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

$A$ straight wire of finite length carrying current $I$ subtends an angle of $60^{\circ}$ at point $P$ as shown. The magnetic field at $P$ is

Connecting wires carrying currents in opposite directions are twisted together in electrical appliances in order to reduce:

$A$ long straight wire carries a current along the $x$-axis. Consider the points $A(0, 1, 0)$,$B(0, 1, 1)$,$C(1, 0, 1)$,and $D(1, 1, 1)$. Which of the following pairs of points will have magnetic fields of the same magnitude?

Two long straight wires are placed along the $x$-axis and $y$-axis. They carry currents $I_1$ and $I_2$ respectively. The equation of the locus of points with zero magnetic induction in the magnetic field produced by them is:

The magnetic field at the centre $O$ of a wire loop formed by two semicircular wires of radii $R_1=2 \pi \text{ m}$ and $R_2=4 \pi \text{ m}$ carrying current $I=4 \text{ A}$ as per the figure given below is $\alpha \times 10^{-7} \text{ T}$. The value of $\alpha$ is . . . . . . . (Centre $O$ is common for all segments)