An electromagnetic wave E=100 sin(kx-ωt) occupies a cylindrical region of length l and radius R with energy U₀. What electric-field equation will give the same energy U₀ in a cylinder of the same length but half the diameter?
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Question

An electromagnetic wave E=100 sin(kx-ωt) occupies a cylindrical region of length l and radius R with energy U₀. What electric-field equation will give the same energy U₀ in a cylinder of the same length but half the diameter?

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G1 Physics · Accepted Answer

EM-wave energy density is proportional to E₀². Halving the diameter halves radius, so volume becomes V/4. To keep total energy unchanged, E₁²(V/4)=E₀²V, hence E₁=2E₀=200 V/m.