 # NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves

NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves provide detailed answers to textbook theory questions, numerical problems, worksheets, and exercises that will help you sort important topics of electromagnetic waves and prepare electromagnetic waves Class 12 notes.

NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves is an important topic in CBSE Class 12 Examination. In Class 12 physics, there are many complicated formulas and equations. In order to score good marks in the Class 12 examination, it is important to solve NCERT questions provided at the end of each chapter.

Most frequently, questions that are asked in CBSE Class 12 Physics Exams are directly fetched from the NCERT textbook. Electromagnetism is one of the most frequently asked topics in exams.

## NCERT Solutions for Class 12 Physics Chapter 8 Electromagnetic Waves

Electromagnetism is a kind of physical attraction that occurs in electrically charged particles and this chapter consists of various subtopics which is equally important to learn. When a capacitor is charged using an external source, there can be a potential difference between two capacitive plates, we will show how to calculate that along with the displacement. This question will be solved using Kirchhoff’s rules.

#### Concepts involved in Class 12 Physics Chapter 8 Electromagnetic Waves

1. Introduction
2. Displacement Current
3. Electromagnetic Waves
1. Sources of electromagnetic waves
2. Nature of electromagnetic waves
4. Electromagnetic Spectrum
2. Microwaves
3. Infrared waves
4. Visible rays
5. Ultraviolet rays
6. X-rays
7. Gamma rays.

We will determine the RMS value of the conduction current and we will be analysing the similarities between conduction current and displacement current. We will be analysing the similarities among the wavelengths of X-rays, red lights, and radio waves. In this solution, you will be seeing questions on the wavelength of electromagnetic waves traveling in a vacuum.

Do you want to know what the frequency of electromagnetic waves produced by the oscillator is? Want to know about the electric field part of the harmonic electromagnetic wave in a vacuum? Check out the answers below. We will be obtaining photo-energy of different parts of the electromagnetic spectrum and perceiving how to obtain different scales of photon energies of electromagnetic radiation.

We will be gaining knowledge on how to prove that the energy density of one field is equal to the average energy density of another field. We know that there are more fundamental forces such as weak and strong nuclear force and gravitational force. You will be finding questions on them in a different chapter. The questions mentioned in this chapter are very common in exams and if prepared thoroughly, will definitely make you understand electromagnetism nice and easy.

### Class 12 Physics NCERT Solutions Electromagnetic Waves Important Questions

Q 8.1) The Figure shows a capacitor made of two circular plates each of radius 12 cm and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A.

(a) Calculate the capacitance and the rate of change of the potential difference between the plates.

(b) Obtain the displacement current across the plates.

(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain. Given Values:

The radius of each circular plate (r) is 12 cm or 0.12 m

The distance between the plates (d) is 5 cm or 0.05 m

The charging current (I) is 0.15 A

The permittivity of free space is $\varepsilon_{0} = 8.85\times 10^{-12}\; C^{2}N^{-1}m^{-2}$

(a) The capacitance between the two plates can be calculated as follows:

$C = \frac{\varepsilon _{0} A}{d}$

where,

A = Area of each plate = $\pi r^{2}$ $C = \frac{\varepsilon _{0} \pi r^{2}}{d}$

= $\frac{8.85\times 10^{-12}\times \pi (0.12)^{2}}{0.05}$

= $8.0032\times 10^{-12}\; F$

= 80.032 pF

The charge on each plate is given by,

q = CV

where,

V is the potential difference across the plates

Differentiation on both sides with respect to time (t) gives:

$\frac{\mathrm{d} q}{\mathrm{d} t} = C \frac{\mathrm{d} V}{\mathrm{d} t}$

But, $\frac{\mathrm{d} q}{\mathrm{d} t}$ = Current (I)

$∴\frac{\mathrm{d} V}{\mathrm{d} t} = \frac{I}{C}$

=>$\frac{0.15}{80.032\times 10^{-12}} = 1.87\times 10^{9}\; V/s$

Therefore, the change in the potential difference between the plates is $1.87\times 10^{9}\; V/s$.

(b) The displacement current across the plates is the same as the conduction current. Hence, the displacement current, id is 0.15 A.

(c) Yes

Kirchhoff’s first rule is valid at each plate of the capacitor provided that we take the sum of conduction and displacement for current.

Q 8.2) A parallel plate capacitor (Fig. 8.7) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with an (angular) frequency of 300 rad s–1.

(a) What is the rms value of the conduction current?

(b) Is the conduction current equal to the displacement current?

(c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

Radius of each circular plate, R = 6.0 cm = 0.06 m

Capacitance of a parallel plate capacitor, C = 100 pF = $100\times 10^{-12}\; F$

Supply voltage, V = 230 V

Angular frequency, $\omega = 300\; rad\;s^{-1}$

(a) Rms value of conduction current, I = $\frac{V}{X_{c}}$

Where,

$X_{c}$ = Capacitive reactance

= $\frac{1}{\omega C}$ $∴ I = V\times \omega C$

= $230\times 300\times 100\times 10^{-12}$

= $6.9\times 10^{-6} A$

= $6.9\; \mu A$

Hence, the rms value of conduction current is $6.9\; \mu A$.

(b) Yes, conduction current is equivalent to displacement current.

(c) Magnetic field is given as:

$B = \frac{\mu_{0}r}{2\pi R^{2}}I_{0}$

Where,

$\mu_{0}$ = Permeability of free space = $4\pi \times 10^{-7}\; N\;A^{-2}$ $I_{0}$ = Maximum value of current = $\sqrt{2}\; I$

r = Distance between the plates from the axis = 3.0 cm = 0.03 m

$∴B = \frac{4\pi\times 10^{-7}\times 0.03\times \sqrt{2}\times 6.9\times 10^{-6}}{2\pi \times (0.06)^{2}}$

= $1.63\times 10^{-11}\; T$

Hence, the magnetic field at that point is $1.63\times 10^{-11}\; T$.

Q 8.3) What physical quantity is the same for X-rays of wavelength 10–10m, the red light of wavelength 6800 Å and radiowaves of wavelength 500m?

The speed of light ($3\times 10^{8}$ m/s) in a vacuum is the same for all wavelengths. It is independent of the wavelength in the vacuum.

Q 8.4) A plane electromagnetic wave travels in vacuum along the z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its
wavelength?

The electromagnetic wave travels in a vacuum along the z-direction. The electric field (E) and the magnetic field (H) are in the x-y plane. They are mutually perpendicular. Frequency of the wave, v = 30 MHz = $30\times 10^{6}\;s^{-1}$

Speed of light in vacuum, C = $3\times 10^{8}$ m/s

Wavelength of a wave is given a:

$\lambda = \frac{c}{v}$

= $\frac{3\times 10^{8}}{30\times 10^{6}}$ = 10 m

Q 8.5) A radio can tune in to any station in the 7.5 MHz to 12 MHz bands. What is the corresponding wavelength band?

A radio can tune to minimum frequency, $v_{1} = 7.5\; MHz = 7.5\times 10^{6}\; Hz$

Maximum frequency, $v_{2} = 12\; MHz = 12\times 10^{6}\; Hz$

Speed of light, c = $3\times 10^{8}\; m/s$

Corresponding wavelength for $v_{1}$ can be calculated as:

$\lambda_{1} = \frac{c}{v_{1}}$ $\frac{3\times 10^{3}}{7.5\times 10^{6}} = 40\;m$

Corresponding wavelength for $v_{2}$ can be calculated as:

$\lambda_{2} = \frac{c}{v_{2}}$ $\frac{3\times 10^{3}}{12\times 10^{6}} = 25\;m$

Thus, the wavelength band of the radio is 40 m to 25 m.

Q 8.6) A charged particle oscillates about its mean equilibrium position with a frequency of 109 Hz. What is the frequency of the electromagnetic waves produced by the oscillator?

The frequency of an electromagnetic wave produced by the oscillator is the same as that of a charged particle oscillating about its mean position i.e., 109 Hz.

Q 8.7) The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B0=510 nT. What is the amplitude of the electric field part of the wave?

Amplitude of magnetic field of an electromagnetic wave in a vacuum,

$B_{0} = 510\; nT = 510\times 10^{-9}\; T$

Speed of light in vacuum, c = $3\times 10^{8}\; m/s$

Amplitude of electric field of an electromagnetic wave is given by the relation,

$E = cB_{0} = 3\times 10^{8}\times 510\times 10^{-9} = 153\; N/C$

Therefore, the electric field part of the wave is 153 N/C.

Q 8.8) Suppose that the electric field amplitude of an electromagnetic wave is $E_{0} = 120\; N/C$ and that its frequency is v = 50 MHz.(a) Determine $B_{0},\; \omega,\; k\;and\; \lambda$ (b) Find expressions for E and B.

Electric field amplitude, $E_{0} = 120\; N/C$

Frequency of source, v = 50 MHz = $50\times 10^{6}$ Hz

Speed of light, c = $3\times 10^{8}$ m/s

(a) Magnitude of magnetic field strength is given as:

$B_{0} = \frac{E_{0}}{c}$

= $\frac{120}{3\times 10^{8}}$

= $4\times 10^{-7}\; T = 400\; nT$

Angular frequency of source is given by:

$\omega = 2nv = 2n\times 50\times 10^{6}$

= $3.14\times 10^{8}$ rad/s

Propagation constant is given as:

$k = \frac{\omega }{c}$

= $\frac{3.14\times 10^{8}}{3\times 10^{8}} = 1.05\; rad/m$

Wavelength of wave is given by:

$\lambda = \frac{c}{v}$

= $\frac{3\times 10^{8}}{50\times 10^{6}}$ = 6.0 m

(b) Suppose the wave is propagating in the positive x-direction. Then, the electric field vector will be in the positive y-direction and the magnetic field vector will be in the positive z-direction. This is because all three vectors are mutually perpendicular.

Equation of electric field vector is given as:

$\overline{E} = E_{0}\;sin(kx – \omega t)\;\widehat{j}$

= $120\;sin[1.05x – 3.14\times 10^{8}t]\;\widehat{j}$

And, magnetic field vector is given as:

$\overline{B} = B_{0}\;sin(kx – \omega t)\;\widehat{k}$ $\overline{B} = (4\times 10^{-7})\; sin[1.05x – 3.14\times 10^{8}t]\;\widehat{k}$

Q 8.9) The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = hν (for the energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for
different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?

The energy of a photon is given as:

E = hv = $\frac{hc}{\lambda}$

Where,

h = Planck’s constant = $6.6\times 10^{-34}\;Js$

c = Speed of light = $3\times 10^{8}\;m/s$ $\lambda$ = Wavelength of radiation

$∴ E = \frac{6.6\times 10^{-34}\times 3\times 10^{8}}{\lambda} = \frac{19.8\times 10^{-26}}{\lambda}\; J$

= $\frac{19.8\times 10^{-26}}{\lambda \times 1.6\times 10^{-19}} = \frac{12.375\times 10^{-7}}{\lambda}\; eV$

The given table lists the photon energies for different parts of an electromagnet spectrum for different $\lambda$.

 $\lambda$ (m) 103 1 $10^{-3}$ $10^{-6}$ $10^{-8}$ $10^{-10}$ $10^{-12}$ E (eV) $12.375\times 10^{-10}$ $12.375\times 10^{-7}$ $12.375\times 10^{-4}$ $12.375\times 10^{-1}$ $12.375\times 10^{1}$ $12.375\times 10^{3}$ $12.375\times 10^{5}$

The photon energies for the different parts of the spectrum of a source indicate the spacing of the relevant energy levels of the source

Q 8.10) In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2.0 × 1010 Hz and amplitude 48 V m–1.
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density of the B field. [ c = $3\times 10^{8}\;m\;s^{-1}$ ]

Frequency of the electromagnetic wave, v = $2\times 10^{10}\;Hz$

Electric field amplitude, $E_{0} = 48\;V\;m^{-1}$

Speed of light, c = $3\times 10^{8}\;m/s$

(a) Wavelength of a wave is given as:

$\lambda = \frac{c}{v}$

= $\frac{3\times 10^{8}}{2\times 10^{10}} = 0.015\; m$

(b) Magnetic field strength is given as:

$B_{0} = \frac{E_{0}}{c}$

= $\frac{48}{3\times 10^{8}} = 1.6\times 10^{-7}\; T$

(c) Energy density of the electric field is given as:

$U_{E} = \frac{1}{2}\; \epsilon _{0} \;E^{2}$

And, energy density of the magnetic field is given as:

$U_{B} = \frac{1}{2\mu_{0}}B^{2}$

Where,

$\epsilon _{0}$ = Permittivity of free space

$\mu_{0}$ = Permeability of free space

E = cB  …(1)

Where,

$c = \frac{1}{\sqrt{\epsilon_{0}\; \mu_{0}}}$  …(2)

Putting equation (2) in equation (1), we get

$E = \frac{1}{\sqrt{\epsilon_{0}\; \mu_{0}}}\; B$

Squaring on both sides, we get

$E^{2} = \frac{1}{\epsilon_{0}\; \mu_{0}}\; B^{2}$ $\epsilon_{0}\; E^{2} = \frac{B^{2}}{\mu_{0}}$ $\frac{1}{2}\; \epsilon_{0}\; E^{2} = \frac{1}{2}\; \frac{B^{2}}{\mu_{0}}$

=> $U_{E} = U_{B}$

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