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Up: PHY531-PHY532 Classical Electrodynamics

PHY532 Problem Set 1. Due February 1, 2001

1.

Jackson problem 6.24, however in part b show instead that the magnetic field far from the solenoid is zero to this order.

2.

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.

3.

Jackson problem 9.5.