Electromagnetic Waves

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Displacement current is an equivalent current that flows due to a changing electric field, just like conduction current produces magnetic field. Maxwell introduced it to resolve the inconsistency in A

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Displacement current: id = ε₀(dΦE/dt), where ε₀ is the permittivity of free space and ΦE is electric flux. For a capacitor with area A and electric field E: id = ε₀A(dE/dt). This equals the conduction

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∮B⃗·dl⃗ = μ₀(i + id) = μ₀i + μ₀ε₀(dΦE/dt), where i is conduction current and id is displacement current. This law states that both conduction current and changing electric field produce magnetic field

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1. ∮E⃗·ds⃗ = q/ε₀ (Gauss law for electricity) 2. ∮B⃗·ds⃗ = 0 (Gauss law for magnetism) 3. ∮E⃗·dl⃗ = -dΦB/dt (Faraday's law) 4. ∮B⃗·dl⃗ = μ₀i + μ₀ε₀(dΦE/dt) (Ampere-Maxwell law)

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An electromagnetic wave consists of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation. It is generated by accelerated charges. The oscillating el

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For a wave propagating in z-direction: Electric field: Ex = E₀ sin(kz - ωt) Magnetic field: By = B₀ sin(kz - ωt) where k = 2π/λ is wave vector magnitude and ω is angular frequency.

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B₀ = E₀/c, where c is speed of light in vacuum. Also, the instantaneous relationship is B = E/c. The magnetic field amplitude is much smaller than electric field amplitude numerically due to the large

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In vacuum: c = 1/√(μ₀ε₀) = 3×10⁸ m/s In a medium: v = 1/√(με), where μ is permeability and ε is permittivity of the medium. Speed in medium is always less than in vacuum.