(adsbygoogle = window.adsbygoogle || []).push({}); B=B_{o}exp[-(kz-ωt)^{2})] i(hat)

Calculate the electric field associated with the above magnetic field pulse.

Calculate the Poynting vector for the EM field and the total energy per unit area.

Use Maxwell's equations in vacuum and assume electric potential is zero.

2. Relevant equations

N=(1/μ_{o})*EXB

Amperes Law

I calculated the electric field to beE=B_{o}c*exp[-(kz-ωt)^{2}] j(hat)

And the Poynting vector to be

N=-(B_{o}^{2}c/μ_{o})*exp[-(kz-ωt)^{2}] k(hat)

I am stuck on how to calculate the the energy per unit area. I think I would have to integrate over time (t=0 to t=∞) at some fixed point but I'm not sure.

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

2. Relevant equations

3. The attempt at a solution

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# Total energy per unit area of a EM pulse

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