aklec03 - 3 Inhomogeneous Wave Equation In the last lecture...

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Unformatted text preview: 3 Inhomogeneous Wave Equation In the last lecture we discussed static fields ) ( ), ( ), ( ), ( r H H r B B r D D r E E produced by the sources ) ( and ) ( r J J r ELECTROSTATICS 2 SOLUTION V r r r r r 3 4 1 ) ( ) ( d V AND MAGNETOSTATICS 2 SOLUTION J A r r r r J r A 3 4 ) ( ) ( d AND E D E D H B J H B with B H A B with E D E V Now we will look at the general case of time-varying sources ) , ( and ) , ( t t r J J r producing the fields ) , ( ), , ( ), , ( ), , ( t t t t r H H r B B r D D r E E which satisfy the Maxwells equations. We will show that the solution may be obtained using delayed or retarded potentials V ( r , t ) and A ( r , t ): 2 2 2 SOLUTION t V V r r r r r r r 3 4 ) , ( ) , ( d c t t V 2 2 2 SOLUTION J A A t r r r r r r J r A 3 4 ) , ( ) , ( d c t t Having V ( r , t ) and A ( r , t ), unknown fields may be found using: t t D J H B E B D and A B A E t V Note that knowing either E or B is sufficient, the other can be determined from Maxwells equations....
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aklec03 - 3 Inhomogeneous Wave Equation In the last lecture...

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