A charged particle is subjected to acceleration in a cyclotron as shown. The charged particle undergoes increase in its speed

A positively charged particle $$q$$ of mass $m$ is passed through a velocity selector. It moves horizontally rightward without deviation along the line $$y=\frac{2 m v}{q B}$$ with a speed $$v$$. The electric field is vertically downwards and magnetic field is into the plane of paper. Now, the electric field is switched off at $$t=0$$. The angular momentum of the charged particle about origin $$O$$ at $$t=\frac{\pi m}{q B}$$ is

The torque acting on a magnetic dipole placed in uniform magnetic field is zero, when the angle between the dipole axis and the magnetic field is .........

A proton and an alpha-particle moving with the same velocity enter a uniform magnetic field with their velocities perpendicular to the magnetic field. The ratio of radii of their circular paths is