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An EM wave has momentum given by the equation: 𝒑 = 𝜇 𝑜

𝜖 𝑜

∭ 𝑺 𝑑

3 𝑥.

For the above and following we assume average values. It transfers momentum given by: 𝑑𝒑 𝑑𝑡

= 𝜇 𝑜

𝜖 𝑜 𝑑 𝑑𝑡

∭ 𝑺 𝑑

3 𝑥.

In a given time the length of the wave incident on an area A is given by c dt. We can thus rewrite the equation: 𝑑𝒑 𝑑𝑡

= 𝜇 𝑜

𝜖 𝑜 𝑑 𝑑𝑡

∫ 𝑐 𝑑𝑡 ∬ 𝑑𝑎 𝑺, which becomes, via the fundamental theorem of calculus: 𝑑𝒑 𝑑𝑡

= 𝜇 𝑜

𝜖 𝑜 𝑐 ∬ 𝑑𝑎 𝑺, 𝑑𝒑 𝑑𝑡

=

1 𝑐

∬ 𝑑𝑎 𝑺

Thus the pressure on an object is given by:

𝑃 =

𝑆 𝑐

= 𝑢 𝑒𝑚

, so we see the pressure is equal to the energy density in the EM waves!

Side note: the above assumes the waves are absorbed by an object. If they reflect, as off of a conductor, we find the change in momentum and pressure should be doubled: 𝑑𝒑 𝑑𝑡

=

2 𝑐

∬ 𝑑𝑎 𝑺,

𝑃 = 2

𝑆 𝑐

= 2 𝑢 𝑒𝑚

.