CBSE Class 12 Physics HOTs All Chapters Answers

HINTS FOR EM WAVE.
 

Question. Why is the quantity \( \varepsilon_0 \frac{d\Phi_E}{dt} \) called the displacement current?
Answer: This quantity is designated as the displacement current because it arises in a region where the electric field (or electric flux) is changing with time.
In simple words: It is called displacement current because it is produced by a changing electric field rather than by moving charges.

Exam Tip: Remember that displacement current has the same unit and dimensions as conduction current, and it satisfies the continuity of current in a circuit.

Question. What is the ratio of the speed of infrared rays and ultraviolet rays in a vacuum?
Answer: Both infrared and ultraviolet rays are electromagnetic waves. Therefore, they both travel in a vacuum with the speed of light, making their velocity ratio equal to 1.
In simple words: Every type of electromagnetic wave travels at the exact same speed in a vacuum, so their speed ratio is always 1.

Exam Tip: In exams, state the ratio as 1:1 and briefly explain that the speed of electromagnetic waves in a vacuum is independent of their frequency or wavelength.

Question. What is the angle between the oscillating electric and magnetic field vectors in an electromagnetic wave?
Answer: The electric field and magnetic field vectors of a propagating electromagnetic wave are perpendicular to each other, so the angle between them is 90 degrees.
In simple words: The electric and magnetic fields in an electromagnetic wave always vibrate at a right angle to one another.

Exam Tip: Explicitly state that the electric field, magnetic field, and direction of wave propagation are all mutually perpendicular to one another.

Question. Identify the parts of the electromagnetic spectrum that correspond to the following applications:
(i) Treatment of cancer (radiotherapy)
(ii) Cellular and radio communication
(iii) Detection of fractures in bones
(iv) Destruction of bacteria in water purifiers
Answer:
(i) Gamma rays
(ii) Radio waves
(iii) X-rays
(iv) Ultraviolet (UV) rays
In simple words: Different regions of the electromagnetic spectrum have unique properties that make them suitable for specific medical, communication, and sterilization uses.

Exam Tip: Memorizing the applications of different bands of the electromagnetic spectrum is highly beneficial as these questions are frequently asked.

Question. Name the electromagnetic waves that are used for the following purposes:
(i) Diagnostic tool in medicine to detect bone fractures or study crystal structures
(ii) Operating radar systems for aircraft navigation
Answer:
(i) X-rays
(ii) Microwaves
In simple words: X-rays are used to see inside the human body, while microwaves are used in radar and telecommunication systems.

Exam Tip: Always specify the sub-parts clearly with matching labels to help the examiner grade your answer easily.

Question. If the area of coverage for a TV telecast is to be doubled, by what factor must the height of the transmitting antenna be increased?
Answer: The coverage area is directly proportional to the height of the antenna, so the height must be doubled to double the area.
In simple words: To double the area covered by a television broadcast, you need to make the transmission tower twice as tall.

Exam Tip: Use the formula \( A = 2\pi R h \) to mathematically show that the coverage area \( A \) is directly proportional to the antenna height \( h \).

Question. Which physical quantity is not transported by electromagnetic waves?
Answer: While electromagnetic waves carry energy and momentum, they do not transport any physical charge.
In simple words: Light and other electromagnetic waves can move energy from place to place, but they cannot carry electric charge.

Exam Tip: Remember that linear momentum and energy are transported by electromagnetic waves, but electric charge is never carried by them.

Question. A variable frequency AC source is connected to a capacitor. How does the displacement current change when the frequency of the AC source is increased?
Answer: The displacement current increases because a higher frequency reduces the capacitive reactance, allowing more current to flow.
In simple words: When the frequency of the alternating current is raised, the displacement current also goes up.

Exam Tip: Reactance is inversely proportional to frequency - \( X_C = \frac{1}{2\pi f C} \). Therefore, a higher frequency leads to lower reactance and higher current.

Question. State the law which asserts that electric field lines cannot form closed loops.
Answer: This principle is established by Gauss's law for electrostatics.
In simple words: Gauss's law shows that electric field lines must start on positive charges and end on negative charges, so they cannot loop back.

Exam Tip: Contrast this with magnetic field lines, which always form closed loops because there are no isolated magnetic poles (Gauss's law for magnetism).

Question. The energy of an electromagnetic wave is of the order of \( 15 \text{ keV} \). To which part of the electromagnetic spectrum does this wave belong?
Answer: This radiation belongs to the X-ray region because its corresponding wavelength is approximately \( 0.825 \text{ Å} \).
In simple words: An electromagnetic wave with 15 keV of energy has a wavelength of 0.825 Å, which falls within the X-ray band.

Exam Tip: Show the formula \( \lambda = \frac{hc}{E} \) or use \( \lambda (\text{Å}) = \frac{12400}{E (\text{eV})} \) to find the wavelength in Ångstroms and verify the spectrum region.

Question. Which type of electromagnetic waves are primarily used in satellite and telecommunication systems?
Answer: Telecommunication and satellite transmission rely mainly on microwaves.
In simple words: Microwaves are used for communication because they can pass through the atmosphere and reach satellites easily.

Exam Tip: Mention that microwaves are preferred for satellite communication because they are not reflected by the ionosphere.

Question. What is the condition required to produce a displacement current between the plates of a capacitor?
Answer: A displacement current can be generated by establishing a time-varying potential difference across the plates.
In simple words: Changing the voltage across the capacitor plates creates a changing electric field, which generates the displacement current.

Exam Tip: Write down the formula for displacement current \( I_d = \varepsilon_0 \frac{d\Phi_E}{dt} \) to show that a change in electric flux (and hence voltage) is required.

Question. Which pair of space and time-varying electric and magnetic fields generates a plane electromagnetic wave propagating along the z-axis?
Answer: Such a wave is generated by an electric field oscillating along the x-axis, \( E_x \), and a magnetic field oscillating along the y-axis, \( B_y \).
In simple words: To make the wave travel along the z-axis, the electric field must point in the x-direction and the magnetic field must point in the y-direction.

Exam Tip: Remember that the cross product of the electric and magnetic fields, \( \vec{E} \times \vec{B} \), gives the direction of propagation. Here, \( \hat{i} \times \hat{j} = \hat{k} \) (the z-axis).

Please refer to attached file for HOTs Answers