#electric field

Polarization and Malus Law

What is the direction of the electric field in a linearly polarized light wave relative to its propagation direction?

**Polarization** transverse wave property, light after polaroid polarized along pass-axis, Malus law I = I₀ cos²θ, θ angle between pass-axes, initial unpolarized intensity I₀ after first polaroid I₁ = I₀/2, after second at 45° I₂ = I₁ cos²45°= I₀/2×0.5= I₀/4, after two perpendicular 90° I=0 because cos90°=0, for 60° I= I₀/2×cos²60°= I₀/2×0.25= I₀/8. In a linearly polarized light wave, the electric field oscillates perpendicular to the direction of propagation. Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ' = λ/n and A = 2a cos(φ/2), calculation gives Perpend

Ref: NCERT > Physics Book > Wave Optics > Polarization and Malus Law

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p-n Junction, Depletion Region and Diode Characteristics

The electric field in the depletion region of a p-n junction is directed from:

**p-n junction formation** diffusion of holes from p to n and electrons from n to p leaves ionized donors positive on n-side and acceptors negative on p-side, forming space-charge depletion region with electric field directed from n to p (positive to negative), barrier potential V_b ≈0.3 V Ge, 0.7 V Si, opposes further diffusion, drift current due to minority carriers swept by field balances diffusion at equilibrium net current zero. The electric field arises from positive ionized donors on the n-side and negative ionized acceptors on the p-side, directed from the n-side (positive) to the p-si

Ref: NCERT > Physics Book > Electronic Devices > p-n Junction, Depletion Region and Diode Characteristics

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Applications of EM Waves in Communication and Medicine

Which of Maxwell's equations relates the electric field to the rate of change of magnetic flux?

**Microwaves in ovens** cause water molecules to rotate at 2.45 GHz, friction heats food, penetration depth few cm, efficient heating, also radar uses reflection of microwaves from objects, Doppler shift measures speed, medical diathermy uses microwaves for tissue heating. Faraday's Law in Maxwell's equations states oint E · d l = -(d Φ_B/d t) , describing the induction of an electric field by a changing magnetic field. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Faraday's Law, illustrating EM wave transverse nature and Maxwell's displaceme

Ref: NCERT > Physics Book > Electromagnetic Waves > Applications of EM Waves in Communication and Medicine

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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.

Ref: NCERT > Physics Book > Electromagnetic Waves > Applications of EM Waves in Communication and Medicine

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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.

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

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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 yie

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

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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 displa

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

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Energy, Intensity and Momentum of EM Waves

What is the significance of the equation \( \oint \mathbf{E} \cdot \mathrm{d} \mathbf{l} = -\frac{d \Phi_B}{dt} \) in Ma

**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. This is Faraday's Law, which states that a changing magnetic flux induces an electric field, a key mechanism for electromagnetic wave propagation. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields It describes the induction of an electric field by changing magnetic flux, illustrating EM wave transverse nature and

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 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.

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 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.

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

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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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EM Wave Characteristics - Transverse Nature and E/B Ratio

What is the nature of the electric and magnetic fields in an electromagnetic wave?

**Relationship E and B** in EM wave E₀ = c B₀, B₀ = E₀/c, for vacuum. Fields sustain each other via Maxwell's equations ∇×E = -∂B/∂t, ∇×B = μ₀ ε₀ ∂E/∂t, time-varying E produces B and vice versa, self-sustaining propagation without medium, speed c. The document states that in an electromagnetic wave, the electric and magnetic fields oscillate sinusoidally, are perpendicular to each other, and are perpendicular to the direction of propagation. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Perpendicular to each other and to the direction of prop

Ref: NCERT > Physics Book > Electromagnetic Waves > EM Wave Characteristics - Transverse Nature and E/B Ratio

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