Suppose that the electric field amplitude of an electromagnetic wave us `E_0=120 N// C` and that its frequency is `50.0 MHz`.
(a) Determine` B_0,omega,k` and `lambda`,
(b) find expressions for `E` and `B`.

Explanation

i) C = `(E_(0))/(B_(0)) ` we get
`B_(0) = (E_(0))/(C ) = (120)/(3 xx 10^(8)) = 4 xx 10^(-7)` T = 400nT
ii) `omega = 2 pi v = 2xx pi xx 50 xx 10^(6)`
= 3.14 `xx 10^(8)` rad/sec
iii) `c = u lambda rArr lambda = (C )/(u) = (3 xx 10^(8))/(50 xx 10^(6)) = 6 m`
iv) K = `(2pi)/(lambda) = (2pi)/(6) = (2 xx 3.14)/(6) = 1.05 m^(-1)`
(b) `vec(E ) = E_(0)sin (kx - omega t)`
120 sin `(1.05 x - 3.14 xx 10^(8) t )`
`B = B_(0) sin (kx - omega t)`
` = 400 xx 10^(-9) sin (1.05x - 3.14 xx 10^(8) t) `