#Maxwell

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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Energy, Intensity and Momentum of EM Waves

What is the primary source of a magnetic field as per Maxwell's generalization?

**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. Maxwell generalized Ampere's circuital law by introducing displacement current. According to this, the source of a magnetic field is not only the conduction current but also the time-varying electric field (displacement current). Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ =

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

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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 o

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 yie

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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

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, evalua

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Electromagnetic Spectrum - Radio Waves and Microwaves

What type of electromagnetic waves did Maxwell predict before their experimental discovery?

**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 document mentions that Maxwell predicted the existence of electromagnetic waves, which were later confirmed to include light, radio waves, and others, but initially, they were general EM waves. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, eval

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

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Displacement Current and Ampere-Maxwell Law

What conclusion did Maxwell reach when the speed of electromagnetic waves matched the speed of light?

**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). The document mentions that Maxwell concluded that light is an electromagnetic wave, as their speeds were nearly identical ( 3 × 10⁸ m/s ). Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Light is an electromagnetic wave, illustrating

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Displacement Current and Ampere-Maxwell Law

A parallel plate capacitor has a time-varying charge such that \( \frac{dQ}{dt} = 1.2 \, \text{A} \). What is the displa

**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. In a capacitor, the displacement current i_d equals the conduction current in the connecting wires, so i_d = (dQ/dt) = 1.2 A . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 1.2 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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