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Question -

In a plane electromagnetic wave,the electric field oscillates sinusoidally at a frequency of 2.0 × 1010 Hz and amplitude 48 V m−1.

(a) What is the wavelength of the wave?

(b) What is the amplitude of theoscillating magnetic field?

(c) Show that the average energydensity of the E fieldequals the average energy density of the B field. [= 3 ×108 m s−1.]



Answer -

Frequency of the electromagneticwave, ν = 2.0 × 1010 Hz

Electricfield amplitude, E0 = 48 V m−1

Speed oflight, c = 3 × 108 m/s

(a) Wavelength of a wave is given as:

(b) Magneticfield strength is given as:

(c) Energydensity of the electric field is given as:

And, energy density of themagnetic field is given as:

Where,

0 = Permittivity of free space

μ0 = Permeability offree space

We havethe relation connecting E and B as:

E = cB … (1)

Where,

 … (2)

Puttingequation (2) in equation (1), we get

Squaring both sides, we get

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