The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,

Question

$E_{y} = 20 \sin (3 \times 10^{6} x - 4.5 \times 10^{14} t) V / m$

(where $x$ , $t$ and other values have S.I. units). The dielectric constant of the medium is _____.

(speed of light is $3 \times 10^{8} m / s$ ) [2026]

Smart Achievers · Accepted Answer

(4)

$Velocity in medium:$

$v = \frac{ω}{k} = \frac{4.5 \times 10^{14}}{3 \times 10^{6}} = \frac{3}{2} \times 10^{8} m/s$

$n = \frac{c}{v} = 2$

$n = \sqrt{μ_{r} ε_{r}}$ $(μ_{r} = 1)$

$2 = \sqrt{ε_{r}} \Rightarrow ε_{r} = 4$

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