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#sinusoidal

3 public questions tagged with this topic.

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

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Damped Oscillations

Which function represents SHM? (\( \omega \) is a positive constant)

**Effect of damping** is gradual amplitude reduction while period remains nearly constant for light damping. Mechanical energy decreases as work done against damping force, E(t) = ½ k A(t)² decaying exponentially, and motion ceases without external energy input, distinguishing from ideal undamped SHM. SHM requires a = -ω² x : (a) 6 sin (2ω t - (π/4)) : a = -6 (2ω)² sin (2ω t - (π/4)) = -ω² x , SHM. (b) sin ω t + cos 3ω t : Not SHM (mixed frequencies). (c) eω t : Not periodic. (d) cos³ ω t : Periodic, not SHM. Applying x = A cos(ωt +

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

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Damped Oscillations

Which function represents simple harmonic motion? (\( \omega \) is a positive constant)

**Effect of damping** is gradual amplitude reduction while period remains nearly constant for light damping. Mechanical energy decreases as work done against damping force, E(t) = ½ k A(t)² decaying exponentially, and motion ceases without external energy input, distinguishing from ideal undamped SHM. SHM requires a = -ω² x : (a) cos ω t + sin 2ω t : Not SHM (mixed frequencies). (b) 4 sin (ω t + (π/6)) : a = -4ω² sin (ω t + (π/6)) = -ω² x , SHM. (c) eω t : Not periodic. (d) sin² ω t : Periodic, not SHM. Applying x = A cos(ωt + φ),

Ref: NCERT > Physics Book > Oscillations > Damped Oscillations

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