In a plane electromagnetic wave, the electric field...

In a plane electromagnetic wave, the electric field oscillates sinusoidaly at a frequency of $2.0 \times 10^{10} \mathrm{~Hz}$. if the peak value of electric field is $60 \mathrm{Vm}^{-1}$ the average energy density (in $\mathrm{Jm}^{-3}$ ) of the magnetic field of the wave will be (given $\left.\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$ (A) $2 \pi \times 10^{-7}$ (B) $(1 / 2 \pi) \times 10^{-7}$ (C) $4 \pi \times 10^{-7}$ (D) $(1 / 4 \pi) \times 10^{-7}$

In a plane electromagnetic wave, the electric field oscillates sinusoidaly at a frequency of $2.0 \times 10^{10} \mathrm{~Hz}$. if the peak value of electric field is $60 \mathrm{Vm}^{-1}$ the average energy density (in $\mathrm{Jm}^{-3}$ ) of the magnetic field of the wave will be (given $\left.\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$
(A) $2 \pi \times 10^{-7}$
(B) $(1 / 2 \pi) \times 10^{-7}$
(C) $4 \pi \times 10^{-7}$
(D) $(1 / 4 \pi) \times 10^{-7}$

Key Concepts

Relationship Between Electric and Magnetic Fields

In a vacuum, the electric and magnetic fields in an electromagnetic wave are intrinsically linked by Maxwell's equations, which imply that their energy densities are equal when averaged over time. This relationship allows one to determine the energy contribution of one field given the parameters of the other, and it plays a crucial role in analyzing energy transport and radiation pressure.

Magnetic Field Energy Density Formula

The energy density associated with the magnetic field component of an electromagnetic wave is given by the expression u_B = B²/(2??), where B is the magnetic field amplitude and ?? is the permeability of free space. This formula is essential for calculating how much energy is stored in the magnetic field portion of the wave and is an important tool in fields such as electromagnetics and optics.

Energy Density in Electromagnetic Fields

Energy density refers to the energy stored per unit volume in a field. In electromagnetic waves, both the electric and magnetic fields carry energy, and the energy density can be expressed as the sum of the energy densities of these two fields. The time-averaged energy density of the combined fields is a key concept in understanding the power and intensity of electromagnetic radiation.

Plane Electromagnetic Wave

A plane electromagnetic wave is a propagating disturbance in the electric and magnetic fields that travels in a uniform direction. In such a wave, the electric and magnetic fields oscillate sinusoidally and are perpendicular to each other as well as to the direction of propagation. This idealized model is fundamental in understanding the behavior of light and radio waves in free space.

Please give Ace some feedback