A uniform electric field and a uniform magnetic field are produced, pointed in the same direction. An electron is projected with its velocity pointing in the same direction

A particle with charge $+Q$ and mass m enters a magnetic field of magnitude $B,$ existing only to the right of the boundary $YZ$. The direction of the motion of the $m$ particle is perpendicular to the direction of $B.$ Let $T = 2\pi\frac{m}{{QB}}$ . The time spent by the particle in the field will be 

Given below are two statements: One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R).$

Assertion $(A)$ : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.

Reason $(R)$ : Moving charged particle experiences magnetic force perpendicular to its direction of motion.

Which one of the following options represents the magnetic field $\vec{B}$ at $O$ due to the current flowing in the given wire segments lying on the $x y$ plane?

A magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{j}}$ exists in the region $\mathrm{a} < \mathrm{x} < 2 \mathrm{a}$ and $\vec{B}=-B_0 \hat{j}$, in the region $2 \mathrm{a} < \mathrm{x} < 3 \mathrm{a}$, where $\mathrm{B}_0$ is a positive constant. $\mathrm{A}$ positive point charge moving with a velocity $\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{\dot{i}}$, where $v_0$ is a positive constant, enters the magnetic field at $x=a$. The trajectory of the charge in this region can be like,

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e,r_p$ and ${r_\alpha }$ respectively in a uniform magnetic field $B$. The relation between $r_e,r_p$ and $\;{r_\alpha }$ is