JEE Main 2026 — Jan 22, Shift 1 — Physics solution

JEE Main2026Jan 22, Shift 1Physics

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)

Your answer

Solution

The phase speed of the wave 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.

Refractive index of the medium: $n = \frac{c}{V} = \frac{3 \times 1 0 ^{8}}{1.5 \times 1 0 ^{8}} = 2$ .

For a non-magnetic medium ( $μ_{r} = 1$ ), $n = μ_{r} ϵ_{r} = ϵ_{r}$ , so $ϵ_{r} = n^{2} = 4$ .

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