An electromagnetic wave travelling in the x-direction has frequency of 2×1014Hz and electric field amplitude of 27 Vm−1. From the options given below, which one describes the magnetic field for this wave?
A
→B(x,t)=(3×10−8T)^jsin[2π(1.5×10−8x−2×1014t)]
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B
→B(x,t)=(9×10−8T)^jsin[(1.5×10−6x−2×1014t)]
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C
→B(x,t)=(9×10−8T)^ksin[2π(1.5×10−6x−2×1014t)]
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D
→B(x,t)=(9×10−8T)^isin[2π(1.5×10−8x−2×1014t)]
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Solution
The correct option is C→B(x,t)=(9×10−8T)^ksin[2π(1.5×10−6x−2×1014t)]
Using Maxwell's equation
E∘B∘=c where c is velocity of light, E∘ and B∘ are amplitudes of electric and magnetic field.
given E∘=27N/C
The amplitude of magnetic field is B∘=273×108=9×10−8
frequency of wave is given as f=2X1014 Hz, it's angular frequency is given as ω=2πf=2π×2X1014
The direction of electromagnetic wave is given as x axis, the direction of magnetic field will be perpendicular to it, hence option B and C can only be the answer, however, in option B the angular frequency is not as calculated above.