A plane electromagentic wave `E=E_(m)cos ( omegat-kr)` where` E_(m) E_(m) e_(y), k = k e_(x), e_(y)` are the unit vectors of the `x,y` axes, propagates in vacuum. Find the vector `H` at the point with radius vector `r=xe_(x)` at the moment `(a)t=0, (b) t=t_(0). ` Consider the case when `E_(m)=160V//m, k=0.51m ^(-1), x = 7.7m ,` and `t_(0)=33ns.`

Explanation

As in the previous problem
`vec(H)=(vec(k) xxvec(E)_(m))/( mu_(0)) cos ( omegat-vec(k). vec(r))=(E_(m))/( mu_(0)c)hat(e)_(x)cos ( kx - omegat)`
` =sqrt((epsilon_(0))/( mu_(0)))E_(m)hat(e)_(x)cos ( kx- omegat )`
Thus
`(a)` at `t=0 ,vec(H) = sqrt((epsilon_(0))/( mu_(0)))E_(m)hat (e)_(x) cos kx`
`(b)` at `t=t_(0),vec(H)=sqrt((epsilon_(0))/(mu_(0)))E_(m)hat(e)_(x)cos ( kx-omegat_(0))`