The magnetic field at the centre of a circular coil of radius $R$ carrying current $I$ is 64 times the magnetic field at a distance $x$ on its axis from the centre of the coil. Then, the value of $x$ is

A uniform magnetic field of strength $B=2 \mathrm{mT}$ exists vertically downwards. These magnetic field lines pass through a closed surface as shown in the figure. The closed surface consists of a hemisphere $S_1$, a right circular cone $S_2$ and a circular surface $S_3$. The magnetic flux through $S_1$ and $S_2$ are respectively.

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