1 2 3 4 5 6 7 8 9 10

Q. 84.0( 12 Votes )

Suppose that the electric field amplitude of an electromagnetic wave is E₀ = 120 N/C and that its frequency is ν = 50.0 MHz. (a) Determine, B₀, ω, k, and λ. (b) Find expressions for E and B.

Class 12th NCERT - Physics Part-I 8. Electromagnetic Waves

Answer :

Given: Electric field amplitude of electromagnetic wave, E₀ = 120 N/C

Frequency of electromagnetic wave, v = 50 MHz

(a) Magnitude of magnetic field is given by the following expression:

B₀ = E₀/c

⇒ B₀ = 40 × 10^-8 T

Converting it into nT, we get B₀ = 400 nT

Angular frequency can be calculated as follows:

ω = 2πv

where ν is the linear frequency.

ω = 2×3.14×50×10⁶Hz

ω = 314 × 10⁶ rad/s

ω = 3.14 × 10⁸ rad/s

Propagation constant k is given by the following expression:

k = ω /c

K = 1.05 rad/m

Wavelength can be calculated by the following expression:

λ = c/v

⇒ λ = 6 m

(b) The expression for electric field and magnetic field can be written as follows:

Let a wave is propagating in positive x- direction.

Since all the three vectors are mutually perpendicular to each other. The electric field vector will be in positive y- direction and magnetic field vector will be in positive z-direction.

Electric field vector can be expressed in the form of equation as given below:

⇒

Substituting values in above equation we get

⇒

Magnetic field vector can be expressed in form of following equation:

⇒

Substituting values in above equation we get

⇒

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSThe 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?NEXTThe terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = hν (for 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?

Related Videos

Source of Electromagnetic wave

Source of Electromagnetic wave

Source of Electromagnetic wave6 mins

Back to 11th | Interactive Quiz: Waves (part-2)

Back to 11th | Interactive Quiz: Waves (part-2)

Back to 11th | Interactive Quiz: Waves (part-2)52 mins

Electromagnetic Induction

Electromagnetic Induction

Electromagnetic Induction50 mins

Back to 11th | Interactive Quiz: Waves (part-1)

Back to 11th | Interactive Quiz: Waves (part-1)

Back to 11th | Interactive Quiz: Waves (part-1)49 mins

S.H.M.

S.H.M.

S.H.M.51 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

caricature

view all courses

RELATED QUESTIONS :

Sea water at frequency v = 4 × 108 Hz has permittivity ε ≈ 80 ε_o, permeability μ ≈ μo and resistivity ρ = 0.25 Ω–m. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source. What fraction of the conduction current density is the displacement current density?

Physics - Exemplar

Displacement current goes through the gap between the plates of a capacitor when the charge of the capacitor

HC Verma - Concepts of Physics Part 2

A long straight cable of length l is placed symmetrically along z-axis and has radius a(<<l). The cable consists of a thin wire and a co-axial conducting tube. An alternating current flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance s from the wire inside the cable is

(i) Calculate the displacement current density inside the cable.

(ii) Integrate the displacement current density across the cross section of the cable to find the total displacement current Id.

(iii) Compare the conduction current I₀ with the displacement current .

Physics - Exemplar

You are given a 2μF parallel plate capacitor. How would you establish an instantaneous displacement current of 1mA in the space between its plates?

Physics - Exemplar

Using B = μ₀ H find the ratio E₀/H₀ for a plane electromagnetic wave propagating through vacuum. Show that is has the dimensions of electric resistance. This ratio is a universal constant called the impedance of free space.

HC Verma - Concepts of Physics Part 2

A plane EM wave travelling along z direction is described by and . Show that

(i) The average energy density of the wave is given by .

(ii) The time averaged intensity of the wave is given by .

Physics - Exemplar

A plane EM wave travelling in vacuum along z direction is given by and

(i) Evaluate over the rectangular loop 1234 shown in Fig 8.2.

(ii) Evaluate over the surface bounded by loop 1234.

(iii) Use equation to prove .

(iv) By using similar process and the equation , prove that

Physics - Exemplar

A variable frequency ac source is connected to a capacitor. How will the displacement current change with decrease in frequency?

Physics - Exemplar

You are given a 2μF parallel plate capacitor. How would you establish an instantaneous displacement current of 1mA in the space between its plates?

Physics - Exemplar