Two concentric and coplanar rings of radius $r$ and $R$ are shown in the figure. Find the magnetic flux linked through the smaller coil when the same current $I$ flows through each in opposite directions $(r << R)$.

Five long wires $A, B, C, D$ and $E$,each carrying current $I$ are arranged to form edges of a pentagonal prism as shown in the figure. Each carries current out of the plane of the paper.
$(a)$ What will be the magnetic induction at a point on the axis $O$? The axis is at a distance $R$ from each wire.
$(b)$ What will be the field if the current in one of the wires (say $A$) is switched off?
$(c)$ What if the current in one of the wires (say $A$) is reversed?

$A$ wire in the form of a square of side $a$ carries a current $i$. Then,the magnetic induction at the centre of the square is (Magnetic permeability of free space $= \mu_0$)

Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries an electric current $I_1$ and $COD$ carries a current $I_2$. The magnetic field at a point lying at a distance $d$ from $O$,in a direction perpendicular to the plane of the wires $AOB$ and $COD$,will be given by

Two concentric coils each of radius equal to $2\pi \text{ cm}$ are placed at right angles to each other. If $3 \text{ A}$ and $4 \text{ A}$ are the currents flowing through the two coils respectively,the magnetic induction (in $\text{Wb m}^{-2}$) at the centre of the coils will be:

$A$ current loop consists of two identical semicircular parts each of radius $R,$ one lying in the $x-y$ plane and the other in the $x-z$ plane. If the current in the loop is $i,$ the resultant magnetic field due to the two semicircular parts at their common centre is