Two protons move parallel to each other,keeping a distance $r$ between them,both moving with the same velocity $\vec{v}$. Then the ratio of the electric force to the magnetic force of interaction between them is:

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

Three infinite wires are arranged in space in three dimensions (along $x$,$y$,and $z$ axes) as shown. Each wire carries current $i$. Find the magnetic field at point $A$ located at $(r, -r, 0)$.

$A$ 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.

Two concentric loops $A$ and $B$ of same radius $R = 2 \pi \,cm = 2 \pi \times 10^{-2} \,m$ are placed at right angles to each other. If the currents flowing through $A$ and $B$ are $I_A = 3 \,A$ and $I_B = 4 \,A$ respectively, then the net magnetic field at their common centre is:

Two parallel beams of protons and electrons,carrying equal currents,are fixed at a separation $d$. The protons and electrons move in opposite directions. $P$ is a point on a line joining the beams,at a distance $x$ from the proton beam. The magnetic field at $P$ is $B$. If $B$ is plotted against $x$,which of the following best represents the resulting curve?