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Question
Consider the following two statements regarding a linearly polarised, 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.
Options
Both A and B are true.
A is false but B is true.
B is false but A is true
Both A and B are false.
Solution
Both A and B are true.
For a linearly polarised, plane electromagnetic wave
`E = E_0 sin ω(t-x"/"c)`
`B = B_0 sin ω(t-x"/"c)`
The average value of either E or B over a cycle is zero ( average of sin(θ) over a cycle is zero).
Also the electric energy density (uE) and magnetic energy density `(u_B)` are equal .
`u_E = 1/2∈_0E^2 = B^2/(2u_0) = u_B`
Energy can be found out by integrating energy density over the entire volume of full space.
As the energy of the electromagnetic wave is equally shared between electric and magnetic field so their average values will also be equal.
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