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Unformatted text preview: HW 2 Phys5406 S03 due 1/30/03 1)In this problem you will be led through the steps to average the microscopic current density, j and obtain equations 6.96-6.100 of JDJ (except for the quadrupole terms which are much smaller). Follow the averaging procedure carried out in class for , divide j in free and bound parts and show, < j > = < j free > + nj [ q j ( n ) ( v n + v jn ) f ( r- r n- r jn )] , (1) where n is the molecule or atom, j is the point charge in the molecule or atom, v n is the velocity of the CM, and v jn is the velocity of the charge relative to the CM. Now expand the bound term of eq. 1 in a Taylor series and aside from quadrupole terms get, < j bound > = nj [ q j ( n ) ( v n + v jn )( f ( r- r n )- r jn f ( r- r n ))] . (2) From now on I will drop the argument of f, it will be understood and will also be the argument of the delta functions below. The above equation has four terms. Show that the first is, < n [ q n v n ] > . (3) This term is usually zero, except for ionized media. When added to the free term the sumThis term is usually zero, except for ionized media....
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