Inside a long straight uniform wire of round cross-section, there is a long round cylindrical cavity, whose axis is parallel to the axis of the wire and displaced from the latter by a distance $l$. A direct current of density $\overrightarrow{j}$ flows along the wire. Find the magnetic induction inside the cavity. Consider, in particular, the case $l=0$.

The figure shows a toroidal solenoid, whose cross-section is rectangular. Find the magnetic flux through this cross-section, if the current through the winding equals $I=1.7 \mathrm{A}$, the total number of turns is $N=1000$, the ratio of the outside diameter to the inside one is $\eta =1.6$ and the height is equal to $h=5.0 \mathrm{cm}$. 

Calculate the magnetic moment of a thin wire with a current, $I=0.8 \mathrm{A}$, wound tightly on half a tore. The diameter of the cross-section of the tore, $d=5.0 \mathrm{cm}$, the number of turns is $N=500$.

A thin insulated wire forms a plane spiral of $N=100$ tight turns carrying a current, $I=8 \mathrm{mA}$. The radii of inside and outside turns are $a=50 \mathrm{mm}$ and $b=100 \mathrm{mm}$. Find, 
$\left(a\right)$ the magnetic induction at the centre of the spiral, 
$\left(b\right)$ the magnetic moment of the spiral with a given current.

A non-conducting thin disc of radius $R$ charged uniformly over one side with surface density $\sigma$ rotates about its axis with an angular velocity $\omega$. Find, 

$\left(a\right)$ the magnetic induction at the center of the disc, 
$\left(b\right)$ the magnetic moment of the disc.