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Question -

Suppose that the electric fieldpart of an electromagnetic wave in vacuum is E = {(3.1 N/C) cos [(1.8 rad/m) +(5.4 × 106 rad/s)t]}

(a) What isthe direction of propagation?

(b) What is the wavelength λ?

(c) What is the frequency ν?

(d) What is the amplitude of themagnetic field part of the wave?

(e) Write an expression for themagnetic field part of the wave..



Answer -

(a) Fromthe given electric field vector, it can be inferred that the electric field isdirected along the negative x direction.Hence, the direction of motion is along the negative directioni.e., .

(b) Itis given that,

The general equation for theelectric field vector in the positive x directioncan be written as:

On comparing equations (1) and(2), we get

Electricfield amplitude, E0 = 3.1 N/C

Angularfrequency, ω = 5.4 × 108 rad/s

Wavenumber, k = 1.8 rad/m

Wavelength,  = 3.490 m

(c) Frequency of wave is given as:

(d) Magneticfield strength is given as:

Where,

c =Speed of light = 3 × 108 m/s

(e) Onobserving the given vector field, it can be observed that the magnetic fieldvector is directed along the negative z direction. Hence, the general equationfor the magnetic field vector is written as:

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