Ch 32 Maxwell's Equations

Ch 32 Maxwell's Equations - Maxwells Equations give us the...

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Unformatted text preview: Maxwells Equations give us the fundamental basis for studying electromagnetic waves. Through is four equations (not really his equations) we will discover that electromagnetic waves are made up of E and B fields that are sinusoidal functions of time and position. These waves will have a definite frequency and wavelength. Unlike waves on a string or water waves, electromagnetic waves do not require any medium I. Gauss' law for electricity II. Gauss' law for magnetism III. Faraday's law of induction IV. Ampere's law Let us recall Maxwells equations Maxwells equations apply to both electric and magnetic fields in a vacuum. If a material is present then the permittivity and permeability of free space are replaced by the permittivity and permeability . If these constants change from point to point they must be transferred to the left hand side of Maxwells equations so they can be integrated. According to Maxwells equations, a point charge at rest produces a static E field but no B fields. Maxwells equations can be used to show that in order for a point charge to produce electromagnetic waves, the charge must accelerate. In fact its a general result of Maxwells equations that every accelerated charge radiates electromagnetic energy. In 1887 electromagnetic waves with macroscopic wavelengths were first produced in the laboratory in by the German Physicist Heinrich Hertz. As a source of waves he used charges oscillating in L-C circuits. Hertz detected the resulting electromagnetic waves with other circuits tuned to the same frequency. Hertz produced electromagnetic standing waves and measured the distance between adjacent nodes (one half wavelength) to determine the wavelength. Knowing the resonant frequency of his circuits, he then found the speed of the waves form the wavelength- frequency relationship v = f and established the speed was that of light . The SI unit of frequency is named in honor of Hertz. One hertz equals 1 cycle per second. The modern value of the speed of light, denoted by c, is: c = 2.99,792,458 m/s One meter is now defined to be the distance light travels in one second. Heinrich Rudolf Hertz (1857 1894) Only a small range of electromagnetic waves are visible to our eyes. Its wavelengths range from about 400 to 700 nm and frequencies from about 7.5 to 4.3 x 10-14 Hz. Electromagnetic Plane Waves and the Speed of Light The properties of electromagnetic waves can be deduced from Maxwells equations. One approach is to solve the second order differential equation obtained from Maxwells third and fourth equations. But to fully solve such a second order differential equation is beyond the scope of this course. To get around this problem, for teaching purposes we let the E and B fields, that make up the electromagnetic wave, be reduced to a more simple form, yet consistent with Maxwells 4- equations ....
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This note was uploaded on 10/05/2011 for the course PHYS 4B taught by Professor W.christensen during the Summer '09 term at Irvine Valley College.

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Ch 32 Maxwell's Equations - Maxwells Equations give us the...

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