Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed $'v'$ in a uniform magnetic field $B$ going into the plane of the paper (See figure). If charge densities ${\sigma _1}$ and ${\sigma _2}$ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)

A charged particle of specific charge $\alpha$ is released from origin at time $t = 0$ with velocity $\vec V = {V_o}\hat i + {V_o}\hat j$ in magnetic field $\vec B = {B_o}\hat i$ . The coordinates of the particle at time $t = \frac{\pi }{{{B_o}\alpha }}$ are (specific charge $\alpha = \,q/m$) 

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $B$ = $B_0\hat{k}$

An electron enters a magnetic field whose direction is perpendicular to the velocity of the electron. Then

A $2\, MeV$ proton is moving perpendicular to a uniform magnetic field of $2.5\, tesla$. The force on the proton is