Question

The total energy density for an electromagnetic wave in vacuum is:
\[\begin{align}
  & A.\,{{\varepsilon }_{0}}\dfrac{{{E}^{2}}}{3} \\
 & B.\,{{\varepsilon }_{0}}{{E}^{2}} \\
 & C.\,\dfrac{{{\varepsilon }_{0}}{{E}^{2}}}{2} \\
 & D.\,\dfrac{{{E}^{2}}}{{{\varepsilon }_{0}}} \\
\end{align}\]

Answer 1

Hint: The energy density in the electromagnetic waves is divided equally between the electric field and magnetic field. Thus, the total energy density equals the sum of the electric energy density and the magnetic energy density. As in the vacuum, the total energy density for an electromagnetic wave is asked, so, no, other external parameters play a role in the density.
Formula used:
\[{{\mu }_{E}}=\dfrac{{{\varepsilon }_{0}}{{E}^{2}}}{2}\]
\[{{\mu }_{B}}=\dfrac{{{B}^{2}}}{2{{\mu }_{0}}}\]

Complete answer:
The waves that get created or generated because of the vibrations between the electric field and the magnetic field are called the electromagnetic waves. These waves are composed of the oscillating electric field and the magnetic field.
The energy density in the electromagnetic waves is divided equally between the electric field and magnetic field.
The electric energy density is, \[{{\mu }_{E}}=\dfrac{{{\varepsilon }_{0}}{{E}^{2}}}{2}\]
Where \[{{\varepsilon }_{0}}\]is the permittivity of free space and E is the magnitude of the electric field.
 The magnetic energy density is, \[{{\mu }_{B}}=\dfrac{{{B}^{2}}}{2{{\mu }_{0}}}\]
Where \[{{\mu }_{0}}\]is the permeability of free space and B is the magnitude of the magnetic field.
Thus, the total energy density is the sum of the electric energy density and the magnetic energy density. As in the vacuum, the total energy density for an electromagnetic wave is asked, so, no other external parameters play a role in the density. So, we have,
The total energy density = The electric energy density + The magnetic energy density
\[\begin{align}
  & \mu ={{\mu }_{E}}+{{\mu }_{B}} \\
 & \therefore \mu =\dfrac{{{\varepsilon }_{0}}{{E}^{2}}}{2}+\dfrac{{{B}^{2}}}{2{{\mu }_{0}}} \\
\end{align}\]
\[\therefore \] The total energy density for an electromagnetic wave in vacuum is\[\dfrac{{{\varepsilon }_{0}}{{E}^{2}}}{2}+\dfrac{{{B}^{2}}}{2{{\mu }_{0}}}\]..

So,option C is the correct answer.

Note:
The electromagnetic waves get formed when the electric field and the magnetic field come in contact with each other. The total energy density equals the sum of the electric energy density and the magnetic energy density, as the energy density in the electromagnetic waves is divided equally between the electric field and magnetic field.