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Suppose that the electric field part of ...

Suppose that the electric field part of an electromagnetic wave in vacuume is
`E=3.1N//C cos [(1.8rad//m)y+(5.4xx10^8rad//s)t]hati`
(a) Wavelength is the direction of motion?
(b) What is the wavelength `lambda`?
(c) What is the frequency v?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave.

Text Solution

Verified by Experts

(a) From the given equation, it is clear that the direction of motion of e.m. wave is along negative y
direction i.e., along `-hatj`.
(b) Comparing the given equation with the equation `E=E_0cos (ky+omegat)`, we have
`k=1.8rad//s, omega=5.4xx10^8rad//s, E_0=3.1 N//C`
`lambda=(2pi)/k=(2xx(22//7))/1.8=3.492m~~3.5m`
(c) `v=omega/(2pi) =(5.4xx10^8)/(2xx(22//7))=8.5xx10^6~~86MHz`
(d) `B_0=(E_0)/c=3.1/(3xx10^8)=1.03xx10^-8T~~10.3nT`
(e) `B=B_0cos (ky+omegat)hatk=(10.3nT)cos [(1.8rad//m)y+(5.4xx10^8rad//s)t]hatk`
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