The magnetic field at the centre of a circular coil of radius $r$ carrying current $I$ is $B_1$. The field at the centre of another coil of radius $2r$ carrying the same current $I$ is $B_2$. The ratio $\frac{B_1}{B_2}$ is

In the Biot-Savart law,the direction of the magnetic field is determined by which of the following cross products in the expression $d\vec B = \frac{\mu_0}{4\pi} \frac{I d\vec l \times \vec r}{r^3}$?

$A$ long straight wire of circular cross-section is made of a non-magnetic material. The wire is of radius $a$. The wire carries a current $I$ which is uniformly distributed over its cross-section. The energy stored per unit length in the magnetic field contained within the wire is

Two long parallel wires carrying currents $8 \text{ A}$ and $15 \text{ A}$ in opposite directions are placed at a distance of $7 \text{ cm}$ from each other. $A$ point $P$ is equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnetic field at $P$ is $X \times 10^{-6} \text{ T}$. Find $X$. (Given: $\sqrt{2} = 1.4, \mu_0 = 4\pi \times 10^{-7} \text{ SI unit}$)

$Weber/m^2$ is equal to

$A$ small cube of side $1 \ mm$ is placed at the center of a circular loop of radius $20 \ cm$. If the current in the loop is $2 \ A$,then the magnetic energy stored inside the cube is (Assume $\mu_0 = 4 \pi \times 10^{-7} \ SI$ units).