The magnetic force depends on $\mathrm{v}$ which depends on the inertial frame of reference. Does then the magnetic force differ from inertial frame to frame ? Is it reasonable that the net acceleration has a different value in different frames of reference ?

A proton beam is going from north to south and an electron beam is going from south to north. Neglecting the earth's magnetic field, the electron beam will deflected (Zero gravity)

A particle having charge of $1 \,\,C$, mass $1 \,\,kg$ and speed $1 \,\,m/s$ enters a uniform magnetic field, having magnetic induction of $1$ $T,$ at an angle $\theta = 30^o$ between velocity vector and magnetic induction. The pitch of its helical path is (in meters) 

A proton and an $\alpha -$ particle (with their masses in the ratio of $1 : 4$ and charges in the ratio of $1:2$ are accelerated from rest through a potential difference $V$. If a uniform magnetic field $(B)$ is set up perpendicular to their velocities, the ratio of the radii $r_p : r_{\alpha }$ of the circular paths described by them will be

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

An electron is moving along positive $x$-axis.Auniform electric field exists towards negative $y$-axis. What should be the direction of magnetic field of suitable magnitude so that net force of electron is zero