An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, ϵ r = 9 , has the electric field, E x = E 0 sin ( k z − 2 π × 1 0 6 t ) Vm − 1 where E 0 is the

Question

An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, ϵ r ​ = 9 , has the electric field, E x ​ = E 0 ​ sin ( k z − 2 π × 1 0 6 t ) Vm − 1 where E 0 ​ is the amplitude and k is the wave vector. Among the following options, the incorrect choice is :NEET 2026 (Re-NEET)

TestHub · Accepted Answer

From the given equation of the electric field $E_{x} = E_{0} sin (k z - 2 π \times 1 0^{6} t)$ , the wave is propagating in the $+ z$ direction.

The angular frequency is $ω = 2 π \times 1 0^{6}$ rad/s, which gives the frequency $f = \frac{ω}{2 π} = 1 0^{6}$ Hz.

The speed of the electromagnetic wave in the dielectric medium is given by $v = \frac{c}{μ _{r} ϵ _{r}}$ .

Assuming a non-magnetic medium ( $μ_{r} = 1$ ), we get $v = \frac{3 \times 1 0 ^{8}}{9} = 1 0^{8}$ ms $^{- 1}$ .

The wavelength of the wave inside the medium is $λ = \frac{v}{f} = \frac{1 0 ^{8}}{1 0 ^{6}} = 100$ m.

Option (3) states the wavelength is $300$ m, which is incorrect.

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