A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) T$. If it has an acceleration of $(\alpha \hat{i}-4 \hat{j}) m / s ^{2}$, then the value of $\alpha$ will be.

Mixed $H{e^ + }$ and ${O^{2 + }}$ ions (mass of $H{e^ + } = 4\,\,amu$ and that of ${O^{2 + }} = 16\,\,amu)$ beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then

An electron accelerated through a potential difference $V$ enters a uniform transverse magnetic field and experiences a force $F$. If the accelerating potential is increased to $2V$, the electron in the same magnetic field will experience a force

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

If cathode rays are projected at right angles to a magnetic field, their trajectory is

$OABC$ is a current carrying square loop an electron is projected from the centre of loop along its diagonal $AC$ as shown. Unit vector in the direction of initial acceleration will be