Two circular coils $1$ and $2$ are made from the same wire,but the radius of the first coil is twice that of the second coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?

The magnetic field at the centre of a circular coil of radius $r$ is $\pi$ times that due to a long straight wire at a distance $r$ from it,for equal currents. Figure shows three cases: in all cases,the circular part has radius $r$ and straight ones are infinitely long. For the same current,the $B$ field at the centre $P$ in cases $1$,$2$,and $3$ have the ratio:

$A$ and $B$ are two parallel conductors carrying a current $i$ in the same direction. $x$ and $y$ are two electron beams moving in the same direction as shown in the figure.

Six point charges,each of magnitude $q$,are arranged in different manners as shown in the image. In each case,a point $M$ and a line $PQ$ passing through $M$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $M$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now,the whole system is set into rotation with a constant angular velocity about the line $PQ$. Let $B$ be the magnetic field at $M$ and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current. Match the conditions in Column $I$ with the configurations in Column $II$.

Column $I$	Column $II$
$(A)$ $E=0$	$(p)$ Charges at corners of a regular hexagon. $M$ is the centre. $PQ$ is perpendicular to the plane.
$(B)$ $V \neq 0$	$(q)$ Charges on a line perpendicular to $PQ$ at equal intervals. $M$ is the mid-point.
$(C)$ $B=0$	$(r)$ Charges on two coplanar concentric rings. $M$ is the common centre. $PQ$ is perpendicular to the plane.
$(D)$ $\mu \neq 0$	$(s)$ Charges at corners and mid-points of a rectangle. $M$ is the centre. $PQ$ is parallel to the longer sides.
	$(t)$ Charges on two coplanar,identical rings. $M$ is the mid-point between centres. $PQ$ is perpendicular to the line joining centres.

Two very long straight parallel wires,parallel to the $y-$axis,carry currents $4I$ and $I$ along the $+y$ direction and $-y$ direction,respectively. The wires pass through the $x-$axis at the points $(d, 0, 0)$ and $(-d, 0, 0)$ respectively. The graph of the magnetic field $z-$component as one moves along the $x-$axis from $x=-d$ to $x=+d$ is best given by:

$A$ charged 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 the figure. Which of the 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.