What path would a charge moving in the x-y plane track, in the presence of a uniform magnetic field out of the page?

The magnetic force on a moving charge is always perpendicular to the directions of both velocity and B-field vectors. This means that in the presence of a uniform magnetic field, a particle will experience a constant force that is always at right angles to its tangential velocity. This is precisely what is required for a body to undergo circular motion! If you like, you can imagine a ball attached to one end of the string, with the other end secured on a tabletop with a pin. If you give the ball an initial velocity it will start moving in a circular arc. The force the string exerts to the ball has the same characteristics as the magnetic force described in the first paragraph. The origin of the two force is of course very different and yet the motion itself is identical.[DIAGRAM]