The rms value of the electric field of the light coming from...

The rms value of the electric field of the light coming from the sun is $720 \mathrm{~N} / \mathrm{c}$. The average total energy density of the electromagnetic wave is (A) $4.58 \times 10^{-6} \mathrm{Jm}^{-3}$ (B) $6.3 \times 10^{-9} \mathrm{Jm}^{-3}$ (C) $81.35 \times 10^{-12} \mathrm{Jm}^{-3}$ (D) $3.3 \times 10^{-3} \mathrm{Jm}^{-3}$

The rms value of the electric field of the light coming from the sun is $720 \mathrm{~N} / \mathrm{c}$. The average total energy density of the electromagnetic wave is
(A) $4.58 \times 10^{-6} \mathrm{Jm}^{-3}$
(B) $6.3 \times 10^{-9} \mathrm{Jm}^{-3}$
(C) $81.35 \times 10^{-12} \mathrm{Jm}^{-3}$
(D) $3.3 \times 10^{-3} \mathrm{Jm}^{-3}$

Key Concepts

RMS Value of a Sinusoidal Function

The root mean square (rms) value is a measure of the effective value of a varying quantity, particularly for sinusoidal functions. It is defined as the square root of the average of the squares of the instantaneous values over a period. For a sinusoid, the rms value is related to the peak amplitude by a factor of 1/?2, allowing for a simplified calculation of averages in power and energy computations.

Electromagnetic Wave Energy Density

The energy density of an electromagnetic wave represents the energy stored per unit volume in the electric and magnetic fields. For a sinusoidal electromagnetic wave in vacuum, the instantaneous energy density is given by the sum of the electric and magnetic field contributions. When averaged over time, these contributions are equal, so that the total average energy density can be expressed in terms of the rms electric field and the permittivity of free space.

Relationship Between Electric and Magnetic Fields in a Wave

In a plane electromagnetic wave propagating in free space, the electric and magnetic fields are interrelated by the speed of light. Specifically, the magnetic field amplitude is equal to the electric field amplitude divided by the speed of light. This intrinsic relationship results in the energy contributions from both fields being equal when averaged over time, leading to a simplified expression for the total energy density.

Permittivity of Free Space

The permittivity of free space (??) is a fundamental physical constant that characterizes the ability of the vacuum to permit electric field lines. It appears in Coulomb's law and plays a critical role in the energy density expressions of electromagnetic fields. In the context of electromagnetic waves, ?? is used to relate the rms electric field to the energy density stored in the wave.

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