Three long straight and parallel wires carrying currents are arranged as shown. The wire $C$ which carries a current of $50 \,A$ is so placed that it experiences no force. The distance of wire $C$ from wire $A$ is (in $\,cm$)

Two identical coils having the same number of turns and carrying equal current have a common centre,and their planes are at right angles to each other. What is the ratio of the magnitude of the resultant magnetic field at the centre to the magnetic field due to one of the coils at the centre?

Two circular coils $P$ and $Q$ are made from two identical wires of the same length. The number of turns in coils $P$ and $Q$ are $4$ and $2$,respectively. The magnetic inductions at the centers of $P$ and $Q$ are $B_P$ and $B_Q$,respectively. The ratio $\frac{B_P}{B_Q}$ is

Calculate the magnetic field at point $M$ for the given current distribution.

Write the equation for the magnetic field of a current-carrying circular loop at: $(i)$ a point on the axis,and $(ii)$ a point on the plane of the loop at a distance $x$ from the center of the loop.

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$, making an angle $\theta$ with the current element, then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$: