Electromagnetic Waves

JEE Main level, single correct, medium

102 of 165

Question 102 of 165

An electromagnetic wave is represented by the electric filed E⃗=E0n^sin⁡⁡[ωt+(6y−8z)].\vec{E}={E}_{0}\hat{n}\sin ⁡\left[\omega t+\left(6y-8z\right)\right]. Taking unit vectors in x,yx,y and zz directions to be i^,j^,k^,\hat{i},\hat{j},\hat{k}, the directions of propogations s^,\hat{s}, is:

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Answer: (B) s^=(−3i^+4j^5)\hat{s}=\left(\dfrac{-3\hat{i}+4\hat{j}}{5}\right)

The standard equation of electromagnetic wave E⃗=E0n^sin⁡[ωt−kx^]\vec{E}={E}_{0}\hat{n}\sin \left[\omega t-k\hat{x}\right]
here x^\hat{x}represents the direction of propagation wave.On comparing the given equation with the standard equation, the direction of propagation is along line −6y+8z-6y+8z . Thus, unit vector along the direction of propagation is,
s^=−6j^+8k^10=−35j^+45k^\hat{s}=\dfrac{-6\hat{j}+8\hat{k}}{10}=-\dfrac{3}{5}\hat{j}+\dfrac{4}{5}\hat{k}

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