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Speed, refractive index or dielectric constant from the EM wave's equation

This type of question, asked 4 times: 2021 Paper 20, 2021 Paper 24, 22 Jan 2026 S1, 28 Jan 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 20

    18
    Electric field in a plane electromagnetic wave is given by E=50sin⁡(500x−10×1010t)V/mE = 50\sin\left( 500x - 10 \times10^{10}t \right)V/m The velocity of electromagnetic wave in this medium is: (Given C=C = speed of light in vacuum)

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  2. Question 2

    2021 Paper 24

    19
    Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by E=20cos⁡(2×1010t−200x)V/mE = 20\cos\left( 2 \times10^{10}t - 200x \right)V/m. The dielectric constant of the medium is equal to: (Take μr=1\mu_{r}= 1 )

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  3. Question 3

    22 Jan 2026 S1

    22
    The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, Ey=20sin⁡(3×106x−4.5×1014t)V/mE_{y} = 20\sin\left( 3 \times 10^{6}x - 4.5 \times 10^{14}t \right)V/m(where x,tx,t and other values have S.I. units). The dielectric constant of the medium is ____\_\_\_\_ (speed of light in free space is 3×108 m/s3 \times 10^{8}\text{ }m/s)

  4. Question 4

    28 Jan 2026 S1

    7
    The electric field of an electromagnetic wave travelling through a medium is given by E→(x,t)=25sin⁡(2.0×1015t−107x)n^\overrightarrow{E}(x,t) = 25\sin\left( 2.0 \times10^{15}t-10^{7}x \right)\widehat{n} then the refractive index of the medium is ____\_\_\_\_.(All given measurement are in SI units)

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