09(T)%20-%20Electromagnetic%20Waves - 9 - ELECTROMAGNETIC...

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9 - ELECTROMAGNETIC WAVES Page 1 9.1 Maxwell’s Theory of Electromagnetic Waves Maxwell presented in the form of differential equations, ( 1 ) Gauss’s law for electricity as o q dS E = describing charge and the electric field, ( 2 ) Gauss’s law for magnetism as 0 dS B = describing the magnetic field, ( 3 ) Faraday’s law of induction as dt B d dS E Φ = - describing the electrical effect of a changing magnetic field and ( 4 ) Ampere’s law as extended by Maxwell, Φ = + + + 0 μ i d o dt E dl B describing the magnetic effect of a changing electric field or of a current. While correlating these equations, he postulated the existence of a missing term, ‘i’ in Ampere’s law which he called the displacement current. Using these equations, he established his electromagnetic theory predicting the existence of electromagnetic radiation propagating in space in a wave form. He also showed that the velocity of these waves is equal to the velocity of light in vacuum and deduced therefrom that light waves are electromagnetic waves. 9.2 Hertz’s Experiment The figure shows a simple experimental set-up of Hertz to produce electromagnetic waves in the laboratory. Two metallic spheres, Q 1 and Q 2, which constitute a capacitor are connected to metallic rods, M and N, which behave as an inductor with a spark gap S between them. A large potential difference is obtained with the help of induction coil to produce spark in the spark gap. Such an arrangement can be considered as an L-C oscillator circuit and is also known as a Hertzian dipole. At any instant when Q 1 has a positive charge, Q 2 has the same amount of negative charge. The polarity on the spheres Q 1 and Q 2 keep changing with a definite time period with charge passing through the spark gap. A second spark gap, R, is arranged to detect the emission of the electromagnetic waves. Q 1 and Q 2 are arranged by sliding them on the rod to produce spark in spark gap R due to resonance. Suppose the spheres are charged as shown in the figure ( next page ) at any instant of time. The electric intensity at points C on the perpendicular bisector of Q 1 Q 2 are shown by a and b due to the charged spheres Q 1 and Q 2 respectively, the resultant of which is E parallel
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9 - ELECTROMAGNETIC WAVES Page 2 to MN as shown in the figure. Similarly, the electric field intensity at D is also parallel to MN but is of the smaller magnitude. Thus there is a gradual decrease in the intensity of the electric field at a given instant as we move away from MN. As the spark is produced in the spark gap, electrons flow from the sphere Q 1 to Q 2 reducing negative charge on Q 1 and positive charge on Q 2 . With one half cycle of time elapsing, the charge on Q 1 becomes positive and that on Q 2 negative. Now the electric fields at C and D are in opposite directions. Such
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This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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09(T)%20-%20Electromagnetic%20Waves - 9 - ELECTROMAGNETIC...

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