The terminology of different parts of the electromagnetic spectrum is given in the text. Use the formula E = h ν (for energy of a quantum of radiation: photon) and obtain the photon energy in units of eV for different parts of the electromagnetic spectrum. In what way are the different scales of photon energies that you obtain related to the sources of electromagnetic radiation?

Explanation

(a) From the given electric field vector, it can be inferred that the electric field is directed along the negative x direction. Hence direction of motion is along the negative y direction i.e., `-hatj`
(b) It is given that,
`vecE=3.1N//C cos [(1.9"rad"//m)y+(5.4xx10^(-8)"rad"//s)t]hati` .......(1)
The general equation for the electric field vector in the positive x direction can be written as:
`vecE=E_(0)sin (kx-ometat) hati` ...(2)
On comparing equations (1) and (2), we get
Electric field amplitude `E_(0)=3.1N//C`
Angular frequency, `omega=5.4xx10^(8)` rad/s
Wave number `k=1.8` rad/m
`gamma=(2pi)/(1.8)=3.490m`
(c) Frequency of wave is given as:
`v=(omega)/(2pi)`
`=(5.4xx10^(8))/(2pi)=8.6xx10^(7)Hz`
(d) Magnetic field strength is given as:
`B_(0)=(E_(0))/(c)`
where, C=speed of light `=3xx10^(8)m//s`
`thereforeB_(0)=(3.1)/(3xx10^(8))=1.03xx10^(-7)T`
(e) On observig the given vector field, it can be observed that the magnetic field vector is directed along the negative z direction Hence, the general equation for the magnetic field vector is written as:
`vecB=B_(0)cos(ky+omegat)hatk`
`={(1.03xx10^(-7)T)cos[(1.8"rad"//m)y+(5.4xx10^(6)"rad"//s)t]}hatk`