A plane electromagnetic wave in a non-magnetic dielectric medium is given by E = E₀ sin (4 × 10⁻⁷ x - 50t) with distance being in meter and time in seconds. The dielectric constant of the medium is: (a) 2.4 (b) 5.8 (c) 8.2 (d) 4.8

Answer: (b). k = 4 × 10⁻⁷ m ⁻¹, ω = 50 rad/s, so v = ω/k = 504 × 10⁻⁷ = 1.25 × 10⁸ m/s n = c/v = 3 × 10⁸1.25 × 10⁸ = 2.4 K = n² = 5.76 ≈ 5.8 So the answer is (b) 5.8.

A plane electromagnetic wave in a non-magnetic dielectric medium is… | JEE Main 2013 (22 Apr, Shift 1)

Q25JEE Main 2013 · 22 APR · SHIFT 1Medium

Speed of EM Waves in a Medium

A plane electromagnetic wave in a non-magnetic dielectric medium is given by

$\vec{E} = \vec{E}_0 \sin(4 \times 10^{-7} x - 50t)$ with distance being in meter and time in seconds. The dielectric constant of the medium is:

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Answer: (b)

$k = 4 \times 10^{-7}$ m $^{-1}$ , $\omega = 50$ rad/s, so $v = \omega/k = \dfrac{50}{4 \times 10^{-7}} = 1.25 \times 10^{8}$ m/s
$n = c/v = \dfrac{3 \times 10^{8}}{1.25 \times 10^{8}} = 2.4$
$K = n^2 = 5.76 \approx 5.8$
So the answer is (b) 5.8.

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Speed of EM Waves in a Medium question from JEE Main 2013 (22 Apr, Shift 1)

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