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 [2006] (A) $3.3 \times 10^{-3} \mathrm{~J} / \mathrm{m}^{3}$ (B) $4.58 \times 10^{-6} \mathrm{~J} / \mathrm{m}^{3}$ (C) $6.37 \times 10^{-9} \mathrm{~J} / \mathrm{m}^{3}$ (D) $81.35 \times 10^{-12} \mathrm{~J} / \mathrm{m}^{3}$

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 [2006]
(A) $3.3 \times 10^{-3} \mathrm{~J} / \mathrm{m}^{3}$
(B) $4.58 \times 10^{-6} \mathrm{~J} / \mathrm{m}^{3}$
(C) $6.37 \times 10^{-9} \mathrm{~J} / \mathrm{m}^{3}$
(D) $81.35 \times 10^{-12} \mathrm{~J} / \mathrm{m}^{3}$

Key Concepts

Relationship between Electric and Magnetic Fields in Electromagnetic Waves

In an electromagnetic wave propagating in free space, the electric and magnetic fields are intrinsically linked by Maxwell's equations. Specifically, the magnetic field can be expressed in terms of the electric field and the speed of light, and the energy densities associated with the electric and magnetic fields are equal. This symmetry is crucial for deriving the total energy density from the RMS value of the electric field.

Vacuum Permittivity

Vacuum permittivity, often denoted as ??, is a fundamental physical constant that characterizes the ability of free space to permit electric field lines. It appears in Maxwell's equations and plays a key role in determining the relationship between the electric field strength and the energy stored in the electric component of an electromagnetic wave.

Electromagnetic Energy Density

This concept refers to the total energy stored per unit volume in an electromagnetic wave. In free space, the energy density is contributed equally by the electric and magnetic fields, and is calculated as the sum of the electric field energy density and the magnetic field energy density. It is essential for understanding how energy is distributed in electromagnetic waves.

Root Mean Square (RMS) Value

The RMS value is a statistical measure used for oscillating functions, such as alternating electric fields, that represents the effective or equivalent constant value of the function. In the context of electromagnetic waves, the RMS value is used to define the effective amplitude of the electric field, which in turn is used in calculations of energy density and power.

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