Maxwell’s Equations & Electromagnetic Waves • We now want to explore how the principles of Electric & Magnetic Fields lead to an understanding of light & other electromagnetic waves. • The connection between EM Theory and Optics may be a surprise. • It was a surprise to physicists also. Towards a complete description of EM phenomena . . . • The century from ~1750 to ~ 1850 saw intensive investigation of electricity & magnetism by Coulomb, Galvani, Volta, Oersted, Ampere, Faraday and many others. • (You should recognize most of these names. Also, there was the mathematician Gauss, whose theorems were crucial to the new theory of fields.) • Finally there was James Clerk Maxwell, a theoretician who showed that all EM phenomena could be described by a succinct but comprehensive theory. This theory is known as Maxwell’s Equations. • In addition to developing the theoretical foundation of the subject, Maxwell was the first to recognize the connection between EM fields and light. 2/25/2013 3 2/25/2013 Lecture XXIV 4 2/25/2013 Lecture XXIV 5 2/25/2013 Lecture XXIV 6 2/25/2013 Lecture XXIV 7 2/25/2013 Lecture XXIV 8 2/25/2013 Lecture XXIV 9 2/25/2013 Lecture XXIV 10 2/25/2013 Lecture XXIV 11 EM theory Known phenomena • Currents produce magnetic field Assumptions • Changing magnetic field • Changing electric field is produces electricity equivalent to current and (induction) also produces magnetic field Unification – James Clark Maxwell (1831-1879): one field – electromagnetic (EM). 2/25/2013 12 EM wave EB Ev Bv 2/25/2013 E y E0 sin(kx t ) B z B0 sin(kx t ) vx v E/B v k 2 2f f v k Lecture XXIV 13 Intensity of waves • Energy of oscillation U is proportional to amplitude squared E2 U E2 • Intensity – I, W/m2 energy / time power I area area • Intensity I is proportional to amplitude squared E2, inversely proportional to r2: IE 2/25/2013 2 1 I 2 r 1 E r 14 How do moving charges create magnetic fields? • Any moving electric charge is surrounded by an electric field and a magnetic field. What happens when electric and magnetic fields change? • A changing magnetic field creates a changing electric field. What happens when electric and magnetic fields change? • A changing magnetic field creates a changing electric field. • One example of this is a transformer which transfers electric energy from one circuit to another circuit. – In the main coil changing electric current produces a changing magnetic field – Which then creates a changing electric field in another coil producing an electric current – The reverse is also true. Making Electromagnetic Waves • When an electric charge vibrates, the electric field around it changes creating a changing magnetic field. Making Electromagnetic Waves • When an electric charge vibrates, the electric field around it changes creating a changing magnetic field. Making Electromagnetic Waves • The magnetic and electric fields create each other again and again. Making Electromagnetic Waves • The electric and magnetic fields vibrate at right angles to the direction the wave travels so it is a transverse wave. Properties of EM Waves • All matter contains charged particles that are always moving; therefore, all objects emit EM waves. • The wavelengths become shorter as the temperature of the material increases. What is the speed of EM waves? • All EM waves travel 300,000 km/sec in free space. (speed of lightnature’s limit!) • EM waves usually travel slowest in solids and fastest in gases. Material Vacuum Speed (km/s) 300,000 Air <300,000 Water 226,000 Glass 200,000 Diamond 124,000 What is the wavelength & frequency of an EM wave? • Wavelength= distance from crest to crest. • Frequency= number of wavelengths that pass a given point in 1 s. • As frequency increases, wavelength becomes smaller. The whole range of EM wave… • Frequencies is called the electromagnetic spectrum. • Different parts interact with matter in different ways. • The ones humans can see are called visible light, a small part of the whole spectrum.