#permittivity

Production of EM Waves and Hertz Experiment

Why does the speed of electromagnetic waves in a medium depend on the medium’s properties?

**Hertz experiment** used induction coil connected to two rods with gap, spark produced oscillating charge, emitted EM wave, received by loop with gap sparking when E induced, measured wavelength by standing wave, demonstrated EM wave properties, validating Maxwell. The speed of electromagnetic waves in a medium is determined by the medium’s permittivity ( ε ) and permeability ( μ ), as v = (1/√(μ ε)) , which modifies the wave’s propagation characteristics. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Dependence on permittivity and permeability, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Production of EM Waves and Hertz Experiment

A parallel plate capacitor with plate area \( A = 0.02 \, \text{m}^2 \) and separation \( d = 5 \, \text{mm} \) is conne

**Production of EM waves** requires accelerated charge, oscillating LC circuit produces changing E and B, antenna radiates when charge accelerates, frequency determined by L and C, f=1/(2π√(LC)). Hertz used spark gap with inductor and capacitor, produced ~10⁸ Hz radio waves, detected with loop, confirmed transverse nature, reflection, refraction, polarization, speed c. Displacement current i_d = ε₀ (d Φ_E/dt) . For a capacitor, i_d = i . Given i = 2 A , we have (d Φ_E/dt) = (i/ε₀) = (2/8.85 × 10⁻¹²) ≈ 2.26 × 10¹¹ Vm/s . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f,

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Energy, Intensity and Momentum of EM Waves

According to Maxwell's equations, what is the relationship between the speed of electromagnetic waves in vacuum and the

**Energy in EM wave** equally divided between electric and magnetic fields, energy density u = ½ ε₀ E² + B²/(2μ₀) = ε₀ E² = B²/μ₀, average u_avg = ½ ε₀ E₀², intensity I = c u_avg = ½ c ε₀ E₀² = E₀ B₀/(2μ₀) = c B₀²/(2μ₀), radiation pressure p = I/c for absorption, 2I/c for reflection. The document states that the speed c of electromagnetic waves in vacuum is given by c = (1/√(μ₀ ε₀)) . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields c = (1/√(μ₀ ε₀)), illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Energy, Intensity and Momentum of EM Waves

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Energy, Intensity and Momentum of EM Waves

A capacitor is charged such that the electric flux through a surface between the plates changes at a rate of \( 5 \times

**Momentum of EM wave** p = U/c, U energy, radiation pressure exerts force F = I A/c, small but measurable, comet tail pushed by sunlight, solar sail concept. For E₀=45 V/m, B₀=1.5×10⁻⁷ T, intensity I =0.5×3×10⁸×8.85×10⁻¹²×45²≈2.69 W/m². Displacement current i_d = ε₀ (d Φ_E/dt) . Substituting the values, i_d = (8.85 × 10⁻¹²) × (5 × 10¹⁰) = 0.4425 A . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 0.4425 A, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Energy, Intensity and Momentum of EM Waves

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Displacement Current and Ampere-Maxwell Law

The velocity of light in a medium with permittivity \( \varepsilon \) and permeability \( \mu \) is:

**Displacement current** I_d = ε₀ dΦ_E/dt, Φ_E = ∫ E·dA electric flux (V·m), ε₀=8.85×10⁻¹² F/m, ensures continuity of current in charging capacitor where conduction current stops between plates, I_d equals conduction current in wires, 3 A conduction ⇒ 3 A displacement, maintaining Ampere's law ∮ B·dl = μ₀(I_c+I_d). As per Maxwell's equations, the velocity of light in a medium is v = (1/√(μ ε)) . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields (1/√(μ ε)), illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Displacement Current and Ampere-Maxwell Law

A capacitor in a circuit has a rate of change of electric flux of \( 4 \times 10^{11} \, \text{Vm/s} \). What is the dis

**Ampere-Maxwell law** ∮ B·dl = μ₀(I_c + ε₀ dΦ_E/dt) generalizes Ampere's law, displacement current arises from time-varying electric field, source of magnetic field like conduction current. For rate of change of flux 2×10¹¹ V·m/s, I_d = ε₀×2×10¹¹ =8.85×10⁻¹²×2×10¹¹=1.77 A. Displacement current i_d = ε₀ (d Φ_E/dt) . Substituting the values, i_d = (8.85 × 10⁻¹²) × (4 × 10¹¹) = 3.54 A . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 3.54 A, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Displacement Current and Ampere-Maxwell Law

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Displacement Current and Ampere-Maxwell Law

According to Maxwell's equations, what is the speed of electromagnetic waves in a medium with permittivity \( \varepsilo

**Charging capacitor** conduction current in wires equals displacement current between plates because dQ/dt = I_c = ε₀ A dE/dt = ε₀ dΦ_E/dt = I_d, preserving charge conservation, magnetic field between plates due to I_d, same as that due to conduction current. The document states that the speed of electromagnetic waves in a medium is v = (1/√(μ ε)) . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields v = (1/√(μ ε)), illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Displacement Current and Ampere-Maxwell Law

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