A charge $q,$ mass $m,$ travelling with speed $v$ enters a region of magnetic field at an angle $\theta$ with magnetic field. Mark the following statements as true or false.

$\left(\mathrm{a}\right)$ Kinetic energy of particle remains constant irrespective of $\theta$

$\left(\mathrm{b}\right)$ Velocity of particle remains constant if $\theta =n\pi ,$ where $n$ is an integer

$\left(\mathrm{c}\right)$ Speed of particle remains constant

$\left(\mathrm{d}\right)$ Acceleration of particle remains constant if $\theta =\left(2n-1\right)\frac{\pi }{2}$

$\left(\mathrm{e}\right)$ Average velocity of particle becomes negligible if $\theta =\left(2n-1\right)\frac{\pi }{2}$ over a long time

A charge $q,$ mass $m$ moving with velocity $v$ enters region of magnetic field $B$ as shown in diagram. Assuming magnetic field to be constant (within corresponding region), find deviation of charge and time spent in it by the charge.

A uniform magnetic field $B$ exists in the region between $x=0$ and $x=\frac{3R}{2}$ (region $2$ in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $P$ directed along $x$-axis enters region $2$ from region $1$ at point $P_1(y=-R)$. If the particle enters into region $3$ through the point $P_2$ on the axis, then magnetic field $B$ is given as $\frac{8}{N}\frac{P}{QR}$, value of $N$ is _______

The figure shows three long straight current carrying conductors. The straight parts are long and the circular part in each case in ${\left(\frac{3}{4}\right)}^{\text{th }}$ of a complete circle. Let $B_a, B_b$ and $B_c$ represents the strength of field at the centre $O$ in the three cases, then

Two thick wires and two thin wires, all of same material and same length form a square in the three different ways $P, Q$ and $R$ as shown. The current flowing through the arrangement is $i.$ Let $B_P, B_Q$ and $B_R$ represent the magnetic field at the centre of squares in the three cases, then

The figure shows a loop of wire carrying a current $i$ as shown. There exists a uniform magnetic field along $x$-axis given by $\overrightarrow{B}=B_0\hat{i}.$ If the length of each side is $a,$ then