Electromagnetic Waves

JEE Main level, single correct, medium

86 of 165

Question 86 of 165

A plane electromagnetic wave of frequency 500MHz500MHz is traveling in a vacuum along the y−y-direction. At a particular point in space and time, B⃗=8.0×10−8z^T\vec{B}=8.0\times {10}^{-8}\hat{z}T. The value of the electric field at this point is:(speed of light =3×108ms−1=3\times {10}^{8}{ms}^{-1}) x^,y^,z^\hat{x},\hat{y},\hat{z} are unit vectors along x,yx,y and zz direction.

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Answer: (A) −24x^Vm−1-24\hat{x}V{m}^{-1}

f=5×108Hzf=5\times {10}^{8}Hz
EMEM wave is travelling towards +j^+\hat{j}
B⃗=8.0×10−8z^T\vec{B}=8.0\times {10}^{-8}\hat{z}T
E⃗=B⃗×C⃗=(8×10−8z^)×(3×108y^)\vec{E}=\vec{B}\times \vec{C}=\left(8\times {10}^{-8}\hat{z}\right)\times \left(3\times {10}^{8}\hat{y}\right)
=−24x^Vm−1=-24\hat{x}V{m}^{-1}

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