The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by E → = 30 2 x ∧ + y ∧ sin 2 π 5 × 10 14 t - 10 7 3 z   V   m - 1 . Which of the following option(s) is(are) correct? [Given: The speed of light in vacuum, c = 3 × 10 8   m   s – 1 ]
D. The refractive index of the medium is 2
Speed of light in medium is v = ω k ⇒ v = 2 π 5 × 10 14 2 π × 10 7 3 ⇒ v = 1 . 5 × 10 8   m   s - 1 Therefore, refractive index μ = c v = 3 × 10 8 1 . 5 × 10 8 = 2 ⇒ μ = 2 Given E → = 30 2 x ∧ + y ∧ sin 2 π 5 × 10 14 t - 10 7 3 z   V   m - 1 The wave is polarised in x y - plane with polarisation angle tan - 1 1 2 with respect to x - axis. Amplitude of magnetic field, B 0 = E 0 V = 30 2 2 + 1 2 1 . 5 × 10 8 = 30 5 1 . 5 × 10 8 Now, direction of B → is v → × E → = k ∧ × 2 i ∧ + j ∧ 5 = - i ∧ + 2 j ∧ 5 . B → = - i ∧ + 2 j ∧ 5 × 30 5 1 . 5 × 10 8 sin 2 π 5 × 10 14 t - 10 7 3 z     Wb   m - 2 = - i ∧ + 2 j ∧ × 2 × 10 - 7 sin 2 π 5 × 10 14 t - 10 7 3 z     Wb   m - 2 Hence, B x = - 2 × 10 - 7 sin 2 π 5 × 10 14 t - 10 7 3 z   Wb   m - 2 and B y = 4 × 10 - 7 sin 2 π 5 × 10 14 t - 10 7 3 z   Wb   m - 2
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