$A$ 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 the net force on the charge may be zero?

Mark the correct statement.

$A$ closed loop $PQRS$ carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments $PS, SR$ and $RQ$ are $F_1, F_2$ and $F_3$ respectively and are in the plane of the paper and along the directions shown,the force on the segment $QP$ is

An $\alpha$ particle of energy $10 \ eV$ is moving in a circular path in a uniform magnetic field. The energy of a proton moving in the same path and the same magnetic field will be [mass of $\alpha$ particle $= 4 \times$ mass of proton]. (in $eV$)

The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0$ is the permeability of free space and $H$ is the magnetic field intensity) 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 $0.1\; kg\; m^{2}$.