#physics fundamentals

Energy, Intensity and Momentum of EM Waves

In the context of electromagnetic wave propagation, what ensures that the wave remains transverse?

**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. Maxwell’s equations dictate that the electric and magnetic fields are perpendicular to each other and to the direction of propagation, ensuring that electromagnetic waves are transverse. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Perpendicular field orientation, illustrating EM wave transverse nature and M

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

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Electric Current, Drift Velocity and Mobility

Under what condition does Ohm’s law fail to hold true for a conductor?

**Mobility** μ = v_d/E = e τ/m, τ relaxation time (s), measures ease of electron drift under field E (V/m). Conductivity σ = n e μ = 1/ρ, linking microscopic τ to macroscopic resistivity, explaining why metals conduct well due to large n and τ. Ohm’s law ( V = I R ) assumes a linear relationship between voltage and current. It fails if the resistance ( R ) changes with current or voltage (e.g., in non-ohmic devices like diodes), making the V -versus- I graph non-linear. Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq

Ref: NCERT > Physics Book > Current Electricity > Electric Current, Drift Velocity and Mobility

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Equations of SHM, Phase and Angular Frequency

What critical condition must the acceleration satisfy for a motion to be classified as simple harmonic?

**SHM representation** using sine or cosine equivalent with phase offset, ω relates to system parameters like mass and stiffness. Understanding ω and φ permits prediction of position at any time and comparison of two SHM via phase difference Δφ = φ₂ - φ₁. In SHM, acceleration must be proportional to displacement and directed opposite to it ( a = -ω² x ), ensuring harmonic oscillation about the mean position. Applying x = A cos(ωt + φ), v = -ωA sin(ωt + φ), a = -ω²x and E = ½kA² = ½mω²A², result It is proportional to displacement and opposite in direction follows, reflecting SHM dependence

Ref: NCERT > Physics Book > Oscillations > Equations of SHM, Phase and Angular Frequency

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Stationary Waves and Standing Waves in Strings

Why does the amplitude of a standing wave vary along its length?

**Stationary waves** form when identical progressive waves traveling opposite directions interfere, y = 2A sin(kx) cos(ωt), nodes where sin(kx)=0, antinodes where |sin(kx)|=1. For string fixed at both ends, allowed wavelengths λₙ = 2L/n, frequencies fₙ = n·v/(2L), n = 1,2,3… harmonic number. In a standing wave, interference of two opposite-traveling waves creates nodes (zero amplitude) and antinodes (maximum amplitude), causing spatial variation due to phase alignment. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Due to interference, illust

Ref: NCERT > Physics Book > Waves > Stationary Waves and Standing Waves in Strings

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Transverse and Longitudinal Waves

What is the key requirement for a wave to be classified as a progressive wave?

**Mechanical waves** require medium and can be transverse or longitudinal. Sound in air is longitudinal since fluids support only compressional motion, while string waves are transverse. Progressive waves transfer energy without net mass transport, distinguishing from standing waves. A progressive wave transfers energy through the medium as it propagates, distinguishing it from standing waves, which do not exhibit net energy flow. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Energy transfer, illustrating frequency-length-speed interdependen

Ref: NCERT > Physics Book > Waves > Transverse and Longitudinal Waves

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