The electric field of an electromagnetic wave in free space is represented as E = E₀cos (ω t - kz)i. The corresponding magnetic induction vector will be: (a) B = E₀ Ccos (ω t + kz)j (b) B = E₀/Ccos (ω t - kz)j (c) B = E₀ Ccos (ω t - kz)j (d) B = E₀/Ccos (ω t + kz)j

Answer: (b). (ω t - kz): wave along +z; B₀ = E₀/c, same phase. k× i = j, so B along j. So the answer is (b) B = E₀/ccos (ω t - kz) j.

The electric field of an electromagnetic wave in free space is… | JEE Main 2024 (30 Jan, Shift 1)

Q18JEE Main 2024 · 30 JAN · SHIFT 1Medium

Nature of EM Waves & Wave Equation

The electric field of an electromagnetic wave in free space is represented as $\vec{E} = E_0\cos(\omega t - kz)\hat{i}$ . The corresponding magnetic induction vector will be:

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Answer: (b)

$(\omega t - kz)$ : wave along $+z$ ; $B_0 = E_0/c$ , same phase.
$\hat k\times\hat i = \hat j$ , so $\vec B$ along $\hat j$ .
So the answer is (b) $\vec B = \dfrac{E_0}{c}\cos(\omega t - kz)\hat j$ .

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