Transverse Geometry and Propagation Direction
For a plane wave in an isotropic medium, E is perpendicular to B, and both are perpendicular to the wave vector k. The propagation direction is parallel to E cross B.
Why this shows up in the exam
Choosing field-vector directions in plane-wave questions · Determining propagation direction from E and B · Checking whether a proposed pair of fields is physically possible
Learn the idea
In a plane electromagnetic wave, E, B, and the propagation direction are mutually perpendicular. The electric and magnetic vectors form two perpendicular arms, and their cross product points along the direction in which energy travels. Reversing either field reverses that cross-product direction.
🧠 Memory hook: E cross B points where the wave goes.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- k_hat = (E x B)/|E x B| — unit propagation direction
- E.B = 0, E.k = 0, B.k = 0 — transverse orthogonality conditions
How to approach it
- 1Read the phase to find the propagation direction
- 2Require E and B to be perpendicular to that direction
- 3Use E cross B to fix the remaining sign
Common slip-ups that cost marks
- •Using B cross E instead of E cross B
- •Making E or B parallel to propagation
- •Checking perpendicularity without checking the cross-product sign
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
An electromagnetic wave in vacuum has wavelength 1 m. Take c = 3 x 10^8 m/s. Find its frequency in units of 10^8 Hz.
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