Question

Question: In an electromagnetic wave, the average energy density is associated
(A) With electric field only
(B) With magnetic field only
(C) Equally with electric and magnetic fields
(D) None of these

Answer 1

Hint: Energy in any part of the electromagnetic part is the sum of its electric field energy and magnetic field energy. In an electromagnetic wave, the average energy density is associated equally with electric and magnetic fields. The energy per unit volume called energy density (u) is the sum of energy density from the electric field and magnetic field.

Formula used:
$u = \dfrac{1}{2}{\varepsilon _0}{E^2} + \dfrac{1}{{2{\mu _0}}}{B^2}$
Where,
$u$ = energy density
${\varepsilon _0}$=permittivity of free space, unit is ${{\text{C}}^{\text{2}}}{\text{/N}}{{\text{m}}^{\text{2}}}$
${\mu _0}$=vacuum permeability ${\text{N}}{{\text{A}}^{{\text{ - 2}}}}$ newton per ampere square
$B$ = magnetic field
$E$ = electric field

Complete step-by-step answer:
We know that, In an electromagnetic wave, the amplitude is the maximum field strength of the electric field and magnetic field. The energy of a wave is determined by the amplitude of the wave. The energy per unit volume called energy density (u) is the sum of energy density from the electric field and magnetic field.
Thus, the expression for energy density is as shown following,
$u = \dfrac{1}{2}{\varepsilon _0}{E^2} + \dfrac{1}{{2{\mu _0}}}{B^2}$ (1)
Now we know the other relation which is between the electrical and magnetic fields.which is as shown below,
 $E = Bc = \dfrac{1}{{\sqrt {{\mu _0}{\varepsilon _0}} }}B$ (2)
From this relation, we conclude that magnetic energy density and electric energy density are equal.
In other words, we can say that for an electromagnetic wave the energy which corresponds to the electric fields is equal to the energy of the magnetic field.
Hence, we can re-write the energy density as shown below,
$u = {\varepsilon _0}{E^2} = \dfrac{1}{{{\mu _0}}}{B^2}$ (3)
We can say that average electrical density is equally with the electric and magnetic fields.
Hence, option (C) is the correct option.
Additional information:
Electric fields and magnetic fields store energy. The energy density associated with the field in 3D is as shown below,
${{\text{n}}_{\text{E}}}{\text{ = }}\dfrac{{{\text{energy}}}}{{{\text{volume}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{2}}}{{\varepsilon }}{{\text{E}}^{\text{2}}}$
This is energy density which calculates the energy stored in a capacitor.
For the magnetic field,
${{\text{n}}_{\text{B}}}{\text{ = }}\dfrac{{{\text{energy}}}}{{{\text{volume}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{2}}}\dfrac{{{{\text{B}}^{\text{2}}}}}{{{\mu }}}$
Which is used to store the energy in the inductor.
Note:
An electromagnetic wave has two components as an electric field and a magnetic field.
The electric field is defined as force per unit stationary charge.
The magnetic field is defined as force per unit moving charge.
When a parallel-plate capacitor is charged, the battery does work in separating the charges. If the battery has moved a charge Q by moving electrons from the positively charged plate to the negatively charged plate. The voltage across the capacitor is $V = \dfrac{Q}{C}$ and the work done by the battery is$W = \dfrac{1}{2}C{V^2}$ . Here the battery has converted chemical energy into electrostatic potential energy.
The energy density of the magnetic field can be defined as the energy stored in an inductor.