Displacement Current and Ampere-Maxwell Law

Displacement Current and Ampere-Maxwell Law

Which type of electromagnetic waves are produced by radioactive decay of the nucleus?

**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. The document states that gamma rays are produced in nuclear reactions and emitted by radioactive nuclei. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Gamma rays, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

View Details

Displacement Current and Ampere-Maxwell Law

A radio tunes to stations in the \( 7.5 \, \text{MHz} \) to \( 12 \, \text{MHz} \) band. What is the corresponding wavel

**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. Using λ = (c/v) , for 7.5 MHz , λ = (3 × 10⁸/7.5 × 10⁶) = 40 m . For 12 MHz , λ = (3 × 10⁸/12 × 10⁶) = 25 m . So the range is 25 m to 40 m . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 25 m

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

View Details

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

View Details

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

View Details

Displacement Current and Ampere-Maxwell Law

According to Maxwell's equations, what does the equation \( \oint \mathbf{B} \cdot \mathrm{d} \mathbf{A} = 0 \) imply?

**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. This is Gauss's Law for magnetism, which implies that there are no magnetic monopoles, as the net magnetic flux through a closed surface is zero. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields No magnetic monopoles exist, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

View Details

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

View Details

Displacement Current and Ampere-Maxwell Law

An electromagnetic wave in vacuum has an electric field given by \( E_x = 150 \sin(5 \times 10^3 z - 1.5 \times 10^{12}

**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. Comparing with E_x = E₀ sin(kz - ω t) , we have ω = 1.5 × 10¹² rad/s . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 1.5 × 10¹² rad/s, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

View Details

Displacement Current and Ampere-Maxwell Law

A capacitor in a circuit has a conduction current of \( 2.5 \, \text{A} \) in the wires. What is the displacement curren

**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 states that in a charging capacitor, the displacement current between the plates equals the conduction current in the wires, so i_d = 2.5 A . Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields 2.5 A, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

View Details

Displacement Current and Ampere-Maxwell Law

In the context of electromagnetic theory, what fundamental principle explains why a changing electric field can generate

**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. The Ampere-Maxwell law states that a changing electric field (via displacement current) acts as a source of a magnetic field, complementing the conduction current's role in generating magnetic fields. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Ampere-Maxwell law, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

View Details

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 EM wave transverse nature and Maxwell's displacement current concept.

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

View Details

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

View Details

Displacement Current and Ampere-Maxwell Law

What enables electromagnetic waves to propagate without a material medium?

**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. The document states that electromagnetic waves are self-sustaining oscillations of electric and magnetic fields, requiring no material medium for propagation. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Self-sustaining oscillations of fields, illustrating EM wave transverse nature and Maxwell's displacement current concept.

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

View Details