Class 12 Physics NCERT Chapter 8: Higher Order Thinking Skills (HOTS) Questions
Chapter 8 Higher Order Thinking Skills (HOTS) Questions provide students with an opportunity to think beyond ordinary exercises and think critically in understanding electromagnetic waves. These questions also assist students to apply concepts in real life and prepare themselves well for both board exams as well as competitive ones like JEE and NEET.
Q1: A red LED emits light at 0.2 watts uniformly around it. The amplitude of the electric field of the light at a distance of 3 m from the diode is ___ V/m.
Answer:
$I=P / 4 \pi r^2$ and $p_{avg}=\frac{1}{2} \varepsilon_0 E_{o}^2$
$\therefore P / 4 \pi r^2=\left(\frac{1}{2}\right) \mathcal{E}_0 E_0^2 C$
Or $E_0=\sqrt{\frac{2 P}{4 \pi \varepsilon_0 r^2 C}}$
$\begin{aligned} & \text { Here } p=0.2 \mathrm{w}, r=3 \mathrm{~m}, c=3 \times 10^8 \mathrm{~ms}^{-2} \\ & \frac{1}{4} \pi \varepsilon_0=9 \times 10^9\end{aligned}$
$\begin{aligned} & E_0=\sqrt{\frac{2 \times 0.2 \times 9 \times 10^9}{9 \times 3 \times 10^8}} \\ & E_0=\sqrt{\frac{0.4 \times 9 \times 10^9}{27 \times 10^8}} \\ & E_0=\sqrt{\frac{36}{27}}\end{aligned}$
$E_0=1.15 \mathrm{~v} / \mathrm{m}$
Q2: The following figure shows a capacitor made of two circular plates. The capacitor is being charged by an external source which supplies a constant current equal to 0.15 A. What is the displacement current (in amperes) across plates?
Answer:
As we know,
Displacement current
$I_d=\frac{\varepsilon_0 d \phi_c}{d t}$
But $\phi_E=E A=\frac{q}{A \varepsilon_0} A=\frac{q}{\varepsilon_0}$
$\therefore \quad I_d=\varepsilon_0 \frac{d}{d t}\left(\frac{q}{\varepsilon_0}\right)=\frac{\varepsilon_0}{\varepsilon_0} \frac{d q}{d t}=\frac{d q}{d t}=I$
Here $I=0.15 \mathrm{~A} \quad \therefore I_d=0.15 \mathrm{~A}$
Q3: A radiation of 200 W is incident on a surface which is 60% reflecting and 40% absorbing. The total force on the surface is
Answer:
Force exerted by incident radiation is $F=\frac{P}{C}$ where $P$ is the power of radiation and $C$ is the velocity of light. For absorbed radiations are $40 \%$ then exerted force is $F_{a b s}=\frac{0.4 P}{c}$ and $60 \%$ part of radiations is reflected by the surface, so force exerted by theses radiations is $ F_{r e f}=2 \times \frac{0.6 P}{C}=\frac{1.2 P}{C} $ Then total force exerted by radiations on the surface is $ \begin{aligned} & F_{\text {total }}=F_{\text {ref }}+F_{\text {abs }} \\ & =\frac{1.2 P}{c}+\frac{0.4 P}{c}=\frac{1.6 P}{c} \\ & =\frac{1.6 \times 200}{3 \times 10^8}=1.07 \times 10^{-6} \mathrm{~N} \end{aligned} $
Q4: The magnetic field of a plane electromagnetic wave is given by :
$
\vec{B}=B_0[\cos (k z-\omega t)] \hat{i}+B_1 \cos (k z+\omega t) \hat{j}
$
where $B_0=3 \times 10^{-5} T$ and $B_1=2 \times 10^{-6} \mathrm{~T}$.
The rms value of the force (in Newton) experienced by a stationary charge $Q=10^{-4} C$ at $Z=0$ is closest to (up to one decimal).
Answer:
$
\begin{aligned}
& B=B_0 \cos (k x-\omega t) \hat{i}+B_1 \cos (k z+\omega t) \hat{j} \\
& B_0=3 \times 10^{-5} T \\
& B_1=2 \times 10^{-6} T
\end{aligned}
$
Amplitude of resultant magnetic field $=B^{\prime}=\sqrt{B_o^2+B_1^2}$
$
\begin{aligned}
Q & =10^{-4} C \\
F_{r m s} & =Q E_{r m s}=Q\left(c B_{r m s}^{\prime}\right) \\
F_{r m s} & =Q \sqrt{\left(\frac{C B_0}{\sqrt{2}}\right)^2+\left(\frac{C B_1}{\sqrt{2}}\right)^2} \\
& =10^{-4} \times \frac{3 \times 10^8}{\sqrt{2}} \sqrt{\left(3 \times 10^{-5}\right)^2+\left(2 \times 10^{-6}\right)^2}
\end{aligned}
$
$
\begin{aligned}
& =10^{-4} \times \frac{3 \times 10^8}{\sqrt{2}} \sqrt{9 \times 10^{-10}+4 \times 10^{-12}} \\
& =10^{-4} \times \frac{3 \times 10^8}{\sqrt{2}} \sqrt{900 \times 10^{-12}+4 \times 10^{-12}} \\
& =\frac{3 \times 10^4}{\sqrt{2}} \sqrt{904} \times 10^{-6} \\
& =0.6 \mathrm{~N}
\end{aligned}
$
Q5: Two light waves are given by, $E_1=2 \sin (100 \pi t-k x+30)$ and $E_2=3 \cos (200 \pi t-k x+60)$. The ratio of the intensity of the first wave to that of the second wave is :
Answer:
As we learned
Intensity of EM wave -
$
I=\frac{1}{2} \epsilon_o E_o^2 c
$
where
$\epsilon_o=$ Permittivity of free space
$E_o=$ Electric field amplitude
$\mathrm{c}=$ Speed of light in vacuum
so
$
I \propto A^2 \therefore \frac{I_1}{I_2}=\frac{2^2}{3^2}=4 / 9
$
CBSE Class 12th Syllabus: Subjects & Chapters
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NCERT Solutions for Class 12 Physics Chapter 8: Topics
NCERT Solutions for Class 12 Physics Chapter 8: Topics cover the key concepts of electromagnetic waves, including their propagation, characteristics, and applications in daily life. These solutions help students understand each topic clearly and provide a structured approach to learning for exams like CBSE, JEE, and NEET.
8.1 Introduction
8.2 Displacement current
8.3 Electromagnetic waves
8.3.1 Sources of electromagnetic waves
8.3.2 Nature of electromagnetic waves
8.4 Electromagnetic spectrum
8.4.1 Radio waves
8.4.2 Microwaves
8.4.3 Infrared waves
8.4.4 Visible rays
8.4.5 Ultraviolet rays
8.4.6 X-rays
8.4.7 Gamma rays
Approach to Solve Questions of Electromagnetic Waves Class 12
To answer questions on Electromagnetic Waves in Class 12 Physics, one should read the question carefully and be able to pick the known and unknown data as well as what is needed, which could be wave properties, speed, wavelength, its frequency, energy or intensity. Learn how speed, frequency, and wavelength are related to one another, how the energy of a photon depends on the related quantities, and what the intensity of the wave is. A labelled diagram of wave propagation and the direction of electric and magnetic fields may be helpful in visualising them. Choose the right formulas, such as $c=f \lambda, E=h f$, or $I=\frac{c \epsilon_0 E^2}{2}$. Input the given values replacing them and maintain consistency in the units. Solve the problem step by step as a series of smaller calculations, and ensure the final answer makes physical sense. Solidify conceptual understanding, derivations, and energy density and intensity of EM waves especially on advanced or HOTS questions. This systematic method offers certainty, precision, and clear understanding of how to answer board and competitive exam questions.
