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?

$A$ particle of charge $q$ and mass $m$ is moving along the $x$-axis with a velocity $v$ and enters a region of electric field $E$ and magnetic field $B$ as shown in the figures below. For which figure may the net force on the charge be zero?

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:

The current flowing along the path $A B C D$ of a cube (shown in the left figure) produces a magnetic field at the centre of the cube of magnitude $B$. Dashed lines depict the non-conducting part of the cube. Consider a cubical shape shown to the right which is identical in size and shape to the left. If the same current now flows in along the path $D A E F G C D$,then the magnitude of the magnetic field at the centre will be

$A$ 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.

Mark the correct statement.