Rms Fields And Intensity

Question

A plane electromagnetic wave in vacuum has a peak electric field of 30 V/m, and an analyst computes its average intensity using free-space constants.

RankGuru · Accepted Answer

Extending NCERT Class 12, Chapter 8 (Electromagnetic Waves), the average intensity of a plane electromagnetic wave is I = ½ ε₀ c E₀², where the factor of one half comes from time-averaging the squared sinusoidal field over a cycle, since the average of sin² over a full period is exactly one half. The intensity represents the mean power carried per unit area by the combined electric and magnetic fields, and it can equally be written as the product of the average total energy density and the speed of light. Substituting ε₀ = 8.85 × 10⁻¹² C²/N·m², c = 3 × 10⁸ m/s, and E₀ = 30 V/m gives I = ½ × 8.85 × 10⁻¹² × 3 × 10⁸ × 900 = 1.19 W/m². The value 2.39 W/m² is double the correct result because it omits the one-half averaging factor. The value 0.60 W/m² is roughly half of the true value, arising from an extra erroneous factor of one half. The value 4.78 W/m² overcounts by a factor of four, likely from mishandling both the averaging factor and the square of the field. A magnitude check confirms that a modest 30 V/m field yields an intensity of about one watt per square metre, consistent with the correct answer.

Rms Fields And Intensity

Select the correct option:

🔒 Solution Hidden from View

More electromagnetic waves Practice Questions

A television transmitter broadcasts at a frequency of 6.0 × 10⁸ Hz, and a technician must determine ...

In a plane electromagnetic wave, how do the frequencies of the oscillating electric field and the os...

Which property of microwaves makes them especially suitable for use in radar systems and in speed de...

Which electromagnetic radiation from sunlight is largely absorbed by the ozone layer, protecting liv...

Among the following electromagnetic radiations, which one originates from transitions within atomic ...

Why can electromagnetic waves travel through the vacuum of outer space while sound waves from the Su...

The electric flux through a certain surface changes at a steady rate of 2.0 × 10⁴ V·m per second, an...

A laser delivers an average intensity of 6.0 W/m² onto a screen, and a researcher needs the average ...

Weather satellites detect a form of electromagnetic radiation strongly emitted by warm bodies, often...

Which modification did Maxwell introduce to Ampere's circuital law so that it would remain valid in ...

A perfectly absorbing solar sail receives light of energy \cup from the Sun over a given interval, ...

A doctor uses a particular electromagnetic radiation to visualise bone fractures because it penetrat...

About This Question

Solution