Superposition if time varying electric vectors

[harshasunder]

Homework Statement

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?

Homework Equations

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.

 

[pam]

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.

 

[harshasunder]

Hey thanks but can't i do it the way i did it?

 

[Meir Achuz]

No. You need to use the curl E Maxwell equation to get B from E.
That is easy for the traveling waves, but would require taking Curl E for your method.