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 respectively are $1.67 \times 10^{-27} \,kg$ and $9.67 \times 10^{-27} \,J / T$. The average variation of the magnetic field over $\Delta r$ is approximately ....... $T$

A coil having $N$ $turns$ is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. When a current $I$ passes through the coil, the magnetic field at the centre is

Tesla is the unit of

A long straight wire, carrying current $I,$ is bent at its midpoint to from an angle of $45^o.$ Induction of magnetic field at point $P,$ distant $R$ from point of bending is equal to :

Acharged particle enters a uniform magnetic field perpendicular to its initial direction travelling in air. The path of the particle is seen to follow the path in figure. Which of statements $1-3$ is/are correct?

$[1]$ The magnetic field strength may have been increased while the particle was travelling in air

$[2]$ The particle lost energy by ionising the air

$[3]$ The particle lost charge by ionising the air

Two thick wires and two thin wires, all of the same materials and same length form a square in the three different ways $P$, $Q$ and $R$ as shown in fig with current connection shown, the magnetic field at the centre of the square is zero in cases