$A$ cylindrical conductor of radius $R$ carries a current $i$. The value of the magnetic field at a point, which is $R/4$ distance inside from the surface, is $10 \ T$. Find the value of the magnetic field at a point, which is $4R$ distance outside from the surface.

$A$ long straight wire carries a current of $35\, A$. What is the magnitude of the magnetic field $B$ at a point $20\, cm$ from the wire?

$A$ straight wire carrying current $I$ is bent into a semi-circular arc of radius $r$,as shown. The magnitude of the magnetic field at point $O$ due to the semi-circular arc is ($\mu_{0} =$ permeability of free space).

When a certain length of wire is turned into one circular loop,the magnetic induction at the centre of the coil due to a current $I$ flowing through it is $B_1$. If the same wire is turned into three loops to make a circular coil,the magnetic induction at the center of this coil for the same current will be:

$AB$ and $CD$ are long straight conductors,separated by a distance $d$,each carrying a current $I$. The magnetic field at the midpoint of $BC$ is

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$,making an angle $\theta$ with the current element,then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$: