Suppose that the electric field amplitude of an electromagnetic wave is `E_(0) = 120 N//C` and that its frequency is ν = 50.0 MHz. (a) Determine,`B_(0) omega, k, and lamda`. (b) Find expressions for E and B.

Explanation

(i) According to formula,
`c=(E_(0))/(B_(0))`
`therefore B_(0)=(E_(0))/(c )`
`=(120)/(3xx10^(8))`
`therefore B_(0)=4xx10^(-7)` (Tesla)
(ii) Angular frequency,
`omega =2pi v`
`=(2)(3.14)(50xx10^(6))`
`therefore omega = 3.14xx10^(8)rad//s`
(iii) Wave - vector,
`k=(omega)/(c ) " " (because c=(omega)/(k))`
`=(3.14xx10^(8))/(3xx10^(8))`
`therefore k =1.047` rad/m
(iv) Wavelength,
`lambda=(c )/(v) " " (because c=v lambda)`
`=(3xx10^(8))/(50xx10^(6))`
`therefore lambda = 6 m`
(v) If given electromagnetic wave propagates along X axis then oscillations of electric field can be taken on Y axis and oscillation of magnetic field can be taken on Z axis, so that equation of electric field,
`vec(E )=vec(E )_(y)=E_(0)sin(kx-omega t)hat(j)`
`therefore vec(E )=120 sin {(1.047x - 3.14xx10^(8)t)}hat(j)("volt")/("meter")`
Equation of magnetic field,
`vec(B)=vec(B)_(z)=B_(0)sin (kx - omega t)hat(k)`
`therefore vec(B)=4xx10^(-7)sin {(1.047x-3.14xx10^(8)t)}hat(k)` tesla.