Two cones, at $=21$ and $=159$ are conducting surfaces and carry total currents of $40$ A$.$

The current flows up $($the $+$r direction$)$ on the $21$ cone. The current follows the interior of a

sphere at r $=0\mathrm{.}25$ m$,$ until reaching the $159$ cone. The current then returns to the origin on

the $159$ cone.

a Find ~H in the region $0<$ r $<0\mathrm{.}25,21<$ $<159,0<$ $<2$$.$

b How much energy is stored in this region?

c Find the inductance of the cone$-$sphere configuration assuming the terminals of the in$-$

ductor are at the center of the sphere, between the vertices of the cones.