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Question

The electric field part of an electromagnetic wave in a medium is represented by

Ex=0

Ey=2.5NCcos2π×106rads-1t(π×10-2radm-1)x

Ez=0

The wave is :


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Solution

Step 1: Given data:

The electric field part of an electromagnetic wave in a medium is represented by,

Ex=0

Ey=2.5NCcos2π×106rads-1t(π×10-2radm-1)x

Step 2: Formula used:

The standard equation of electromagnetic wave is given by:

Ey=E0cos(ωtkx)

Where,

Ey is the Electric field in y direction at 'x‘ distance and ’t' time

E0 is the maximum Electric field

ω is the angular frequency

k is the propagation constant

k=2πλ

Where, λ is the wavelength

f=ω2π

Where f is the frequency

Step 3: Compare with the standard equation:

The given equation of electromagnetic wave is,

Ey=2.5NCcos2π×106rads-1t(π×10-2radm-1)x

Compare this with the standard equation of electromagnetic wave Ey=E0cos(ωtkx),

Therefore,

The angular frequency is ω=2π×106rads-1

The propagation constant is k=π×10-2radm-1

Step 4: Wavelength

The propagation constant is k=π×10-2radm-1

So, k=2πλ Where, λ is the wavelength

That is, λ=2πk

Substituting the value of propagation constant,

λ=2ππ×10-2λ=2×102=200m

Step 5: Frequency

The angular frequency is ω=2π×106rads-1

So, f=ω2π Where, λ is the wavelength

Substitute the value of angular frequency,

f=2π×1062πf=106Hz

Thus, the wave is having a frequency of 106Hz and wavelength is 2π×106rads-1.


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