During the propagation of electromagnetic waves in a medium,
Show Hint
Energy is equally divided between the electric and magnetic fields. The Electric energy density is equivalent to the magnetic energy density.
- electric energy density is double of the magnetic energy density
- electric energy density is half of the magnetic energy density
- electric energy density is equal to the magnetic energy density
- Both electric and magnetic energy densities are zero
The Correct Option is C
Approach Solution - 1
Energy is equally divided between the electric and magnetic fields. The Electric energy density is equivalent to the magnetic energy density.
Here, uE= ½ ϵ0E2
uB=B2/2μ0
Also, E=cB and c=1/√μ0ϵ0
Therefore, we get uE = ½ ϵ0E2 = ½ ϵ0(cB)2
=½ ϵ0\(1 \over \mu_o \epsilon_o\)B2
uE= uB
So, the correct answer is C) During the propagation of electromagnetic waves in a medium, electric energy density is equal to the magnetic energy density.
Approach Solution -2
The formulas used in order to solve this question are given by
- Electric energy density, \(U_{E}=\frac{1}{2}εE^{2}\)
- \(U_{B}=\frac{1}{2μ}B^{2}\)
- \(c=\frac{1}{\sqrt{με}}\)
Here, UE and UB respectively denote the electric and the magnetic field densities corresponding to an EM wave, c is the speed of the electromagnetic field in a medium with magnetic permeability is \(μ\) and the electric permittivity is \(ε\).
Complete step-by-step solution:
Electric energy density - \(U_E=\frac{1}{2}εE^2\) (1)
Magnetic field - \(U_B=\frac{1}{2μ}B^2\) (2)
Dividing (1) by (2) we get
\(\frac{U_E}{U_B}=\frac{\frac{1}{2}εE^2}{\frac{1}{2μ}B^2}\)
\(⇒\frac{U_E}{U_B}=με(\frac{E}{B})^2\) (3)
We know that the speed of an electromagnetic field is related to the amplitudes of the electric and the magnetic field by \(\frac{E}{B}=c\)
Putting it in (3) we get
⇒\(\frac{U_E}{U_B}=μεc^2\) (4)
Speed of the electromagnetic wave in a medium is given by \(c=\frac{1}{\sqrtμε}\)
On squaring both sides, we get
\(c=\frac{1}{\sqrtμε}\) (5)
Putting (5) in (4) we finally get
\(\frac{U_E}{U_B}=με(\frac{1}{με})\)
\(⇒\frac{U_E}{U_B}=1\)
This can also be written as
\(U_E=U_B\)
Thus, the electric energy density of an electromagnetic wave is equal to its magnetic energy density.
Hence, the correct answer is option C.
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Concepts Used:
Electromagnetic waves
The waves that are produced when an electric field comes into contact with a magnetic field are known as Electromagnetic Waves or EM waves. The constitution of an oscillating magnetic field and electric fields gives rise to electromagnetic waves.
Types of Electromagnetic Waves:
Electromagnetic waves can be grouped according to the direction of disturbance in them and according to the range of their frequency. Recall that a wave transfers energy from one point to another point in space. That means there are two things going on: the disturbance that defines a wave, and the propagation of wave. In this context the waves are grouped into the following two categories:
- Longitudinal waves: A wave is called a longitudinal wave when the disturbances in the wave are parallel to the direction of propagation of the wave. For example, sound waves are longitudinal waves because the change of pressure occurs parallel to the direction of wave propagation.
- Transverse waves: A wave is called a transverse wave when the disturbances in the wave are perpendicular (at right angles) to the direction of propagation of the wave.