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

A metallic rod of mass per unit length $$0.5 \mathrm{~kg} \mathrm{~m}^{-1}$$ is lying horizontally on a smooth inclined plane which makes an angle of $$30^{\circ}$$ with the horizontal. A magnetic field of strength $$0.25 \mathrm{~T}$$ is acting on it in the vertical direction. When a current $$I$$ is flowing through it, the rod is not allowed to slide down. The quantity of current required to keep the rod stationary is