The magnetic field at the centre of a circular coil of radius $R$ due to current $i$ flowing through it is $B$. The magnetic field at a point along the axis at a distance $R$ from the centre is

$A$ wire of length $l$ is bent into a circular loop of radius $R$ and carries a current $I$. The magnetic field at the centre of the loop is $B$. The same wire is now bent into a double loop of equal radii. If both loops carry the same current $I$ and it is in the same direction, the magnetic field at the centre of the double loop will be

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. $A$ point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is

The magnetic field at the centre of a current-carrying circular coil of radius $R$ is $B_c$ and the magnetic field at a point on its axis at a distance $R$ from its centre is $B_a$. The value of $\frac{B_c}{B_a}$ is

Two parallel wires of equal lengths are separated by a distance of $3 \,m$ from each other. The currents flowing through the first and second wires are $3 \,A$ and $4.5 \,A$ respectively in opposite directions. The resultant magnetic field at the mid-point of both the wires is ($\mu_{0} =$ permeability of free space).

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