$A$ circular coil of radius $R$ carries an electric current $I$. The magnetic field due to the coil at a point on the axis of the coil located at a distance $r$ from the centre of the coil,such that $r \gg R$,the magnetic field at that point is proportional to

The magnetic field due to a straight conductor of uniform cross-section of radius $a$ and carrying a steady current is represented by

$A$ current $I$ flows in a wire bent in the shape of a quarter ring of radius $R$ as shown in the figure. The magnetic field induction $B$ at point $O$ is

$A$ conducting wire carrying current $I$ is arranged as shown in the figure. Find the magnetic field at point $O$.

Write the equation for the magnetic field due to a circular current-carrying loop at a point on the axis of the loop. Give its special cases.

Two infinitely long parallel wires carry currents of magnitude $I_1$ and $I_2$ and are at a distance $4 \, cm$ apart. The magnitude of the net magnetic field is found to reach a non-zero minimum value between the two wires at a distance of $1 \, cm$ from the first wire. The ratio of the two currents and their mutual direction is