Problem $1$: A surface current density K

exists on a hollow sphere of radius a

centered at the origin.

Find the magnetic field at the origin.

Hint: Ignore the magnetic field due to the

filament current on the z$-$axis.

Show quantitiaive method.

Problem $2$: The sheet $-$d$/2<$ x $<$ d$/2$ in the x $-$ y plane carries current I$1$ in the $-$ y direction. A filament

carrying current I$2$ in the $+$ y direction lies parallel to the y$-$axis at z $=$ L in the y $-$ z plane. Determine the

Force per unit length between the two currents.

Problem $4$: An infinitely long coaxial cable with inner radius a and outer radius b has the intervening space

filled with one circular regions of three different permeabilities. Find the inductance per unit length.