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Physics · Electromagnetic Waves

JEE Advanced 2023 — Paper 2 — Question 20

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by

E→=30(2x^+y^)sin⁡[2π(5×1014t−1073z)]Vm−1\overrightarrow{\mathrm{E}}=30(2 \hat{\mathrm{x}}+\hat{\mathrm{y}}) \sin \left[2 \pi\left(5 \times 10^{14} \mathrm{t}-\frac{10^{7}}{3} \mathrm{z}\right)\right] \mathrm{Vm}^{-1}. Which of the following option(s) is(are) correct ? [Given: The speed of light in vacuum, c=3×108 m s−1\mathrm{c}=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1} ]

  1. Option A:

    Bx=−2×10−7sin⁡[2π(5×1014t−1073z)]Wbm−2\mathrm{B}_{\mathrm{x}}=-2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} \mathrm{t}-\frac{10^{7}}{3} \mathrm{z}\right)\right] \mathrm{Wb} \mathrm{m}^{-2}.

    Correct
  2. Option B:

    By=2×10−7sin⁡[2π(5×1014t−1073z)]Wbm−2\mathrm{B}_{\mathrm{y}}=2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} \mathrm{t}-\frac{10^{7}}{3} \mathrm{z}\right)\right] \mathrm{Wbm}^{-2}

  3. Option C:

    The wave is polarized in the xyx y-plane with polarization angle 30∘30^{\circ} with respect to the xx-axis

  4. Option D:

    The refractive index of the medium is 2

    Correct

Answer: A, D

Step-by-step solution

Speed of light in dielectric medium =5×1014(1073)=1.5×108 m/s=\frac{5 \times 10^{14}}{\left(\frac{10^{7}}{3}\right)}=1.5 \times 10^{8} \mathrm{~m} / \mathrm{s} ∴\therefore refractive index =2=2 E=BC\mathrm{E}=\mathrm{BC} 305=B(1.5×108)30 \sqrt{5}=\mathrm{B}\left(1.5 \times 10^{8}\right) B=205×10−8B=20 \sqrt{5} \times 10^{-8} Bx=Bsin⁡θ=2×10−7\mathrm{B}_{\mathrm{x}}=\mathrm{B} \sin \theta=2 \times 10^{-7} By=Bcos⁡θ=4×10−7B_{y}=B \cos \theta=4 \times 10^{-7} For the given equation of EMW for electric field, magnetic field can be expressed as Bx=−2×10−7sin⁡[2π(5×1014t−1073z]Wbm−2B_{x}=-2 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^{7}}{3} z\right] \mathrm{Wbm}^{-2}\right. By=4×10−7sin⁡[2π(5×1014t−10−73z]Wbm−2B_{y}=4 \times 10^{-7} \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^{-7}}{3} z\right] \mathrm{Wbm}^{-2}\right. The wave is polarized in xy-plane with polarization angle tan⁡−1(12)\tan ^{-1}\left(\frac{1}{2}\right) with respect to x -axis

Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2023
Paper
Paper 2
Subject
Physics
Chapter
Electromagnetic Waves
Topic
Displacement Current and Equation of EM Waves