Consider the following two statements regarding a linearly polarized, plane electromagnetic wave:

(A) The electric field and the magnetic field have equal average values.


(B) The electric energy and the magnetic energy have equal average values.


Explanation: Let us assume the linearly polarized plan wave travels


in z direction so the electric and magnetic fields of the wave are


given by




Their average values over one cycle would be the average from time


t=0 to t=T.


Average of electric field






(because and )


Therefore, the average of electric field is zero.


Similarly average of magnetic field is also zero as






So electric and magnetic field have their average value zero.


Therefore (A) is correct.


Now the electric energy associated with the electric field is given by


…(i)


where ϵ0 is the electric permittivity of free space(vacuum) and is


equal to 8.85 × 10-12 C2 N-1 m-2 and Ude is the energy density of


electric field.


Similarly, the magnetic energy associated with the magnetic field is


given by


…(ii)


where μ0 is the magnetic permeability of free space and its value is


4π × 10-7 T m A-1, Udb is the magnetic field energy density.


Also the amplitudes of electric and magnetic fields are related as


…(iii)


where C is the speed of light in vacuum.


and


Using (iii) in (i)


…. (iv)


The electrical permittivity and magnetic permeability of free space


related as


…. (v)


Using (v) in (iv)




Therefore, the electric and magnetic energy densities are same in


magnitude and so their average values will be same.


Average of electric energy over one cycle will be







So electric and magnetic energy and have non zero average values.


Therefore (B) is also correct.

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