An electromagnetic wave travelling along z-axis is given as E = E0cos(kz−ωt). 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
k⋅→E=0,k⋅→B≠0.
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D
k⋅→E=0,k⋅→B=0.
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Solution
The correct option is Ck⋅→E=0,k⋅→B≠0. 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.→B≠0 Hence, the correct option is (C)