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22 February, 19:18

The electric field of an electromagnetic wave ina vacuum is Ey = (20 V/m) sin ((6.28x108) x - 2πft), where x is in m and t is in s. What are the wave's (a) wavelength, (b) frequency, and (c) magnetic field amplitude?

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  1. 22 February, 19:19
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    (a) 10 nm

    (b) 1 Hz

    (c) 20 V/m

    Explanation

    The equation of a progressive wave is given by:

    y = Asin (kx ± ωt)

    where;

    A is the amplitude of the wave in meters

    y (x, t) is the displacement in meters

    k = 2π/λ is the propagation constant

    ω = 2πf is the angular frequency in radian per seconds

    The equation now becomes;

    y = Asin ((2πx) / λ ± 2πft)

    (a) Comparing Ey = (20 V/m) sin ((6.28x10⁸) x - 2πft) with the general equation

    (2πx) / λ = 6.28 * 10⁸

    λ = 2π / 6.28 * 10⁸

    λ = 1.0 * 10⁻⁸ m

    λ = 10 * 10⁻⁹ m

    λ = 10 nm

    (b) Comparing Ey = (20 V/m) sin ((6.28x10⁸) x - 2πft) with the general equation

    2πft = 2πft

    f = 1 Hz

    (c) Comparing Ey = (20 V/m) sin ((6.28x10⁸) x - 2πft) with the general equation

    A = 20 V/m
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