Ph272- General Physics II (Electricity and Magnetsism)

Lecture 23-24: Ch. 32 - Maxwell's Equation, Electromagnetic waves

Key Topics

Overview

• All classical (i.e. non quantum) electromagnetic phenomena can be described by four equations due to Maxwell.
• You have already learn these equation (except one of them (Ampere's Law) needs to be modified).

Maxwell's Equation.

• All electromangetic phenomena are described in terms of E-field and B-field.
• Mathematicall, these are vector functions. It turns out that if we know the flux and the circulation of the vector function, then we know "everything" about the function.
• The four Maxwell's Equations are (on P.947):

(1) Flux of E-field: Gauss's law (Eq. 29-6a)

(2) Circulation of E-field: Faraday's Law (Eq. 29-6c)

(3) Flux of B-field (through a closed surface) = 0 (Eq. 29-6b) (There is no name for this one, but it comes from the fact that there are no magnetic monopoles).

(4) Circulation of B-field: "Modified Ampere's Law (Eq.29-6d)

• The modified Ampere's Law has an addition term which depends on the time derivative of the E-field (called the displacement current).
• The important point is that changing E-field induces a B-field just like changing B0field induces an E-field (Faraday's Law).
• The result is that a time- varying E-field and a time-varying B-field sustain each other. This is why electromagnetic waves exist and able to travel over very long distance.

Electromagnetic Waves (Characteristics)

• The speed of electromagnetic wave in vacuum is given by equation below Eq. 29-10.
• Electromagnetic waves are transverse waves, i.e the E-field and B- field are perpendicular to the direction of propagation.
• Furthermore, E and B are perpendicular to each other. E x B (croos product) is in the direction of propagation.
• E & M wave from "point" source is a spherical wave. But when the radius of curvature gets very large, the wave front are approximately planes, these are called plane waves.
• E&M waves usually consisted of many different frequency. An E&M wave with a single frequency is called a monochromatic wave (single color).
• The expression for the E-field and B-field of a monochromatic plane wave is given in Example 29-3, P. 952.
• An E &M wave carries both energy (Eq. 29-17) and momentum (Eq. 29-24).
• The intensity of an E& M wave is given by Eq. 29-18 and 29-21.

Sources of E &M wave

• Classical Description: Accelerated charges generates E & M waves
• Quantum description: Quantum transition froma higher energy level to a lower energy level produces "photon", a quantum of electromagnetic wave.
• Low frequency E&M waves such as radio wave can be generated by putting current throught a LC circuit.
• Infrared can be generated by heat, i.e, molecualr energy levels transitions.
• Visible: valence electronic level transitions.
• X-ray: core-electronic level transitions
• Gamma ray: nuclear level transitions.

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