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Question

An electromagnetic wave travelling along z-axis is given as E = E0cos(kzωt). Choose the correct option from the following :

A
The associated magnetic field is given as B=1c^k×E=1ω(B×E)
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B
The electromagnetic field can be written in terms of the associated magnetic field as E=c(B×^j)
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C
kE=0,kB0.
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D
kE=0,kB=0.
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Solution

The correct option is C kE=0,kB0.
Since the direction of propagation of the wave is along the Z-axis the Electric field will be perpendicular to the Z-axis will be acting in the negative Y-axis.
Then the associated magnetic field will be along the direction (^k×^E)

B=1c(^k×^E)=1ω(^k×^E)

Now, the electric field will be along the direction (B×^k) i.e perpendicular to the magnetic field and direction of motion.

The electromagnetic field can be written in terms of the associated magnetic field as
E=c(B×^k)

The angle between the ^k and E will be 900 whereas between the ^k and B will be 1800
So, here, ^k.E=0,^k.B0
Hence, the correct option is (C)

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