A plane electromagnetic wave E⃗=E⃗ₘ cos(ωt-k⃗·r⃗) propagates in vacuum. If E⃗ₘ and k⃗ are known, which expression gives H⃗ at r⃗=0?
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Question

A plane electromagnetic wave E⃗=E⃗ₘ cos(ωt−k⃗·r⃗) propagates in vacuum. If E⃗ₘ and k⃗ are known, which expression gives H⃗ at r⃗=0?

G1 Physics · Accepted Answer

For a plane wave in vacuum, H⃗=(1/Z₀) k̂×E⃗ where 1/Z₀=√(ε₀/μ₀). At r⃗=0, E⃗=E⃗ₘcosωt. Hence H⃗=√(ε₀/μ₀)(k⃗×E⃗ₘ/|k⃗|)cosωt, option A.