Electromagnetic Waves

JEE Main level, single correct, medium

101 of 165

Question 101 of 165

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

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Answer: (A) B⃗=2×10−7sin⁡⁡(0.5×103z−1.5×1011t)i^\vec{B}=2\times {10}^{-7}\sin ⁡\left(0.5\times {10}^{3}z-1.5\times {10}^{11}t\right)\hat{i}

B=Ec=603×108=2×10−7B=\dfrac{E}{c}=\dfrac{60}{3\times {10}^{8}}=2\times {10}^{-7}
The magnetic field can be written as,
k=2πλ=2πc/f≈500k=\dfrac{2\pi }{\lambda }=\dfrac{2\pi }{c/f}\approx 500
ω=2πf≈1.5×1011\omega =2\pi f\approx 1.5\times {10}^{11}
B⃗=2×10−7sin⁡⁡(0.5×103z−1.5×1011t)i^\vec{B}=2\times {10}^{-7}\sin ⁡(0.5\times {10}^{3}z-1.5\times {10}^{11}t)\hat{i}

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