Two circular coils $X$ and $Y$,having an equal number of turns,carry equal currents in the same sense and subtend the same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$,then if we represent the magnetic induction due to the bigger coil $Y$ at $O$ as $B_Y$ and that due to the smaller coil $X$ at $O$ as $B_X$,then:

$A$ light charged particle is revolving in a circle of radius $r$ due to the electrostatic attraction of a static heavy particle with an opposite charge. How does the magnetic field $B$ at the centre of the circle, produced by the moving charge, depend on $r$?

$A$ mass spectrometer is a device which selects particles of equal mass. An ion with electric charge $q > 0$ and mass $m$ starts at rest from a source $S$ and is accelerated through a potential difference $V$. It passes through a hole into a region of constant magnetic field $\vec B$ perpendicular to the plane of the paper as shown in the figure. The particle is deflected by the magnetic field and emerges through the bottom hole at a distance $d$ from the top hole. The mass of the particle is:

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:

$A$ charged particle moves with constant velocity in a region where no effect of gravity is felt, but an electrostatic field $\vec{E}$ together with a magnetic field $\vec{B}$ may be present. Which of the following cases are possible?

$A$ particle of charge $+q$ and mass $m$ moving under the influence of a uniform electric field $E\hat i$ and a uniform magnetic field $B\hat k$ follows a trajectory from $P$ to $Q$ as shown in the figure. The velocities at $P$ and $Q$ are $v\hat i$ and $-2v\hat j$ respectively. Which of the following statement$(s)$ is/are correct?