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Energy Density And Intensity Of EM Waves MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Energy Density and Intensity of EM waves is considered one the most difficult concept.

  • 48 Questions around this concept.

Solve by difficulty

A radiation of energy 'E' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (C=Velocity of light)

Out of the following options which one can be used to produce a propagating electromagnetic wave?

Concepts Covered - 1

Energy Density and Intensity of EM waves

Energy Density and Intensity of EM waves-

1. Energy Density-

The electric and magnetic fields in a plane electromagnetic wave are given by

E=E0sinω(tx/c) and, B=B0sinω(tx/c)


In any small volume dV, the energy of the electric field is

UE=12ε0E2dV
 

And the energy of the magnetic field is UB=12μ0B2dV

Thus, the total energy is U=12ε0E2dV+12μ0B2dV

The energy density is u=12ε0E2+12μZ0B2

u=12ε0E02sin2ω(tx/c)+12μ0B02sin2ω(tx/c)


For taking average over a long time, the sin2 terms have an average value of 1/2
So, uav=14ε0E02+14μ0B02
Now, as we know, E0=cB0 and μ0ε0=1c2 so that, μ0=1ε0c2 and,

B0=E0c14μ0B02=ε0c24(E0c)2=14ε0E02
 

or, uav=14ε0E02+14ε0E02=12ε0E02
Also uav=14μ0B02+14μ0B02=12μ0B02

Intensity (I) : The energy crossing per unit area per unit time, perpendicular to the direction of propagation of EM wave is called intensity.
So,

 i.e. I= Total EM energy  Surface area × Time = Total energy density × Volume  Surface area × Time I=uav×c=12ε0E02c=12B02μ0c Watt m2
 

Momentum : Electromagnetic waves also carries momentum. As we know that that the linear momentum is associated with energy and speed, similarly if a portion of EM wave of energy u propagating with speed c, then linear momentum

So we can write that if wave incident on a completely absorbing surface then momentum delivered will be equal to - 

                                                                                     

p=uc


But if the wave is incident on totally reflected surface, then the momentum will be equals to -

p=2uc


Poynting vector (S) : It is defined as the rate of flow of energy crossing a unit area in electromagnetic waves. So,

S=1μo(E×B)=c2ε0(E×B)


Unit of Poynting vector is Watt /m2. Now, as we know that in electromagnetic waves, E and B are perpendicular to each other. So,

|S|=1μ0EBsin90=EBμ0=E2μC


Importance of poynting vector is that the direction of the poynting vector S at any point gives the wave's direction of travel and direction of energy transport the point.

Average value of poynting vector -

S=12μ0E0B0=12ε0E02c=cB022μ0


As we can notice that direction of poynting vector can be given by vector product so, The direction of S does not oscillate but it's magnitude varies between zero and a maximum each quarter of period.

Radiation pressure : It is defined as the momentum imparted per second pre unit area on which the light falls
So, for the perfectly absorbing body, we can write in terms of poynting vector -

Pa=Sc


And for perfectly reflecting surface -

Pr=2Sc
 

 

Wave impedance (Z) : As the word impedance tell that obstruction in flowing of something, similarly here ,the medium offers hindrance to the propagation of wave. Such hindrance is called wave impedance and it is given by - 

Z=με=μrεrμ0ε0


For vacuum or free space -

Z=μ0ε0=376.6Ω
 

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Energy Density and Intensity of EM waves

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