At t=0, the electric field of a plane-polarized electromagnetic wave in free space is E⃗(x, z,0)=10 ĵ cos(6x+8z). Which expression gives B⃗(x, z, t)? Here c is the speed of light.
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Question

At t=0, the electric field of a plane-polarized electromagnetic wave in free space is E⃗(x,z,0)=10 ĵ cos(6x+8z). Which expression gives B⃗(x,z,t)? Here c is the speed of light.

G1 Physics · Accepted Answer

The spatial phase at t=0 is 6x+8z, so k⃗=6î+8k̂ and |k⃗|=10. In free space ω=c|k|=10c. With phase k⃗·r⃗−ωt, E⃗=10ĵ cos(6x+8z−10ct). Since B⃗=(1/c)k̂×E⃗ and k̂=(6î+8k̂)/10, k̂×(10ĵ)=6k̂−8î. Therefore B⃗=(6k̂−8î)cos(6x+8z−10ct)/c. Hence option B.