Simulation · Physics · Class 12
Which way does the wave go?
From the lesson Nature of electromagnetic waves in Electromagnetic Waves. Change the values and watch what happens.
Which way does the wave go?Physics · Class 12
The idea behind it
NCERT §8.3.2
- The E and B fields of an electromagnetic wave are at right angles to each other, and both are at right angles to the direction of travel: the wave is transverse. The capacitor hints at this: E between the plates is perpendicular to them, and the B it produces runs in circles parallel to them.
- For a plane wave travelling along z with E along x and B along y: Ex = E₀ sin(kz − ωt) and By = B₀ sin(kz − ωt). Both vary sinusoidally with position and time and are in phase.
- Here k = 2π/λ is the size of the wave vector (propagation vector) k, whose direction is the direction of travel, and ω is the angular frequency. The wave moves with speed ω/k.
- Maxwell's equations give ω = ck with c = 1/√(μ₀ε₀). Written with ν = ω/2π and λ = 2π/k this is νλ = c.
- The amplitudes are related by B₀ = E₀/c. Because c is so large, the magnetic field in tesla is a tiny number next to the electric field in V/m.
- The wave travels in the direction of E × B. Given two of the three directions, this fixes the third.
- Example 8.1: a 25 MHz wave travels along x, and at some point E = 6.3 ĵ V/m. Then B = E/c = 6.3/(3 × 10⁸) = 2.1 × 10⁻⁸ T, and since ĵ × k̂ = î, B = 2.1 × 10⁻⁸ k̂ T.
- Example 8.2: By = (2 × 10⁻⁷ T) sin(0.5 × 10³x + 1.5 × 10¹¹t). Then λ = 2π/(0.5 × 10³) m = 1.26 cm and ν = (1.5 × 10¹¹)/2π = 23.9 GHz. E₀ = B₀c = 60 V/m, and E lies along z: Ez = 60 sin(0.5 × 10³x + 1.5 × 10¹¹t) V/m.