superposition if time varying electric vectors

1. The problem statement, all variables and given/known data

two electric field vectors- E1= E0 cos (kz-wt) i(carat) and E2=E0 cos (kz+wt) i(carat) . what is the magnetic field vector corresponding to the the superposition of these 2 waves?

2. Relevant equations

3. The attempt at a solution

E=E1 + E2 = E0 [2cos{( kz-wt+kz+wt)/2}cos{(kz-wt-kz-wt)/2}]]
=E0[2coskz][cos wt]
here the new max amplitude is Emax=E0(2 coskz )
is this right?? this is a standing wave. then B0= Emax/c= E0(2coskz)/c
and the final equation for the magnetic field vector will be - B=B0(cos wt) because B and E are in phase in an em wave.

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 Find B for each traveling wave E1 and E2 separately by $$B\sim{\hat k}\times E$$, being careful about the direction of $$\hat k$$. Then add B1 and B2.
 Hey thanks but can't i do it the way i did it???

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