$A$ circular loop of radius $0.0157\,m$ carries a current of $2.0\,A$. The magnetic field at the centre of the loop is $(\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A)$.

As shown in the figure,two infinitely long straight parallel wires $P$ and $Q$ carrying equal currents in opposite directions are arranged parallel to the $Y$-axis. If the magnetic field due to wire $P$ at the origin '$O$' of the coordinate system is $B$,then match the resultant magnetic fields at various points given in Column $A$ with the points given in Column $B$.

Column $A$	Column $B$
$A) \frac{B}{4}$	$i) (0, 0)$
$B) \frac{B}{2}$	$ii) (a, 0)$
$C) \frac{2B}{3}$	$iii) (2a, 0)$
$D) 2B$	$iv) (3a, 0)$

$A$ long straight conductor is bent into the shape as shown. If it carries a current $i$ and the radius of the circular part is $R$,then find the magnetic field $B$ at the centre of the circular coil.

$A$ 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 ....... $T$.

$A$ non-conducting disc of radius $R$ has a surface charge density which varies with distance from the centre as $\sigma(r) = \sigma_0 \left[1 + \sqrt{\frac{r}{R}}\right]$, where $\sigma_0$ is a constant. The disc rotates about its axis with angular velocity $\omega$. If $B$ is the magnitude of magnetic induction at the centre, then $\frac{B}{\mu_0 \sigma_0 \omega R}$ will be

Give two different properties of a current-carrying coil and state Ampere's suggestion.