An $\alpha – $ particle travels in a circular path of radius $0.45\, m$ in a magnetic field $B = 1.2\,Wb/{m^2}$ with a speed of $2.6 \times {10^7}\,m/\sec $. The period of revolution of the $\alpha – $ particle is

Maximum kinetic energy of the positive ion in the cyclotron is

When a charged particle moving with velocity $\vec v$ is subjected to a magnetic field of induction $\vec B$, the force on it is non-zero. This implies that

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement$(s)$ is/are true?

$(A)$ They will never come out of the magnetic field region.

$(B)$ They will come out travelling along parallel paths.

$(C)$ They will come out at the same time.

$(D)$ They will come out at different times.

A proton and a deutron ( $\mathrm{q}=+\mathrm{e}, m=2.0 \mathrm{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is: