The electric field in an electromagnetic wave is given by E = i 40cos ω(t - z/c) NC⁻¹. The magnetic field induction of this wave is (in SI unit): (a) B = j40/ccos ω(t - z/c) (b) B = i40/ccos ω(t - z/c) (c) B = j 40cos ω(t - z/c) (d) B = k40/ccos ω(t - z/c)

Answer: (a). ω(t - z/c): wave moves along +z; B = ( k× E)/(c). k× i = j, B₀ = 40/c. So the answer is (a) B = j 40/ccos ω(t - z/c).

The electric field in an electromagnetic wave is given by E = i 40cos… | JEE Main 2024 (4 Apr, Shift 1)

Q17JEE Main 2024 · 4 APR · SHIFT 1Medium

Nature of EM Waves & Wave Equation

The electric field in an electromagnetic wave is given by $\vec{E} = \hat{i}\,40\cos\omega(t - z/c)\text{ NC}^{-1}$ . The magnetic field induction of this wave is (in SI unit):

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Answer: (a)

$\omega(t - z/c)$ : wave moves along $+z$ ; $\vec B = \dfrac{\hat k\times\vec E}{c}$ .
$\hat k\times\hat i = \hat j$ , $B_0 = 40/c$ .
So the answer is (a) $\vec B = \hat j\,\dfrac{40}{c}\cos\omega(t - z/c)$ .

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