Electromagnetic WavesNEET Physics · Class 12 · NCERT Chapter 8

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• Doubling the rate of voltage change dV/dt doubles the displacement current. Linear relation.
• Halving plate separation d doubles capacitance, so doubles I_D for the same dV/dt.
• In free space, no plates needed: a changing E-field anywhere acts as a displacement current and produces a magnetic field.
• NEET hook: I_D and conduction current are equal in magnitude when the capacitor is charging at a steady dV/dt.

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• Try setting wave speed to zero: it freezes a snapshot. The E and B waves are perpendicular and in phase.
• Increase wavelength: fewer cycles fit in the box. Same speed means lower frequency (c = f λ).
• In a medium, v drops, so for the same f the wavelength shortens (wavelength = v / f).
• Right-hand rule: E × B points along the direction of propagation. That is the Poynting vector S.

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• B_0 in tesla looks tiny because c is so large in SI. Both fields carry equal energy density.
• Direction rule: E × B points along the direction of propagation. The Poynting vector is S = (1/mu_0) E × B.
• Sun on a clear day at Earth: E_0 ≈ 1000 V/m, so B_0 ≈ 3.3 µT.
• Memory hook: u_E = u_B → (1/2) epsilon_0 E_0^2 = B_0^2 / (2 mu_0). Use B_0 = E_0 / c to verify.

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• In water (n = 1.33), light slows from 3 × 10⁸ m/s to 2.26 × 10⁸ m/s.
• Frequency does not change when an EM wave enters a denser medium. Wavelength shortens, speed drops.
• For non-magnetic media (mu_r = 1), n = root(epsilon_r). For visible light, glass has epsilon_r ≈ 2.25.
• Diamond is dense (n = 2.42); v ≈ 1.24 × 10⁸ m/s. The slow speed is why diamonds sparkle: total internal reflection is easy.

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• Try 633 nm (red HeNe laser): photon energy ≈ 1.96 eV.
• Visible light is roughly 1.65 eV (red) to 3.27 eV (violet).
• Photon energy in eV times wavelength in nm equals about 1240. Quick mental check: 1240 nm photon = 1 eV.
• X-rays are around 100 eV to 100 keV; gamma rays start above ~100 keV.

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• Order from highest to lowest frequency: gamma → X-ray → UV → visible → IR → microwave → radio.
• Visible light occupies a tiny slice: 4 × 10¹⁴ to 7.5 × 10¹⁴ Hz (red is lowest f, violet is highest).
• Microwave ovens use 2.45 GHz; water molecules rotate strongly at that frequency.
• X-rays were discovered by Roentgen in 1895; he called them "X" because their nature was unknown.

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• Sun at Earth (above atmosphere): I ≈ 1361 W/m² (the solar constant). Try E_0 ≈ 1015 V/m to match.
• Indoor lighting: I ≈ a few W/m². E_0 of order 30-60 V/m.
• u_E equals u_B because E_0 = c B_0. Plug in: (1/2) ε_0 E_0² = B_0² / (2 µ_0).
• Average intensity uses E_rms, not E_peak. Same logic as AC voltage: divide peak by root 2 first.

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• A reflector feels twice the pressure of an absorber. Same intensity, but momentum reverses on reflection.
• Sun on Earth: I ≈ 1361 W/m². Pressure on a black surface = 4.5 × 10⁻⁶ Pa. Tiny but real.
• Solar sails use radiation pressure to push spacecraft. Bigger, more reflective sails win.
• A comet's tail points away from the Sun because radiation pressure pushes the dust outwards.