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JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)

JEE Main 2023 Physics question on Electromagnetic Waves

In E⃗\vec{E} and K⃗\vec{K} represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by:

(ω\omega - angular frequency):
  1. A.
    K⃗×E⃗\vec{K} \times \vec{E}
  2. B.
    1ω(K⃗×E⃗)\dfrac{1}{\omega}\left(\vec{K} \times \vec{E}\right)
  3. C.
    ω(K⃗×E⃗)\omega\left(\vec{K} \times \vec{E}\right)
  4. D.
    ω(E⃗×K⃗)\omega\left(\vec{E} \times \vec{K}\right)
Show answer and solution

Correct option: B

Solution

From Maxwell's equations for EM waves, the relationship between fields is B = (K × E)/ω. This comes directly from Faraday's law in wave form: ∇ × E = -∂B/∂t, which in terms of plane wave quantities gives K × E = ωB, so B = (1/ω)(K × E). The direction of K × E correctly gives the direction of B (since E, B, and K form a right-handed triad), and the magnitude gives |B| = |E|/c, consistent with |K|/ω = 1/c in vacuum.

[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]

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