Find the resultant magnetic field at the origin due to four infinitely long wires. Each wire produces a magnetic field of magnitude $B$ at the origin.

$A$ 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 $(\mu_0 = \text{permeability of free space})$:

Two identical long current-carrying wires are bent into the shapes shown in the following figures. If the magnitudes of the magnetic fields at the centers $P$ and $Q$ of the semicircular arcs are $B_1$ and $B_2$ respectively,then the ratio $\frac{B_1}{B_2}$ 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?

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side $1\,m$ which is carrying a current of $10\,A$ is:......$\mu T$ [Take $\mu _0 = 4\pi \times 10^{-7}\,NA^{-2}$]

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by