⚡ Quick Revision

Complete chapter revision in 30 minutes | 1 day before exam

This page contains everything you need for last-minute revision. Use 1 day before exam or for quick recap. Estimated time: 30-40 minutes

📐 Formula Dump (Must Memorize)

Core Formulas

c = νλ = 3 × 10⁸ m/s

c = 1/√(μ₀ε₀)

v = c/n = 1/√(με)

E/B = c (or E₀/B₀ = c)

E = E₀ sin(kx - ωt)

k = 2π/λ, ω = 2πν

Energy & Intensity

u_E = (1/2)ε₀E²

u_B = (1/2μ₀)B²

u = ε₀E² = B²/μ₀

I = (1/μ₀)EB = cε₀E²

I_avg = (1/2)cε₀E₀²

I_avg = c × u_avg

Momentum & Pressure

p = U/c = h/λ

P = I/c (absorption)

P = 2I/c (reflection)

P = u (absorption)

P = 2u (reflection)

Photon & Polarization

E = hν = hc/λ

E(eV) = 1240/λ(nm)

I = I₀ cos²θ (Malus)

I = I₀/2 (unpolarized)

I_d = ε₀(dΦ_E/dt)

🌈 EM Spectrum Quick Reference

Type	Frequency	Wavelength	Production	Key Application
Radio	< 10⁹ Hz	> 0.1 m	LC oscillator	Broadcasting
Microwave	10⁹-10¹² Hz	1mm-0.1m	Klystron	Radar, Ovens
Infrared	10¹²-4×10¹⁴ Hz	700nm-1mm	Hot bodies	Night vision
Visible	4×10¹⁴-7.5×10¹⁴ Hz	400-700nm	Atoms	Vision
UV	7.5×10¹⁴-10¹⁷ Hz	10-400nm	Mercury lamp	Sterilization
X-ray	10¹⁷-10²⁰ Hz	0.01-10nm	X-ray tube	Medical imaging
Gamma	> 10²⁰ Hz	< 0.01nm	Radioactive decay	Cancer treatment

Memory trick: Raman Made Indian Very Unique Xpert Genius
(Radio, Microwave, Infrared, Visible, UV, X-ray, Gamma)

🧠 Key Concepts (One-Liners)

Properties of EM Waves

✓ Transverse waves (E ⊥ B ⊥ direction)
✓ No medium needed (vacuum travel)
✓ Speed in vacuum = c (constant)
✓ E and B oscillate in phase
✓ Carry energy and momentum
✓ Can be polarized

Maxwell's Equations

Gauss E: ∮E·dA = Q/ε₀
Gauss B: ∮B·dA = 0
Faraday: ∮E·dl = -dΦ_B/dt
Ampere-Maxwell: ∮B·dl = μ₀I + μ₀ε₀dΦ_E/dt

Common Mistakes

✗ Thinking frequency changes in medium
✗ Using P=I/c for reflection (should be 2I/c)
✗ Forgetting 1/2 in average intensity
✗ Confusing E field magnitude with B field

What Changes in Medium?

Unchanged: Frequency (ν)
Decreases: Speed (v = c/n)
Decreases: Wavelength (λ = λ₀/n)

🎴 Interactive Flashcards

Click to flip. Test your understanding!

What is displacement current?

Click to reveal

Current due to changing electric field, not moving charges.

I_d = ε₀(dΦ_E/dt)

Exists between capacitor plates during charging.

E and B phase relation?

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In phase

Both reach maximum together, both zero together.

Different from LC circuit where they're 90° out of phase!

Energy split in EM wave?

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50-50 split

Electric field: 50% energy
Magnetic field: 50% energy

u_E = u_B

What changes in medium?

Click to reveal

Unchanged: ν (frequency)

Decrease: v (speed), λ (wavelength)

v = c/n, λ = λ₀/n

Radiation pressure for reflection?

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P = 2I/c

(Factor of 2 because momentum change is 2p)

For absorption: P = I/c

Why can EM waves travel in vacuum?

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Self-propagating fields

Changing E creates B
Changing B creates E

This feedback doesn't need medium!

Maxwell's key contribution?

Click to reveal

Displacement current

Added μ₀ε₀(dΦ_E/dt) term to Ampere's law

This predicted EM waves!

Highest energy EM wave?

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Gamma rays

Highest frequency → Highest energy (E = hν)

Shortest wavelength, most penetrating

Intensity from E₀?

Click to reveal

I_avg = (1/2)cε₀E₀²

Quick approximation:

I ≈ 1.3×10⁻³ × E₀²

📊 Important Constants (Must Know)

Constant	Value
Speed of light (c)	3 × 10⁸ m/s
Planck's constant (h)	6.626 × 10⁻³⁴ J·s
ε₀	8.85 × 10⁻¹² C²/N·m²
μ₀	4π × 10⁻⁷ T·m/A
1 eV	1.6 × 10⁻¹⁹ J

Quick Calculations

(1/2)cε₀ ≈ 1.3 × 10⁻³

Use for intensity from E₀

hc ≈ 1240 eV·nm

For photon energy in eV

c/λ(nm) ≈ frequency in Hz

Remember to convert nm to m!

💯 Most Tested Numerical Types

Type 1: Find wavelength from frequency ▼

Given: ν = 600 THz

Find: λ

Solution: λ = c/ν = (3×10⁸)/(600×10¹²) = 500 nm

Always identify: Which part of spectrum?

Type 2: E₀ to B₀ conversion ▼

Given: E₀ = 90 V/m

Find: B₀

Solution: B₀ = E₀/c = 90/(3×10⁸) = 3×10⁻⁷ T

Type 3: Intensity calculation ▼

Given: E₀ = 60 V/m

Find: I_avg

Solution: I_avg = (1/2)cε₀E₀² = (1/2)(3×10⁸)(8.85×10⁻¹²)(60²) ≈ 4.8 W/m²

Type 4: Radiation pressure ▼

Given: I = 12 W/m², perfectly reflecting

Find: Pressure

Solution: P = 2I/c = 2(12)/(3×10⁸) = 8×10⁻⁸ N/m²

Key: Factor of 2 for reflection!

✅ Last Minute Checklist (Night Before Exam)

Formulas to Write Down

□ c = νλ = 3×10⁸ m/s
□ E₀/B₀ = c
□ I_avg = (1/2)cε₀E₀²
□ P = I/c (absorption)
□ P = 2I/c (reflection)
□ E = hc/λ = 1240/λ(nm) eV
□ I_d = ε₀(dΦ_E/dt)

Concepts to Recall

□ EM spectrum order (RMIVUXG)
□ 2-3 applications each wave
□ Frequency unchanged in medium
□ E and B in phase
□ Equal energy in E and B fields
□ Maxwell's displacement current
□ Malus's law: I = I₀cos²θ

You've got this! 💪

You've covered everything needed for EM Waves. Trust your preparation. Stay calm during exam. Good luck!

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