Electromagnetic Waves

The shortest chapter of Class 12 Physics — and one of the highest marks-per-page anywhere: 3-4 Board marks and a near-certain 1-2 questions in JEE/NEET, mostly from memory. Maxwell noticed that Ampere's circuital law fails for a charging capacitor — different surfaces with the same boundary give different answers — and fixed it with a stroke of genius: a changing electric field acts as a current, the displacement current $i_d = \varepsilon_0\frac{d\Phi_E}{dt}$, completing the Ampere-Maxwell law $\oint\vec{B}\cdot d\vec{l} = \mu_0 i_c + \mu_0\varepsilon_0\frac{d\Phi_E}{dt}$. With this, time-varying electric and magnetic fields regenerate each other and race through empty space as electromagnetic waves, sourced by accelerated (oscillating) charges. The waves are transverse — $\vec{E}\perp\vec{B}\perp$ propagation — with $E_x = E_0\sin(kz-\omega t)$, $B_y = B_0\sin(kz-\omega t)$, $B_0 = E_0/c$, travelling at $c = 1/\sqrt{\mu_0\varepsilon_0} \approx 3\times10^8$ m/s — which matched the measured speed of light and revealed that light itself is an electromagnetic wave (confirmed by Hertz, extended by Bose and Marconi). The chapter closes with the electromagnetic spectrum from gamma rays ($\sim10^{-12}$ m) to long radio waves ($\sim10^6$ m): radio, microwave, infrared, visible, ultraviolet, X-ray and gamma — each band's production, detection and uses, from microwave ovens tuned to water molecules to the ozone layer's UV shield. Every formula, comparison and exam-favourite factoid is covered.