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An electromagnetic wave E0 sin(3y + 4z + wt) i-hat: its direction of travel, wave vector, angular frequency and magnetic field

The plane wave E0 sin(3y + 4z + wt) i-hat drawn in the y-z plane: a tracker riding a crest moves against k = (0, 3, 4), a ruler finds the wavelength 1.257 m so |k| = 5 per metre, w = c|k| = 1.5e9 rad/s, and Faraday's law gives B = (E0/c)(-4j + 3k)/5 sin(...) - answer (A), (C).

Sub-topics covered

• Plane wave sin(k.r + wt): wavefronts k.r = const move along -k-hat (along +k-hat for -wt)
• |k| = 2 pi/lambda from the spatial part; vacuum dispersion w = c|k|
• Faraday's law dB/dt = -curl E fixes B: perpendicular to E and to the travel, |B| = |E|/c
• Poynting vector E x B points along the direction of travel

What it teaches

• k = 3j + 4k-hat, |k| = 5 m^-1 - statement (B) (0.5) false
• A crest 3y + 4z + wt = const moves so that 3y + 4z falls: along -(3j + 4k)/5 - statement (A)
• w = c|k| = 3e8 x 5 = 1.5e9 rad/s - statement (C)
• Faraday's law gives B = (E0/c) sin(...)(-4j + 3k)/5; statement (D)'s (E0/c)(4j - 3k) is -5 times it (wrong sign and size) - false

Simulation ID

• ADV-2026-P1-PHY-Q08 · revision 1

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