$A$ 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:

$A$ $100$ turn closely wound circular coil of radius $10\; cm$ carries a current of $3.2\; A$.
$(a)$ What is the field at the centre of the coil?
$(b)$ What is the magnetic moment of this coil?
The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. $A$ uniform magnetic field of $2\; T$ in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of $90^{\circ}$ under the influence of the magnetic field.
$(c)$ What are the magnitudes of the torques on the coil in the initial and final position?
$(d)$ What is the angular speed acquired by the coil when it has rotated by $90^{\circ}$? The moment of inertia of the coil is $0.1\; kg\; m^{2}$.

The net magnetic field at the centre $O$ of the circle due to the current-carrying loop as shown in the figure is $(\theta < 180^\circ)$.

Choose the correct statement.

There exists a uniform magnetic field of magnitude $1\, T$ and a uniform electric field of magnitude $1\, V/m$ along the positive $y-$ axis. $A$ charged particle of mass $1\, kg$ and charge $1\, C$ has an initial velocity of $1\, m/s$ along the $x-$ axis and is at the origin at $t = 0$. Find the coordinates of the particle at time $t = \pi$ seconds.

The neutral temperature of a thermocouple is $350\,^{\circ}C$ when the cold junction is at $0\,^{\circ}C$. When the cold junction is immersed in a bath of $30\,^{\circ}C$,the inversion temperature is .............. $^{\circ}C$.