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Up: PHY531-PHY532 Classical Electrodynamics

PHY532 Problem Set 1. Due February 1, 2001

Jackson problem 6.24, however in part b show instead that the magnetic field far from the solenoid is zero to this order.
Find the conditions on $\mbox{\boldmath$\space {J} $}$0 and $\mbox{\boldmath$\space {J} $}$1 , if any, for the current density

$\displaystyle\mbox{\boldmath$ {J} $}$($\displaystyle\mbox{\boldmath$ {r} $}$,t) = $\displaystyle\mbox{\boldmath$ {J} $}$0($\displaystyle\mbox{\boldmath$ {r} $}$) + $\displaystyle\mbox{\boldmath$ {J} $}$1($\displaystyle\mbox{\boldmath$ {r} $}$)t , (1)

to give a magnetic field at time t1 identical to that given by a static current density

$\displaystyle\mbox{\boldmath$ {J} $}$s($\displaystyle\mbox{\boldmath$ {r} $}$,t) = $\displaystyle\mbox{\boldmath$ {J} $}$($\displaystyle\mbox{\boldmath$ {r} $}$,t1) . (2)

Discuss part b of the previous problem in terms of your result.

Jackson problem 9.5.