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JEE Main 2020 (3 Sep, Shift 1) · Nature of EM Waves & Wave Equation

Nature of EM Waves & Wave Equation question from JEE Main 2020 (3 Sep, Shift 1)

Q54JEE Main 2020 · 3 SEP · SHIFT 1Medium

Nature of EM Waves & Wave Equation

The magnetic field of a plane electromagnetic wave is

B⃗=3×10−8sin⁡[200π(y+ct)]i^\vec{B} = 3\times 10^{-8}\sin\left[200\pi(y + ct)\right]\hat{i} T

where c = 3 ×\times 108 ms–1 is the speed of light. The corresponding electric field is:

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Answer: (b)

  1. (y+ct)(y + ct): wave moves along −y-y; E0=cB0=3×108×3×10−8=9E_0 = cB_0 = 3\times10^{8}\times3\times10^{-8} = 9 V/m.
  2. Need E^×i^=−j^\hat E\times\hat i = -\hat j: (−k^)×i^=−j^(-\hat k)\times\hat i = -\hat j, so E⃗\vec E along −k^-\hat k.
  3. So the answer is (b) E⃗=−9sin⁡[200π(y+ct)]k^\vec E = -9\sin[200\pi(y + ct)]\hat k V/m.
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