The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, $\mathrm{E}_{\mathrm{y}}=20 \sin \left(3 \times 10^{6} \mathrm{x}-4.5 \times 10^{14} \mathrm{t}\right) \mathrm{V} / \mathrm{m}$ (where $\mathrm{x}, \mathrm{t}$ and other values have S.I. units). The dielectric constant of the medium is (speed of light in free space is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ )

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · EM Waves

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

E_{y} = 20 sin (3 \times 1 0^{6} x - 4.5 \times 1 0^{14} t) V / m

(where

x, t

and other values have S.I. units). The dielectric constant of the medium is
(speed of light in free space is

3 \times 1 0^{8} m / s

)

Answer: 4

For a plane wave the phase speed in the medium is

v = \frac{ω}{k} = \frac{4.5 \times 1 0 ^{14}}{3 \times 1 0 ^{6}} = 1.5 \times 1 0^{8} m/s

. The refractive index then follows from

n = \frac{c}{v} = \frac{3 \times 1 0 ^{8}}{1.5 \times 1 0 ^{8}} = 2

. In a non-magnetic medium

μ_{r} = 1

, so

n = ε_{r}

. The dielectric constant of the medium is

ε_{r} = n^{2} = 4

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Integer answer