An electric field in free space is written as

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics

Problem

An electric field in free space is written as E(x,t)=E0sin⁡(2.0×107x−6.0×1015t) N C−1E(x,t)=E_0 \sin(2.0\times10^{7} x - 6.0\times10^{15} t)\,\text{N C}^{-1}, where xx is in metres and tt in seconds. Taking c=3.0×108 m s−1c=3.0\times10^{8}\,\text{m s}^{-1}, decide whether this expression can represent a plane electromagnetic wave in vacuum. (a) No, because using λ=1/k\lambda = 1/k gives a phase speed of 4.8×107 m s−14.8\times10^{7}\,\text{m s}^{-1}, smaller than 3.0×108 m s−13.0\times10^{8}\,\text{m s}^{-1} (b) Yes, because the phase speed equals 3.0×108 m s−13.0\times10^{8}\,\text{m s}^{-1} (c) No, because ωk\omega k must equal 1/μ0ε01/\mu_0\varepsilon_0, which is not satisfied (d) No, because an electromagnetic wave requires mutually perpendicular electric and magnetic fields, which this expression does not show

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