Question

The electric and magnetic fields at t=0 are \(\vec{E} = E_0 f(z)\hat{x}\) and \(\vec{B} = B_0 f(z)\hat{y}\), with \(f(z) = \exp(-az^2)\). a) Find the electromagnetic energy and momentum density and their ratio. b) Show that at t>0 there are two wave packets traveling in the directions \(\hat{z}\) and \(-\hat{z}\). c) At what ratio \(\alpha = E_0 / B_0\) do we have only one wave packet? d) How much of the initial energy is carried in the \(\hat{z}\) and \(-\hat{z}\) directions?

          The electric and magnetic fields at t=0 are
\(\vec{E} = E_0 f(z)\hat{x}\) and \(\vec{B} = B_0 f(z)\hat{y}\),
with \(f(z) = \exp(-az^2)\).
a) Find the electromagnetic energy and momentum density and their ratio.
b) Show that at t>0 there are two wave packets traveling in the directions \(\hat{z}\) and \(-\hat{z}\).
c) At what ratio \(\alpha = E_0 / B_0\) do we have only one wave packet?
d) How much of the initial energy is carried in the \(\hat{z}\) and \(-\hat{z}\) directions?

The electric and magnetic fields at t=0 are
E⃗ = E0 f(z)x̂ and B⃗ = B0 f(z)ŷ,
with f(z) = (-az^2).
a) Find the electromagnetic energy and momentum density and their ratio.
b) Show that at t>0 there are two wave packets traveling in the directions ẑ and -ẑ.
c) At what ratio α = E0 / B0 do we have only one wave packet?
d) How much of the initial energy is carried in the ẑ and -ẑ directions?

Added by Miguel S.

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