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Question

The electric field of an electromagnetic wave in free space is given by
E=10cos(107t+kx)^j V/m, where t and x are in seconds and metres respectively. It can be inferred that
(i) the wavelength λ is 188.4 m.
(ii) the wave number k is 0.33 rad/m.
(iii) the wave amplitude is 10 V/m.
(iv) the wave is propagating along +x direction.
Which one of the following pairs of statements is correct?

A
(c) and (d)
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B
(a) and (b)
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C
(b) and (c)
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D
(a) and (c)
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Solution

The correct option is D (a) and (c)
As given:
E= 10cos(107t+kx)
Comparing it with standard equation of e.m. wave,
E= E0cos(ωt+kx)
Amplitude, E0=10 V/m

and ω=107 rad/s
c=vλ=ωλ2π or λ=2πcω=2π×3×108107=188.4 m
Also,
c= ωk or k= ωc=1073×108 = 0.033

The wave is propagating along y direction.

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