The magnetic field of an E.M. wave is given by B = (√(3)/2i + 1/2j)30sin [ω(t - z/c)] (S.I. Units). The corresponding electric field in S.I. units is: (a) E = (1/2i + √(3)/2j)30csin [ω(t + z/c)] (b) E = (1/2i - √(3)/2j)30csin [ω(t - z/c)] (c) E = (√(3)/2i - 1/2j)30csin [ω(t + z/c)] (d) E = (3/4i + 1/4j)30ccos [ω(t - z/c)]

Answer: (b). ω(t - z/c): wave moves along +z; E = c B× k with the same phase. ((√3)/(2) i + 12 j)× k = -(√3)/(2) j + 12 i E = (12 i - (√3)/(2) j)30csin [ω(t - z/c)] So the answer is (b).

The magnetic field of an E.M. wave is given by B = (√(3)/2i +… | JEE Main 2025 (28 Jan, Shift 2)

Q10JEE Main 2025 · 28 JAN · SHIFT 2Medium

Nature of EM Waves & Wave Equation

The magnetic field of an E.M. wave is given by $\vec{B} = \left(\frac{\sqrt{3}}{2}\hat{i} + \frac{1}{2}\hat{j}\right)30\sin\left[\omega\left(t - \frac{z}{c}\right)\right]$ (S.I. Units). The corresponding electric field in S.I. units is:

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Answer: (b)

$\omega(t - z/c)$ : wave moves along $+z$ ; $\vec E = c\,\vec B\times\hat k$ with the same phase.
$\left(\tfrac{\sqrt3}{2}\hat i + \tfrac12\hat j\right)\times\hat k = -\tfrac{\sqrt3}{2}\hat j + \tfrac12\hat i$
$\vec E = \left(\tfrac12\hat i - \tfrac{\sqrt3}{2}\hat j\right)30c\sin[\omega(t - z/c)]$
So the answer is (b).

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