.
Formula: \(\oint \vec{\mathrm{E}} \cdot \mathrm{~d} \vec{\mathrm{A}}=\frac{\mathrm{Q}}{\varepsilon_0}\)
2) Gauss’s law for magnetism: The net magnetic flux through any closed surface is always zero.
Formula: \(\oint \vec{\mathrm{B}} \cdot \mathrm{~d} \vec{\mathrm{A}}\) = 0

3) Faraday’s law for magnetism:The induced emf produced in a circuit is numerically equal to rate of change of magnetic flux through it.
Formula: \(\oint \vec{\mathrm{E}} \cdot \mathrm{~d} \vec{\mathrm{l}}=\frac{-\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\)

4) Ampere-Maxwell law: The line integral of the magnetic field along a closed path is equal to (X0 times the sum of conduction current and displacement current enclosed by the path.
Formula: \(\oint \vec{\mathrm{B}} \cdot \mathrm{~d} \vec{\mathrm{l}}\) = μ₀i_c + μ₀ ε₀\(\frac{d \phi_E}{d t}\)

Question 2.
What is Greenhouse effect and its mntriliulion ton aids the surface temperature of earth? .
Answer:
Greenhouse effect is the natural process occurring around the earth which keeps the earth’s surface warm enough to support our life. Without the Greenhouse effect, earth’s temperature would have been -18°C.

Greenhouse effect on earth’s surface temperature :
Greenhouse effect is the net result of heating up of Earth’s surface and atmosphere due to the absorption and re-emission of the earth’s thermal radiation by Greenhouse gases like CO₂, CH₄, N₂O etc. Due to the green house effect of gases, the earth becomes warmer and its average temperature increases. This is known as global warming.

Process of Greenhouse effect:

Incoming Energy: Sunlight (shortwave radiation) passes through the ozone layer of Earth’s atmosphere-and warms the surface.
Absorption & Radiation: The surface absorbs this energy and radiates it outward as infrared heat (longwave radiation).
Heat Trapping: Greenhouse gases like CO₂, water vapor, and methane absorb this outgoing infrared heat and re-radiate it in all directions, including back toward Earth’s surface.

This process acts like an insulating blanket, retaining heat near the surface.

Question 3.
Wliaf is electromagnetic spectrum? Briefly describe different types of electromagnetic naves.
Answer:
Electromagnetic spectrum: It is the orderly arrangement of the complete range of
electromagnetic radiation in increasing frequency (from low to high) or decreasing wavelength (from high to low).
Types of electromagnetic waves:
1) Radio waves:
a) Frequency of radio waves ranges from 500 kHz to 1000 MHz. (very low)
b) They are used in radio and television communication systems.

2) Microwaves:
a) Frequency range of microwaves lies in the gigahertz (GHz) region.
b) They are used in electrical microwave ovens, wi-fi networking.

3) Infrared waves:
a) The frequency of infrared waves lies just below (Infra) to red colour of VIBGYOR.
b) They are used in remote controllers, treatment of skin diseases.

4) Visible rays:
a) Frequency range of visible rays is 4 × 10¹⁴ Hz to 7 × 10¹⁴ Hz.
b) Visible light helps us to see things in the world.

5) Ultraviolet rays:
a) Wavelength of UV rays ranges just above to violet colour of VIBGYOR (4 × 10^-7 m to 6 × 10^-10 m.)
b) UV rays are used to kill germs in water purifiers.

6) X-rays:
a) Wavelength of X-rays ranges from 10^-8 m to 10^-13 m.
b) X-rays are used to detect broken bones, joints and heart diseases.

7) Gamma rays:
a) Wavelength of y-rays ranges from 10^-10 m to 10^-14 m (very low)
b) They are used in treatment of cancer, sterilisation.

VI. Long Answer Questions

Question 1.
Write a brief history about the discovery and understanding of electromagnetic waves.
Answer:
The discovery of electromagnetic waves is one of the greatest achievements in physics.
The development took place through the contributions of several scientists.
1. Contribution of Michael Faraday:
Michael Faraday introduced the concept of electric and magnetic fields.
In 1831, he discovered electromagnetic induction.
He showed that a changing magnetic field can produce electric current.
His ideas formed the foundation for the electromagnetic field theory.

2. Maxwell’s Electromagnetic Theory:
J.C. Maxwell unified electricity and magnetism through mathematical equations called Maxwell’s equations. These equations state the following.
A changing electric field produces a magnetic field.
A changing magnetic field produces an electric field.
From these equations, Maxwell predicted the existence of electromagnetic waves travelling with a speed equal to the speed of light.
Hence, Maxwell concluded that Light is an electromagnetic wave.

3. Hertz’s Experimental Verification:
Hertz demonstrated that electromagnetic waves travel through space, undergo reflection and refraction, and have the same properties as light. Thus, Hertz confirmed Maxwell’s theory.

4. Further Developments:
Other scientists expanded the applications of electromagnetic waves.
Guglielmo Marconi developed wireless communication using radio waves.
Jagadish Chandra Bose performed experiments on microwaves and radio waves.

Question 2.
State six characteristics of electromagnetic waves. What is Greenhouse effect?
Answer:
Characteristics of Electromagnetic waves:

An electromagnetic wave consists of electric and magnetic fields that are perpendicular to each other and perpendicular to the direction of wave propagation.
Electromagnetic waves are transverse in nature.
All the electromagnetic waves travel with same velocity of light (c) given by c= \(\frac{E_0}{B_0}\)
Electromagnetic waves carry energy (U) and momentum (U/c)
Electromagnetic waves exert pressure when they strike a surface.
Electromagnetic waves obey principle of superposition of waves.
Electromagnetic waves don’t require material medium for their propagation.

Greenhouse effect is the natural process occurring around the earth which keeps the earth’s surface warm enough to support life. Without the Greenhouse effect, earth’s temperature would have been -18°C.

Textual Solved Problems

Question 1.
A plane electromagnetic wave of frequency 25 MHz travels in free space along the x- direction. At a particular point in space and time, E = 6.3 \(\hat{\mathrm{j}}\) V/m. What is B at this point?
Solution:
Given equation \(\vec{\mathrm{E}}\) = 6.3\(\) V/m. Hence we have E = 6.3 V/m, We know c = 3 × 10⁸
Now c = \(\frac{E}{B}\) ⇒ B = \(=\frac{E}{c}=\frac{6.3}{3 \times 10^8}\) = 2.1 × 10^-8 \(\hat{\mathrm{k}}\)T
\(\vec{\mathrm{B}}\) = 2.1 × 10^-8
Unit vectors along x-axis, y-axis, z-axis are \(\hat{\mathrm{i}}, \hat{\mathrm{j}}, \hat{\mathrm{k}}\)
From the given data, the direction of propagation of wave is along x-axis and direction E is along y-axis ( \(\hat{\mathrm{j}}\)).
Hence, the direction of \(\vec{\mathrm{B}}\) should be along positive z-axis ( \(\hat{\mathrm{k}}\)) which is perpendicular to both x & y -axis

Question 2.
The magnetic field in a plane electromagnetic wave is given by B_y = 2 × 10^-7 sin (0.5 × 10³ x + 1.5 × 10¹¹t)T.
a) What is the wavelength and frequency of the wave?
b) Write an expression for the electric field.
Solution:
a) Comparing the given equation with B_y = B₀ sin\(\left[2 \pi\left(\frac{\mathrm{x}}{\lambda}+\frac{\mathrm{t}}{\mathrm{~T}}\right)\right]\)
wavelength λ = \(\frac{2 \pi}{0.5 \times 10^3}\) = 1.26m, frequency \(\frac{1}{T}\) = v = \(\frac{1.5 \times 10^{11}}{2 \pi}\) = 23.9GHz

b) Electric field: E₀ = B₀c = 2 × 10^-7 × 3 × 10⁸ ; = 6 × 10 V/m=60V/m
The electric field component is perpendicular to the direction of propagation of magnetic field.
Electric field component along the z-axis is E_z = 60 sin (0.5 × 10³x + 1.5 × 10¹¹t) V/m

Exercise Problems

Question 1.
Suppose that the electric field part of an electromagnetic wave in vacuum is
F, = (3.1 N/C) cos|(1.8 rad/m)y + (5.4 × 10⁶ rad/s)t|\(\hat{\mathrm{i}}\).
a) What is the direction of propagation?
b)What is the wavelength λ ?
c) What is the frequency v ?
d) Amplitude of magnetic field
e) Write an expression for the magnetic field part of the wave.
Answer:
Comparing E = 3.1cos[1.8y + 5.4 × 10⁶t]\(\hat{\mathrm{i}}\) with E = E₀cos(ky + ωt) we get E₀ = 3.1 NC^-1,k = 1.8 rad m^-1, ω = 5.4 × 10⁶ rad/s
a) \(\hat{\mathrm{i}}\) indicates that \(\vec{\mathrm{E}}\) is in the direction of x-axis. The +ve sign given in the cos term indicates
that the wave is travelling in the negative direction of y-axis.

b) Wave length λ = \(\frac{2 \pi}{k}=\frac{2 \times 3.14}{1.8}\) = 3.49m
c) Frequency v = \(\frac{\omega}{2 \pi}=\frac{5.4 \times 10^6}{2 \times 3.14}\) = 8.6 × 10⁵ Hz
d) Amplitude of magnetic field B₀ = \(\frac{E_0}{c}=\frac{3.1}{3 \times 10^8}\) = 1.03T
e) Magnetic field \(\vec{\mathrm{B}}\) = B₀(cosky + ωt)(-\(\hat{\mathrm{j}}\)) = 1.03 × 10^-8 cos(1.8y + 5.4 × 10⁶t)(-\(\hat{\mathrm{j}}\))

Question 2.
A plane EM wave has an electric field amplitude of 48 v/m. What is the amplitude of the magnetic field?
Answer:
Amplitude of electric field E₀ = 48v/m, Velocity of light c = 3 × 10⁸ m/s
∴ Amplitude of magnetic field B₀ = \(\frac{E_0}{c}=\frac{48}{3 \times 10^8}\) = 16 × 10^-8 = 1.6 × 10^-7T

Question 3.
Compute the speed of the electromagnetic wave in a medium. If the amplitude of electric and magnetic fields are 3 × 10⁴ N/C and 2 × 10^-4 T respectively.
Answer:
Given Amplitude of electric field E₀ = 3 × 10⁴ / c, Amplitude of magnetic field B₀ = 2 × 10^-4 T
∴ Speed of electromagnetic wave v = \(\frac{E_0}{B_0}=\frac{3 \times 10^4}{2 \times 10^{-4}}\) = 1.5 × 10⁸ m/s

Question 4.
Consider a parallel plate capacitor which is maintained at potential of 200 V. If the separation distance between the plates of the capacitor and area of the plates are 1mm and 20 cm². Calculate the displacement current for the 1 μs time.
Answer:
Given Potential V = 200V, Distance d = 1mm = 10^-3m;
Area A = 20cm² = 20 × 10^-4m² = 2 × 10^-3 m²; Time interval ∆t = 1 μs = 10⁶ s
Permittivity ε₀ = 8.854 × 10^-12 F/m
Capacitance c = \(\frac{\varepsilon_0 A}{d}=\frac{8.854 \times 10^{-12} \times 2 \times 10^{-3}}{10^{-3}}\) = 1.7708 × 10^-11
Displacement current I_d = \(\frac{\mathrm{cV}}{\Delta \mathrm{t}}=\frac{1.7708 \times 10^{-11} \times 200}{10^{-6}}\) = 3.5416 × 10^-3A = 3.54 mA

Question 5.
If the relative permeability and relative permittivity of the medium is 1.0 and 2.25 respectively. Find the speed of the electromagnetic wave in this medium.
Answer:
Given Relative permeability μ_r = 1; Relative permittivity ε_r = 2.25
Speed of electromagnetic wave is v = \(\frac{c}{\sqrt{\mu_{\mathrm{r}} \times \varepsilon_{\mathrm{r}}}}=\frac{3 \times 10^8}{\sqrt{1 \times 2.25}}=\frac{3 \times 10^8}{1.5}=\) = 2 × 10⁸ m/s

Question 6.
A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time) \(\vec{\mathrm{E}}\) = 9.6 \(\hat{\mathrm{j}}\) V/m, then the value of magnetic field at this point is
Answer:
Given frequency of EM wave f = 35MHz= 35 × 10⁶ Hz
Given that \(\vec{\mathrm{E}}\) = 9.6 \(\hat{\mathrm{j}}\) v/m E = 9.6 v/m. Also c= 3 × 10⁸ m/sec
Wavelength λ = \(\frac{c}{f}=\frac{3 \times 10^8}{35 \times 10^6}\) = 8.57 m
Magnetic field B = \(\frac{E}{c}=\frac{9.6}{3 \times 10^8}\) = 3.2 × 10^-8
∴ Magnetic field \(\vec{\mathrm{B}}\) = 3.2 × 10^-8\(\hat{\mathrm{k}}\) T

Objective Questions

Question 1.
A 100 Ω resistance and a capacitor of 100 Ω reactance are connected in series across a 220 V source. When the capacitor is 50% charged, the peak value of the displacement current is 1) 2.2 A
2) 11A
3) 4.4 A
4) 11V2 A
Answer:
1) 2.2 A

Question 2.
For a plane electromagnetic wave propagating in x-direction, which one of; the following combination gives the i correct possible directions for electric field (E) and magnetic field(B) respectively?
1) \(-\hat{\mathrm{j}}+\hat{\mathrm{k}}, -\hat{\mathrm{j}}+\hat{\mathrm{k}}\)
2) \(\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{j}}+\hat{\mathrm{k}}\)
3) \(-\hat{\mathrm{j}}+\hat{\mathrm{k}}, -\hat{\mathrm{j}}-\hat{\mathrm{k}}\)
4) \(\hat{\mathrm{j}}+\hat{\mathrm{k}}, -\hat{\mathrm{j}}-\hat{\mathrm{k}}\)
Answer:
3) \(-\hat{\mathrm{j}}+\hat{\mathrm{k}}, -\hat{\mathrm{j}}-\hat{\mathrm{k}}\)

Question 3.
Light with an average flux of 20 W/cm² falls on a non-reflecting surface at normal incidence having surface area 20 cm². The energy received by the surface during time span of 1 minute is
1) 10 × 10³J
2) 12 × 10³J
3) 24 × 10³J
4) 48 × 10³J
Answer:
3) 24 × 10³J

Question 4.
The ratio of contributions made by the electric field and magneticfield components to the intensity of an electromagnetic wave is (c=speed of electromagnetic waves)
1) c : 1
2) 1 : 1
3) 1 : c
4) 1 : c²
Answer:
2) 1 : 1

Question 5.
In an electromagnetic wave in free space the root mean square value of the electric field is E_rms = 6Vm^-1. The peak value of the magnetic field is
1) 2.83 × 10^-8T
2) 0.70 × 10^-8T
3) 4.23 × 10^-8T
4) 1.41 × 10^-8T
Answer:
1) 2.83 × 10^-8T

Question 6.
An electromagnetic wave of frequency υ = 3.0 MHz passes from vacuum into a dielectric medium with relative permittivity ε = 4.0. Then
1) Wavelength is doubled and frequency becomes half
2) Wavelength is halved and frequency remains unchanged.
3) Wavelength and frequency both remain unchanged.
4) Wavelength is doubled and frequency unchanged
Answer:
2) Wavelength is halved and frequency remains unchanged.

Question 7.
The electric field associated with an em wave in vacuum is given by |E = \(\hat{\mathrm{i}}\) 40 cos (kz – 6 × 10⁸t|; where E, z and t are in volt/m, meter and seconds respectively. The value of wave vector k is
1) 2 m^-1
2) 0.5 m^-1
3) 6 m^-1
4) 3 m^-1
Answer:
1) 2 m^-1

Question 8.
The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to
1) the speed of light in vacuum
2) reciprocal of speed of light in vacuum
3) the ratio of magnetic permeability to the electric susceptibility of vacuum
4) unity.
Answer:
2) reciprocal of speed of light in vacuum

Question 9.
The velocity of electromagnetic radiation in a medium of permittivity s0 and permeability μ₀ is given by
1) \(\frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)
2) \(\sqrt{\frac{\mu_0}{\varepsilon_0}}\)
3) \(\sqrt{\frac{\varepsilon_0}{\mu_0}}\)
4) \(\sqrt{\mu_0 \varepsilon_0}\)
Answer:
1) \(\frac{1}{\sqrt{\mu_0 \varepsilon_0}}\)

Question 10.
The electric and magnetic field of an electromagnetic wave are
1) in opposite phase and perpendicular to each other
2) in opposite phase and parallel to each other
3) in phase and perpendicular to each other
4) in phase and parallel to each other.
Answer:
3) in phase and perpendicular to each other

Question 11.
The velocity of electromagnetic wave is parallel to
1) \(\vec{\mathrm{B}} \times \vec{\mathrm{E}}\)
2) \(\vec{\mathrm{E}} \times \vec{\mathrm{B}}\)
3) \(\vec{\mathrm{E}}\)
4) \(\vec{\mathrm{B}}\)
Answer:
2) \(\vec{\mathrm{E}} \times \vec{\mathrm{B}}\)

Question 12.
Wavelength of light of frequency 100 Hz is
1) 4 × 10⁶m
2) 3 × 10⁶ m
3) 2 × 10⁶ m
4) 5 × 10^-5m .
Answer:
2) 3 × 10⁶ m

Question 13.
If ε₀ and μ₀ are the electric permittivity and magnetic permeability in a free space, s and p are the corresponding quantities in medium, the index of refraction of the
1) \(\sqrt{\frac{\varepsilon_0 \mu_0}{\varepsilon \mu}}\)
2) \(\sqrt{\frac{\varepsilon \mu}{\varepsilon_0 \mu_0}}\)
3) \(\sqrt{\frac{\varepsilon_0 \mu}{\varepsilon \mu_0}}\)
4) \(\sqrt{\frac{\varepsilon}{\varepsilon_0}}\)
Answer:
2) \(\sqrt{\frac{\varepsilon \mu}{\varepsilon_0 \mu_0}}\)

Question 14.
The frequency of electromagnetic wave, which best suited to observe a particle of radius 3 × 10^-4 cm is of the order of
1) 10¹⁵
2) 10¹⁴
3) 10¹³
4) 10,sup>12
Answer:
2) 10¹⁴

Question 15.
The energy of the em waves is of the order of 15 keV. To which part of the spectrum does it belong?
1) Ultraviolet rays
2) γ-rays
3) X-rays
4) Infra-red rays
Answer:
3) X-rays

Question 16.
If λ_v, λ_x, and λ_m represent the wave lengths of visible light, X-rays and microwaves respectively, then
1) λ_m > λ_x > λ_v
2) λ_m > λ_v > λ_x
3) λ_v > λ_x > λ_m
4) λ_v > λ_m > λ_x
Answer:
2) λ_m > λ_v > λ_x

Question 17.
Which of the following rays are not electromagnetic waves?
1) X-rays
2) γ-rays
3) β-rays
4) heat rays
Answer:
3) β-rays

Question 18.
What is the cause of Green house effect?
1) Infra-red rays
2) Ultra violet rays
3) X-rays
4) Radio waves
Answer:
1) Infra-red rays

Question 19.
Biological importance of ozone layer is
1) it stops ultraviolet rays
2) ozone layer reduces green house effect
3) ozone layer reflects radio waves
4) ozone layer controls O₂/H₂ ratio in atmosphere
Answer:
1) it stops ultraviolet rays

Question 20.
Ozone layer blocks the radiations of wavelength
1) more than 3 × 10^-7 m
2) equal to 3 × 10^-7 m
3) less than 3 × 10^-7 m
4) all of these
Answer:
4) all of these

Question 21.
Which of the following electromagnetic radiation have the smaller wavelength?
1) X-rays
2) γ-rays
3) UV waves
4) microwaves
Answer:
1) X-rays

Question 22.
A signal emitted by an antenna from a certain point can be received at another point of the surface in the form of
1) sky wave
2) ground wave
3) sea wave
4) both (1) and (2)
Answer:
4) both (1) and (2)

Question 23.
The structure of solids is investigated by using
1) cosmic rays
2) X-rays
3) γ-rays
4) infra-red radiations
Answer:
2) X-rays

Question 24.
Which of the following electromagnetic radiations have the longest wavelength?
1) X-rays
2) y-rays
3) Microwaves
4) Radiowaves
Answer:
4) Radiowaves