A plane electromagnetic wave propagating in x -direction is described by Ey = (200 V m⁻¹) sin [1.5 × 10⁷ t - 0.05 x]; The intensity of the wave is: (Use ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²) (a) 35.4 W m⁻² (b) 53.1 W m⁻² (c) 26.6 W m⁻² (d) 106.2 W m⁻²

Answer: (b). I = 1/2ε₀ c E₀² I = 1/2 × 8.85 × 10⁻¹² × 3 × 10⁸ × (200)² = 1.3275 × 10⁻³ × 4 × 10⁴ I ≈ 53.1 W m ⁻² So the answer is (b) 53.1 W m ⁻².

A plane electromagnetic wave propagating in x -direction is described… | JEE Main 2024 (27 Jan, Shift 1)

Q7JEE Main 2024 · 27 JAN · SHIFT 1Easy

Energy Density & Intensity

A plane electromagnetic wave propagating in $x$ -direction is described by

$E_y = \left(200\text{ V m}^{-1}\right) \sin\left[1.5 \times 10^{7} t - 0.05 x\right]$ ;

The intensity of the wave is:

(Use $\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^2\text{ N}^{-1}\text{ m}^{-2}$ )

Show answer and solution

Answer: (b)

$I = \tfrac{1}{2}\varepsilon_0 c E_0^2$
$I = \tfrac{1}{2} \times 8.85 \times 10^{-12} \times 3 \times 10^{8} \times (200)^2 = 1.3275 \times 10^{-3} \times 4 \times 10^{4}$
$I \approx 53.1$ W m $^{-2}$
So the answer is (b) $53.1$ W m $^{-2}$ .