An electron enters the space between the plates of a charged capacitor as shown. The surface charge density on the plates is $\sigma$. The electric field intensity in the space between the plates is $E$. $A$ uniform magnetic field $B$ also exists in the space,perpendicular to the direction of $E$. The electron moves perpendicular to both $\overrightarrow{E}$ and $\overrightarrow{B}$ without any change in direction. The time taken by the electron to travel a distance $l$ in the space is:

$A$ charge $Q$ is moving through a distance $d\vec{l}$ in a magnetic field $\vec{B}$. Find the value of the work done by the magnetic field.

$A$ particle moving in a magnetic field increases its velocity,then its radius of the circle

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

$A$ 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 the $x$-axis enters region $2$ from region $1$ at point $P_1(y=-R)$. Which of the following option$(s)$ is/are correct?
$[A]$ For $B > \frac{2}{3} \frac{p}{QR}$,the particle will re-enter region $1$.
$[B]$ For $B = \frac{8}{13} \frac{p}{QR}$,the particle will enter region $3$ through the point $P_2$ on the $x$-axis.
$[C]$ When the particle re-enters region $1$ through the longest possible path in region $2$,the magnitude of the change in its linear momentum between point $P_1$ and the farthest point from the $y$-axis is $p/\sqrt{2}$.
$[D]$ For a fixed $B$,particles of same charge $Q$ and same velocity $v$,the distance between the point $P_1$ and the point of re-entry into region $1$ is inversely proportional to the mass of the particle.

At $t = 0$,a charge $q$ is at the origin and moving in the $y$-direction with velocity $\vec{v} = v\hat{j}$. The charge moves in a magnetic field that is for $y > 0$ out of the page and given by $B_1\hat{k}$ and for $y < 0$ into the page and given by $-B_2\hat{k}$. The charge's subsequent trajectory is shown in the sketch. From this information,we can deduce that: