#displacement current

Applications of EM Waves in Communication and Medicine

A capacitor in a circuit has a conduction current of \( 1.8 \, \text{A} \) in the wires. What is the displacement curren

**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. The document states that in a charging capacitor, the displacement current between the plates equals the conduction current in the wires, so i_d = 1.8 A . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 1.8 A, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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Applications of EM Waves in Communication and Medicine

What is the expression for displacement current as given in the document?

**X-rays and gamma rays in medicine** X-rays imaging because bone absorbs more than tissue, contrast, CT scan uses multiple X-ray projections, gamma knife uses focused gamma rays to destroy tumor with minimal surrounding damage, illustrating high-energy EM wave medical use. The document provides the expression for displacement current as i_d = ε₀ (d Φ_E/dt) , where Φ_E is the electric flux. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields i_d = ε₀ (d Φ_E/dt), 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

What is the role of displacement current in Maxwell's generalization of Ampere's law?

**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. Maxwell introduced displacement current to account for the magnetic field produced by a time-varying electric field, ensuring consistency in Ampere's circuital law when applied to capacitors. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields It produces a magnetic field due to a changing electric field, 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 does the Ampere-Maxwell Law include as the source of a magnetic field?

**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 Ampere-Maxwell Law includes both conduction current and displacement current (due to the time rate of change of electric flux) as sources of a magnetic field, as per the document. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Conduction current and displacement current, 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

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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Electromagnetic Spectrum - Radio Waves and Microwaves

What role does the displacement current play in a region where there is no conduction current?

**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. The document explains that in regions with no conduction current but a time-varying electric field, displacement current acts as a source of magnetic field, enabling electromagnetic wave propagation. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields It acts as a source of magnetic field, 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

What does the Ampere-Maxwell law relate in Maxwell's equations?

**Radio waves** λ≈10⁻¹ to 10⁴ m, f≈10⁴ to 10⁹ Hz, produced by rapid acceleration/deceleration of electrons in aerials/antenna, used for long-distance communication because low frequency diffracts around obstacles and reflects from ionosphere, enabling ground wave and sky wave propagation, effective for broadcasting. The Ampere-Maxwell law relates the magnetic field to both the conduction current and the displacement current, given by oint B · d l = μ₀ i_c + μ₀ ε₀ (d Φ_E/dt) . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Magnetic field to conduction and displacement currents, 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

Why does the concept of displacement current become essential in understanding electromagnetic wave propagation in free

**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. Displacement current accounts for the magnetic field generated by a changing electric field in regions where no conduction current exists, such as in free space, enabling the continuous propagation of electromagnetic waves. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields It explains magnetic fields in free space, illustrating EM wave

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

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EM Wave Characteristics - Transverse Nature and E/B Ratio

What does the introduction of displacement current by Maxwell explain about electromagnetic phenomena?

**EM wave in vacuum** transverse, E and B perpendicular to propagation and to each other, E×B along propagation, in phase, E/B = c =3×10⁸ m/s, c =1/√(μ₀ ε₀), μ₀=4π×10⁻⁷ H/m, ε₀=8.85×10⁻¹² F/m. For E₀=45 V/m, B₀=E₀/c=45/3×10⁸=1.5×10⁻⁷ T=150 nT, illustrating B much smaller than E. The document explains that displacement current explains the generation of magnetic fields by time-varying electric fields, crucial for the propagation of electromagnetic waves and consistency in Ampere's law. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Generation of magnetic fields by changing electric fields, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

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Displacement Current and Ampere-Maxwell Law

Which of the following is true about the displacement current in a charging capacitor?

**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). Inside a charging capacitor, there is no conduction current ( i_c = 0 ), but there is a displacement current due to the changing electric field between the plates, as explained by Maxwell. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields It exists inside the plates

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

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Displacement Current and Ampere-Maxwell Law

What does Maxwell's displacement current ensure in the generalized Ampere's law?

**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 explains that displacement current ensures consistency in the magnetic field calculation across different surfaces, resolving the contradiction in Ampere's original law. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Consistency in magnetic field calculation, 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

What inconsistency did Maxwell notice in Ampere's circuital law before introducing displacement current?

**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). Maxwell noticed that Ampere's law gave different results for the magnetic field outside a capacitor depending on the surface used, leading to a contradiction when calculating the field at a point. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Different magnetic fields for different surfaces, illustrating

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

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