aklec06 - 6 Spherical Waves Earlier we learned that given...

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6 Spherical Waves Earlier we learned that given J ( r , t ), we can calculate A ( r , t ) as Time domain: 0 2 2 0 0 2 SOLUTION J A A t r r r r r r J r A 3 0 4 ) , ( ) , ( d c t t or we can work in frequency domain, and calculate ) ( ~ r A using ) ( ~ r J : Frequency domain: r r r r J r A J r A r A r r SOLUTION 3 0 0 2 2 4 ) ( ~ ) ( ~ ~ ) ( ~ ) ( ~ d e k jk
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Now we will investigate the magnetic vector potential created by short current filaments that have sinusoidal time variation. We will see that these currents produce spherical waves at distant points from these short current elements. The radiated fields due to these currents will be studied in the next lecture. We will next examine the implications of magnetic vector potential results from Lecture 4 for an infinitesimal current element defined as   otherwise , 0 2 2 , 0 , 0 for , cos ) , ( z z z y x t I t I r where I is in amperes. The current density for this current can be written as
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    2 m A ˆ cos rect ) ( ) ( otherwise , 0 2 2 for , ˆ cos ) ( ) ( ) , ( z t z z y x I z z z z t y x I t r J Here we used delta functions or impulses
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aklec06 - 6 Spherical Waves Earlier we learned that given...

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