Question

When a plane electromagnetic wave travels in vacuum, the average electric energy density is given by (here $E_{0}$ is the amplitude of the electric field of the wave) is (a) $\frac{1}{4} \varepsilon_{0} E_{0}^{2}$ (b) $\frac{1}{2} \varepsilon_{0} E_{0}^{2}$ (c) $\mathrm{E}_{0} \boldsymbol{F}_{\mathrm{O}}^{2}$ (d) $2 e_{0} \mathbb{E}_{0}^{2}$

Name: Problem 74, Chapter 22: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-16T09:38:07-08:00
Duration: 1 min 19 s
Channel: Satpal Satpal
Description: When a plane electromagnetic wave travels in vacuum, the average electric energy density is given by (here E0 is the amplitude of the electric field of the wave) is (a) (1)/(4) ε0 E0^2 (b) (1)/(2) ε0 E0^2 (c) E0 FO^2 (d) 2 e0 𝔼0^2

   When a plane electromagnetic wave travels in vacuum, the average electric energy density is given by (here $E_{0}$ is the amplitude of the electric field of the wave) is
(a) $\frac{1}{4} \varepsilon_{0} E_{0}^{2}$
(b) $\frac{1}{2} \varepsilon_{0} E_{0}^{2}$
(c) $\mathrm{E}_{0} \boldsymbol{F}_{\mathrm{O}}^{2}$
(d) $2 e_{0} \mathbb{E}_{0}^{2}$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 22, Problem 74

Instant Answer

Solved by Expert Satpal Satpal

01/16/2022

Step 1

Step 1: The average electric energy density (uE) of a plane electromagnetic wave traveling in a vacuum is given by the formula: \[uE = \frac{1}{2} \varepsilon_{0} E_{RMS}^{2}\] Show more…

Show all steps

Thanks for your feedback!

When a plane electromagnetic wave travels in vacuum, the average electric energy density is given by (here $E_{0}$ is the amplitude of the electric field of the wave) is (a) $\frac{1}{4} \varepsilon_{0} E_{0}^{2}$ (b) $\frac{1}{2} \varepsilon_{0} E_{0}^{2}$ (c) $\mathrm{E}_{0} \boldsymbol{F}_{\mathrm{O}}^{2}$ (d) $2 e_{0} \mathbb{E}_{0}^{2}$

Play audio

Feedback

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Time Averaging of Sinusoidal Functions

When evaluating properties of sinusoidal functions, such as the square of a sine or cosine function, the time average over one complete cycle is 1/2. This averaging process is essential in converting the instantaneous energy density into its average value over time.

Electric Energy Density

The electric energy density associated with a field is given by (1/2) times the permittivity of free space multiplied by the square of the electric field. For a time-varying sinusoidal field, such as in a plane wave, this expression must be averaged over one period to account for the oscillatory nature of the field.

Electromagnetic Wave Propagation in Vacuum

In vacuum, electromagnetic waves consist of oscillating electric and magnetic fields that travel at the speed of light. These fields are governed by Maxwell's equations, and their energy contributions can be analyzed separately by considering the energy density carried by each field.

Please give Ace some feedback