A positive charge $'q'$ of mass $'m'$ is moving along the $+ x$ axis. We wish to apply a uniform magnetic field $B$ for time $\Delta t$ so that the charge reverses its direction crossing the $y$ axis at a distance $d.$ Then
$B\, = \,\frac{{mv}}{{qd}}$ and $\Delta t\, = \,\frac{{\pi d}}{v}$
$B\, = \,\frac{{mv}}{{2qd}}$ and $\Delta t\, = \,\frac{{\pi d}}{2v}$
$B\, = \,\frac{{2mv}}{{qd}}$ and $\Delta t\, = \,\frac{{\pi d}}{2v}$
$B\, = \,\frac{{2mv}}{{qd}}$ and $\Delta t\, = \,\frac{{\pi d}}{v}$
Two electrons are moving along parallel lines unidirectionarly with same velocity they will
A negatively charged particle projected towards east is deflected towards north by a magnetic field. The field may be
A uniform magnetic field $B$ exists in the region between $x=0$ and $x=\frac{3 R}{2}$ (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 $P_1(y=-R)$. 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 $B=\frac{8}{13} \frac{\mathrm{p}}{QR}$, the particle will enter region $3$ through the point $P_2$ on $\mathrm{x}$-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 $y$-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
The magnetic force acting on a charged particle of charge $-2\, \mu C$ in a magnetic field of $2\, T$ acting in $y$ direction, when the particle velocity is $(2i + 3 j) \times 10^6\,\, m/s$ is
An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is $\sigma $. Electric intensity in the space between the plates is $E$. A uniform magnetic field $B$ also exists in that space perpendicular to the direction of $E$. The electron moves perpendicular to both $\vec E$ and $\vec B$ without any change in direction. The time taken by the electron to travel a distance $\ell $ is the space is