The y component of the electric field of an electromagnetic wave traveling in the +x direction through vacuum obeys the equation Ey = (375 N/C) cos[kx - (2.20 × 1014 rad/s)t]. What is the wavelength of this electromagnetic wave? (c = 3.0 x 108 m/s)

Explanation:

Given that,

Ey = 375•Cos[kx - (2.20 × 10¹⁴t)]

Speed of light

c = 3×10^8m/s

What is the wavelength?

Generally,

The wavelength of electromagnetic wave is give as

Ey = Emax•Cos(kx—wt)

k = 2π/λ

w = 2πf

Ey = Emax•Cos(2πx/λ—2πft)

Comparing this to the wave equation given,

We notice that,

2πx/λ = kx

Also,

2.20 × 10¹⁴t = 2πft

t cancels out

2.20 × 10¹⁴ = 2πf

f = 2.20 × 10¹⁴ / 2π

f = 3.5 × 10¹³ Hz

Since we are given that

c = 3×10^8m/s

Then, using relationship between c, v and λ.

c = fλ.

λ. = c/f

λ. = 3×10^8 / 3.5 ×10¹³

λ. = 8.57 × 10^-6m

λ. = 8.57 μm

The wavelength of the electromagnetic wave is 8.57 micro meter (8.57 μm)

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explanation:

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