a)

Suppose you have an electromagnetic wave with the Eand Bvectors like in the figure below. Than the direction of wave propagation is along the z axis (see the figure).We can write

`E_x = E_max*sin[2*pi*(z/lambda -t/T)]`

`B_y =B_max*sin[2*pi*(z/lambda-t/T)]`

The Maxwell equation relating the vectors **E** and
**B** is

`grad xx E = -(delB)/(delt)`

which for the case of the wave that has only `E_x` and `B_y` components is written as

`(delE_x)/(delz) =-(delB_y)/(delt)` or replacing with the values above

`(2*pi)/lambda*E_max =(2*pi)/T*B_max`

`E_max = lambda/T *B_max = c*B_max`

`B_max = 600/(3*10^8) = 2*10^-6 T`

b)

The average energy density is

`w = (epsilon_0*E_max^2)/2 = B_max^2/(2*mu_0)`

`w = 8.854*10^-12*600^2/2 =1.59*10^-6 J/m^3`

c)

The antenna is half wave, this means that the length of each wire is

`L =lambda/2 =(1/2)*(c/nu) =0.5*3*10^8/3.2*10^9 =`

`=4.6875*10^-2 m =4.6875 cm`

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