The magnetic field at the center of a current-carrying circular loop is $B_{1}$. The magnetic field at a distance of $\sqrt{3}R$ from the center on its axis is $B_{2}$,where $R$ is the radius of the loop. The value of $B_{1} / B_{2}$ is:

Two circular loops $L_1$ and $L_2$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_1$ is $R_1$ and that of $L_2$ is $R_2$. The distance between the centres of the loops is $\sqrt{3} R_1$. The magnetic field at the centre of $L_2$ shall be zero if

$A$ coil having $N$ turns carries a current $I$ as shown in the figure. The magnetic field intensity at point $P$ is

Two long parallel straight metal wires $A$ and $B$ carrying currents $12 \,A$ and $36 \,A$ respectively,in the same direction are separated by $50 \,cm$. The point relative to $A$,where the resultant magnetic induction between the two wires due to the currents is zero,will be (in $\,cm$)

An equilateral triangle is made by uniform wires $AB, BC, CA$. A current $I$ enters at $A$ and leaves from the midpoint of $BC$. If the length of each side of the triangle is $L$, the magnetic field $B$ at the centroid $O$ of the triangle is:

Two circular coils $1$ and $2$ are made from the same wire. The radius of the first coil is twice that of the second coil. What is the ratio of potential difference applied across them $V_1 / V_2$,so that the magnetic field at their centre is the same?