Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is

Two long parallel wires carry currents $I_1$ and $I_2$ $(I_1 > I_2)$. When currents are flowing in the same direction,the magnetic field at a point midway between the wires is $6 \times 10^{-6} \ T$. If the direction of $I_2$ is reversed,the field at the midpoint becomes $3 \times 10^{-5} \ T$. The ratio $I_1 : I_2$ is

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces a magnetic field $B_1$ at its centre when a current $I$ passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces a magnetic field $B_2$ at the centre of the loops when a current $I/3$ passes through it. The ratio $B_1 : B_2$ is

The figure shows a straight wire of length $l$ carrying current $i$. The magnitude of the magnetic field produced by the current at point $P$ is:

$A$ beam of neutrons performs circular motion of radius $r = 1 \, m$ under the influence of an inhomogeneous magnetic field with inhomogeneity extending over $\Delta r = 0.01 \, m$. The speed of the neutrons is $54 \, m/s$. The mass and magnetic moment of the neutrons are $1.67 \times 10^{-27} \, kg$ and $9.67 \times 10^{-27} \, J/T$ respectively. The average variation of the magnetic field over $\Delta r$ is approximately ....... $T$.

$A$ current carrying circular loop of radius '$R$' and a current carrying long straight wire are placed in the same plane. $I_c$ and $I_w$ are the currents through the circular loop and the long straight wire,respectively. The perpendicular distance between the centre of the circular loop and the wire is '$d$'. The magnetic field at the centre of the loop will be zero when the separation '$d$' is equal to: