A linearly polarized electromagnetic wave in vacuum E = 3.1 cos [(1.8)z - (5.4 × 10⁶)t] i N/C is incident normally on a perfectly reflecting wall at z = a. Choose the correct option (a) The wavelength is 5.4 m (b) The frequency of electromagnetic wave is 54 × 104 Hz. (c) The transmitted wave will be 3.1 cos [(1.8)z - (5.4 × 10⁶)t] i N/C (d) The reflected wave will be 3.1 cos [(1.8)z + (5.4 × 10⁶)t] i N/C

Answer: (d). k = 1.8 m ⁻¹: λ = 2π/1.8 ≈ 3.5 m, so (a) is wrong. ω = 5.4 × 10⁶ rad/s: f = ω/2π ≈ 8.6 × 10⁵ Hz, so (b) is wrong. A perfectly reflecting wall transmits nothing, so (c) is wrong. The reflected wave travels along -z, so the phase becomes (1.8z + 5.4 × 10⁶ t). So the answer is (d).

A linearly polarized electromagnetic wave in vacuum E = 3.1 cos… | JEE Main 2021 (25 Jul, Shift 1)

Q47JEE Main 2021 · 25 JUL · SHIFT 1Difficult

Nature of EM Waves & Wave Equation

A linearly polarized electromagnetic wave in vacuum

$E = 3.1 \cos\left[(1.8)z - (5.4 \times 10^{6})t\right] \hat{i}\text{ N/C}$

is incident normally on a perfectly reflecting wall at z = a. Choose the correct option

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Answer: (d)

$k = 1.8$ m $^{-1}$ : $\lambda = 2\pi/1.8 \approx 3.5$ m, so (a) is wrong.
$\omega = 5.4 \times 10^{6}$ rad/s: $f = \omega/2\pi \approx 8.6 \times 10^{5}$ Hz, so (b) is wrong.
A perfectly reflecting wall transmits nothing, so (c) is wrong.
The reflected wave travels along $-z$ , so the phase becomes $(1.8z + 5.4 \times 10^{6} t)$ .
So the answer is (d).

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Nature of EM Waves & Wave Equation question from JEE Main 2021 (25 Jul, Shift 1)

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