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A plane electromagentic wave E=E_(m) cos ( omegat - kr)propagates in vacuum. Assuming the vectors E_(m) and k to be known, find the vector H as a function of time t at the point with radius vector r=0 . |
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Answer» Solution :`VEC(nabla)xxvec(E)=-(deltavec(B))/( deltat)=- mu _(0)(deltavec(H))/( deltat)` `=nablacos ( omegat - vec(k). vec(r))xxvec(E)_(m) =vec(k) xx vec(E)_(m) sin ( omegat- vec(k). vec(r))` At ` vec (r)=0` `(deltavec(H))/(deltat)=-(vec(k) xxvec(E)_(m))/( mu_(0))sin omegat` So integrating `(` ignoring a CONSTANT `)` and using `C=(1)/(sqrt(epsilon_(0)mu_(0)))` ` vec (H)= (vec(k) xx vec(E)_(m))/( mu_(0))cos c k t xx(1)/(ck)=sqrt((epsilon_(0))/( mu_(0)))(vec(k)xxvec(E)_(m))/( k ) cos c k t ` |
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