How to derive Electromagnetic Waves from Maxwell's eq. in 1 Tweet
1)∇.B = 0
2)∇.E = 0
3)∇xE = -∂B/∂t
4)∇xB = μ₀ε₀∂E/∂t
Using ∇x(∇xA) = ∇(∇⋅A)-∇²A for E & B
∂²E/∂t² = 1/μ₀ε₀∇²E
∂²B/∂t² = 1/μ₀ε₀∇²B
E and B obey the wave eq. with c = √1/μ₀ε₀💡!
The derivatives of the Position vector (x) with respect to time have interesting names
Velocity (v) = change in Position
Acceleration (a) = change in Velocity
Jerk (j) = change in Acceleration
Snap (s) = change in Jerk
Crackle (c) = change in Snap
Pop (p) = change in Crackle
🙂
Wanna learn some astronomy lingo? When the Moon is closest to Earth, that's called perigee. When it's furthest, that's called apogee. The diff between those = 27,000 miles (avg dist = 239,000 mi). The Moon is 14% larger in the sky at perigee compared with apogee and 30% brighter.
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