#electromagnetic wave

Applications of EM Waves in Communication and Medicine

An electromagnetic wave in vacuum has an electric field amplitude of \( 60 \, \text{V/m} \). What is the magnetic field

**Radio waves** effective for long-distance communication because low frequency waves diffract around Earth curvature and reflect from ionosphere, enabling beyond line-of-sight, used in AM (≈10⁶ Hz) ground wave, short wave sky wave. Microwaves used for satellite due to high frequency penetrates ionosphere and directional beam. Using B₀ = (E₀/c) , we have B₀ = (60/3 × 10⁸) = 2 × 10⁻⁷ T . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 2 × 10⁻⁷ T, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Production of EM Waves and Hertz Experiment

An electromagnetic wave in vacuum has a frequency of \( 40 \, \text{MHz} \). What is its wavelength? (Given \( c = 3 \ti

**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. Using v λ = c , we have λ = (c/v) = (3 × 10⁸/40 × 10⁶) = 7.5 m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 7.5 m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Production of EM Waves and Hertz Experiment

An electromagnetic wave has a magnetic field amplitude of \( B_0 = 6 \times 10^{-8} \, \text{T} \). What is the electric

**Aerials produce radio waves** by rapid acceleration/deceleration of electrons in antenna driven by AC, frequency equals driving frequency, for 60 MHz, λ=c/f=3×10⁸/60×10⁶=5 m, half-wave antenna length λ/2=2.5 m, efficient radiation when antenna size comparable to λ. Using E₀ = B₀ c , we have E₀ = (6 × 10⁻⁸) × (3 × 10⁸) = 18 V/m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 18 V/m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Production of EM Waves and Hertz Experiment

What is the general form of the electric field component of a plane electromagnetic wave propagating along the \( z \)-d

**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. The document provides the form E_x = E₀ sin(kz - ω t) , where E_x is along the x -axis for a wave propagating along the z -direction. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields E_x = E₀ sin(kz - ω t),

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Production of EM Waves and Hertz Experiment

An electromagnetic wave has a magnetic field given by \( B_y = 5 \times 10^{-8} \sin(3 \times 10^3 z - 9 \times 10^{11}

**Aerials produce radio waves** by rapid acceleration/deceleration of electrons in antenna driven by AC, frequency equals driving frequency, for 60 MHz, λ=c/f=3×10⁸/60×10⁶=5 m, half-wave antenna length λ/2=2.5 m, efficient radiation when antenna size comparable to λ. Comparing with B_y = B₀ sin(kz - ω t) , we have k = 3 × 10³ rad/m . Wavelength λ = (2 π/k) = (2 π/3 × 10³) ≈ 2.09 × 10⁻³ m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 2.09 × 10⁻³ m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Production of EM Waves and Hertz Experiment

An electromagnetic wave in vacuum has a magnetic field amplitude of \( B_0 = 3 \times 10^{-8} \, \text{T} \). What is th

**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. Using E₀ = B₀ c , we have E₀ = (3 × 10⁻⁸) × (3 × 10⁸) = 9 V/m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 9 V/m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Production of EM Waves and Hertz Experiment

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Energy, Intensity and Momentum of EM Waves

An electromagnetic wave in vacuum has an electric field amplitude of \( 90 \, \text{V/m} \). What is the magnetic field

**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. Using B₀ = (E₀/c) , we have B₀ = (90/3 × 10⁸) = 3 × 10⁻⁷ T . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 3 × 10⁻⁷ T, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Energy, Intensity and Momentum of EM Waves

An electromagnetic wave in vacuum has a magnetic field amplitude of \( B_0 = 2 \times 10^{-8} \, \text{T} \). What is th

**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. Using E₀ = B₀ c , we have E₀ = (2 × 10⁻⁸) × (3 × 10⁸) = 6 V/m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 6 V/m, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Energy, Intensity and Momentum of EM Waves

An electromagnetic wave in vacuum has an angular frequency \( \omega = 4 \times 10^{11} \, \text{rad/s} \). What is its

**Poynting vector** S = E×B/μ₀ gives energy flow (W/m²), magnitude S = E B/μ₀, average = E₀ B₀/(2μ₀) = intensity, direction of propagation, showing energy transport perpendicular to E and B. Frequency v = (ω/2π) . Given ω = 4 × 10¹¹ rad/s , v = (4 × 10¹¹/2 π) ≈ 6.37 × 10¹⁰ Hz . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 6.37 × 10¹⁰ Hz, 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

An electromagnetic wave in vacuum has a wavelength of \( 20 \, \text{m} \). What is its frequency? (Given \( c = 3 \time

**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. Using v λ = c , we have v = (c/λ) = (3 × 10⁸/20) = 1.5 × 10⁷ Hz . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 1.5 × 10⁷ Hz, illustrating EM wave transverse

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Electromagnetic Spectrum - Radio Waves and Microwaves

An electromagnetic wave in vacuum has a wavelength of \( 15 \, \text{m} \). What is its frequency? (Given \( c = 3 \time

**Hertz experiment** produced radio waves using spark gap LC oscillator, detected with loop antenna, confirming Maxwell's prediction, frequency ≈10⁸ Hz, wavelength ≈3 m, demonstrating EM waves travel at c, transverse, can be reflected, refracted, polarized. Using v λ = c , we have v = (c/λ) = (3 × 10⁸/15) = 2 × 10⁷ Hz . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 2 × 10⁷ Hz, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Electromagnetic Spectrum - Radio Waves and Microwaves

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Electromagnetic Spectrum - Radio Waves and Microwaves

The amplitude of the electric field in an electromagnetic wave is \( E_0 = 120 \, \text{V/m} \). What is the amplitude o

**Hertz experiment** produced radio waves using spark gap LC oscillator, detected with loop antenna, confirming Maxwell's prediction, frequency ≈10⁸ Hz, wavelength ≈3 m, demonstrating EM waves travel at c, transverse, can be reflected, refracted, polarized. Using B₀ = (E₀/c) , we have B₀ = (120/3 × 10⁸) = 4 × 10⁻⁷ T . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 4 × 10⁻⁷ T, illustrating EM wave transverse nature and Maxwell's displacement current concept.

Ref: NCERT > Physics Book > Electromagnetic Waves > Electromagnetic Spectrum - Radio Waves and Microwaves

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