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Question:

A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the electric field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave?

B→=2×10⁷sin(0.5×10³z+1.5×10¹¹t)i^

B→=2×10⁻⁷sin(0.5×10³z−1.5×10¹¹t)i^

B→=2×10⁻⁷sin(1.5×10²x+0.5×10¹¹t)j^

B→=60sin(0.5×10³x+1.5×10¹¹t)k^

Solution:

Correct option is B. B→=2×10⁻⁷sin(0.5×10³z−1.5×10¹¹t)i^
Magnetic field when electromagnetic wave propagates in +z direction
B=B₀sin(kz−ωt)
where
B₀=60/(3×10⁸)=2×10⁻⁷
k=2π/λ=0.5×10³
ω=2πf=1.5×10¹¹