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 $\,cm$)

Two concentric coplanar circular loops of radii $r_1$ and $r_2$ carry currents $i_1$ and $i_2$ in opposite directions (one clockwise and the other anticlockwise). The magnetic induction at the center of the loops is half that due to $i_1$ alone at the center. If $r_2 = 2r_1$,find the value of $\frac{i_2}{i_1}$.

$A$ long straight wire along the $z$-axis carries a current $I$ in the negative $z$-direction. The magnetic vector field $\vec{B}$ at a point having coordinates $(x, y)$ in the $z = 0$ plane is

$PQRS$ is a square loop made of uniform conducting wire. If the current enters the loop at $P$ and leaves at $S$, then the magnetic field will be

The figure shows a square loop $ABCD$ with edge length $a$. The resistance of the wire $ABC$ is $r$ and that of $ADC$ is $2r$. The value of the magnetic field at the centre of the loop is:

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have a common axis. The currents through $P$ and $Q$ are $I$ and $4I$ respectively in the clockwise direction as seen from $O$. The net magnetic field at $O$ is: