A charged particle carrying charge $1\,\mu C$  is moving with velocity $(2 \hat{ i }+3 \hat{ j }+4 \hat{ k })\, ms ^{-1} .$ If an external magnetic field of $(5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\, T$ exists in the region where the particle is moving then the force on the particle is $\overline{ F } \times 10^{-9} N$. The vector $\overrightarrow{ F }$ is :

When a magnetic field is applied in a direction perpendicular to the direction of cathode rays, then their

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

An electron having charge $1.6 \times {10^{ – 19}}\,C$ and mass $9 \times {10^{ – 31}}\,kg$ is moving with $4 \times {10^6}\,m{s^{ – 1}}$ speed in a magnetic field $2 \times {10^{ – 1}}\,tesla$ in a circular orbit. The force acting on electron and the radius of the circular orbit will be

The magnetic force acting on charged particle of charge $2\,\mu C$ in magnetic field of $2\, T$ acting in $y-$ direction , when the particle velocity is $\left( {2\hat i + 3\hat j} \right) \times {10^6}\,m{s^{ – 1}}$ is