JEE Physics Electromagnetic Waves Notes Set 01

Displacement Current and Maxwell's Equations

1. A changing electric field between capacitor plates acts like a current, called displacement current, \( I_d=\varepsilon_0\,d\Phi_E/dt \). It equals the conduction current in the wires, so the total current is continuous.
2. Maxwell's four equations describe Gauss's law for electricity and magnetism, Faraday's law of induction and the Ampere-Maxwell law. Together they predict waves moving with speed \( c=1/\sqrt{\mu_0\varepsilon_0}\approx3\times10^{8} \) m/s.

Nature of Electromagnetic Waves

1. An accelerating charge produces changing electric and magnetic fields that sustain each other and travel as a transverse wave. \( \vec E \) and \( \vec B \) are in phase, perpendicular to each other, and the wave moves along \( \vec E\times\vec B \).
2. The fields are related by \( E_0=cB_0 \). In a medium the speed is \( v=1/\sqrt{\mu\varepsilon} \) and the refractive index is \( n=c/v \). Frequency is fixed by the source.
3. Hertz produced and detected the waves in 1887, after Maxwell's prediction. No medium is needed for propagation.

Energy, Intensity and Radiation Pressure

1. Energy density is shared equally: \( u_E=\tfrac12\varepsilon_0E^2=u_B=B^2/2\mu_0 \), so the average total is \( \tfrac12\varepsilon_0E_0^2 \).
2. Intensity is \( I=\tfrac12\varepsilon_0cE_0^2=\varepsilon_0cE_{rms}^2 \). From a point source of power P, \( I=P/4\pi r^2 \).
3. Radiation pressure on a perfect absorber is \( I/c \); on a perfect reflector it is \( 2I/c \). Momentum carried by energy U is \( U/c \).

Electromagnetic Spectrum

1. In order of increasing frequency: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. All travel at the same speed in vacuum.
2. Radio waves carry broadcast signals, microwaves are used in radar and ovens, infrared gives heat and the greenhouse effect, ultraviolet is absorbed by the ozone layer, X-rays are used in imaging and gamma rays in cancer treatment.
3. Radio bands: MF 0.3 to 3 MHz, HF 3 to 30 MHz, VHF 30 to 300 MHz, UHF 300 to 3000 MHz, SHF 3 to 30 GHz.