The acceleration of an electron at a moment in a magentic field $\vec B\, = \,2\hat i + 3\hat j + 4\hat k$ is $\vec a\, = \,x\hat i - 2\hat j + \hat k$. The value of $x$ is

A particle of mass $m,$ charge $Q$ and kinetic energy $K$ enters a transverse uniform magnetic field of induction $B.$ After $3$ $seconds$ the kinetic energy of the particle will be .......$K$

A proton (or charged particle) moving with velocity $v$ is acted upon by electric field $E$ and magnetic field $B$. The proton will move undeflected if

A particle of mass $m = 1.67 \times 10^{-27}\, kg$ and charge $q = 1.6 \times 10^{-19} \, C$ enters a region of uniform magnetic field of strength $1$ $tesla$ along the direction shown in the figure. If the direction of the magnetic field is along the outward normal to the plane of the paper, then the time spent by the particle in the region of the magnetic field after entering it at $C$ is nearly :-......$ns$

A particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$ direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$ direction, extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ is

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let $r_{d}$ and $r_{\alpha}$ be their respective radii of circular path. The value of $\frac{r_{d}}{r_{\alpha}}$ is equal to