An electron is travelling along the $x$-direction. It encounters a magnetic field in the $y$-direction. Its subsequent motion will be

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

At $t$ = $0$, a positively charged particle of mass $m$ is projected from the origin with velocity $u_0$ at an angle $37^o $ from the $x-$axis as shown in the figure. A constant magnetic field ${\vec B_0} = {B_0}\hat j$  is present in space. After a time interval $t_0$ velocity of particle may be:-

A charge having $q/m$ equal to $10^8\, C/kg$ and with velocity $3 \times 10^5\, m/s$ enters into a uniform magnetic field $0.3\, tesla$ at an angle $30^o$ with direction of field. The radius of curvature will be ......$cm$

Which of the following particle will describe the smallest circle when projected with the same  velocity perpendicular to the magnetic field ?

A proton of mass $1.67 \times {10^{ - 27}}\,kg$ and charge $1.6 \times {10^{ - 19}}\,C$ is projected with a speed of $2 \times {10^6}\,m/s$ at an angle of $60^\circ $ to the $X - $ axis. If a uniform magnetic field of $0.104$ $Tesla$ is applied along $Y - $ axis, the path of proton is