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 he electromagnetic wave ?

Engineering

Physics

Electromagnetic Waves

Question

$\vec{B} = 2 \times 10^{- 7} \sin (0 .5 \times 10^{3} z + 1 .5 \times 10^{11} t) \hat{i}$

$\vec{B} = 60 \sin (0 .5 \times 10^{3} x + 1 .5 \times 10^{11} t) \hat{k}$

$\vec{B} = 2 \times 10^{- 7} \sin (0 .5 \times 10^{3} z - 1 .5 \times 10^{11} t) \hat{i}$

$\vec{B} = 2 \times 10^{- 7} \sin (1 .5 \times 10^{2} x + 0 .5 \times 10^{11} t) \hat{j}$

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v = 23.9 GHz

E₀ = 60 V/m

$∵ \frac{E_{0}}{B_{0}} = C \Rightarrow B_{0} = \frac{E_{0}}{C} = \frac{60}{3 \times 10^{8}} = 2 \times 10^{- 7}$

Since the wave is propagating in positive z-direction

So acceptable magnetic field component wll be

$\vec{B} = 2 \times 10^{- 7} \sin (0 .5 \times 10^{3} z - 1 .5 \times 10^{11} t) \hat{i}$