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The electric field on an electromagnetic...

The electric field on an electromagnetic wave in free space is given by
`E=10 cos (10^7t+kx) hatj V//m`,
Where t and x are in seconds and metres respectively. It can be inferred that
(1) the wavelength `lambda` is `188.4m`.
(2) the wave number k is `0.33rad//m`
(3) the wave amplitude is `10V//m`
(4) the wave is propagating along +x direction.
which one of the following pairs of statement is correct?

A

(2) and (4)

B

(1) and (2)

C

(2) and (3)

D

(1) and (3)

Text Solution

Verified by Experts

The correct Answer is:
D
Given
`E=10cos(10^(7)t+kx)V//m`
Comparing it with standard equation of electromagnetic wave,
`E=E_(0)cos(omega t+kx)`
We get,
Amplitude `E_(0)=10V//m and omega=10^(7)"rad/s"`
`because" "c = upsilon lambda=(omega lambda)/(2pi)`
`"or "lambda=(2pic)/(omega)=(2pixx3xx10^(8))/(10^(7))=188.4m`
Also, `c=(omega)/(k) or k=(omega)/(c) or k=(omega)/(c)=(10^(7))/(3xx10^(8))="0.k33 rad/m"`
The wave is propagating along `-x` direction.
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