An electron and a proton are moving on straight parallel path with same velocity. They enter a region of semi infinite magnetic field perpendicular to velocity. What will happen there? Will both of them never come out of the field? Or they come out with same velocity at same time?
Hint: A semi-infinite uniform magnetic field would be one which would be described by something like this: $B=0$ (for $x<0$) and $B=constant$ (for $x\ge0$).
The question describes a situation of this sort: (The $X$s indicate that the region has a magnetic field directed into/out of the page):
You need to know how the trajectory of a charged particle is going to be in a uniform field region. (This trajectory would describe the particles motion only when the particle is in the region where the field is present.)
The electron will turn to one side and the proton will turn to the other side. Say, the electron will describe a spiral path to the left (this depends from the direction of the magnetic field), then the proton will describe a spiral path to the right. This happens because both particles have a magnetic dipole moment and an intrinsic spin. Aligning the magnetic dipole moments the spins get deflected. Due to the gyroscopic effect this is the reason for the spirale path of both elements. But why the get deflected to different directions? Say, the magnetic dipole moment and the intrinsic spin of the electron oriented parallel. Then this parameters for the proton oriented anti-parallel.
The spirale paths are from different curvature. The electrons spirale is more bended then the protons. This is because they have the different masses.
Last not least why they move in spirale paths and not in a circle. This is because both particles emit photons when get deflected. Photons have momentum and this momentum they get from the particles which loose this moment and move slower and slower until they stop.